Grant really stands out to me for staying grounded in the face of people trying to overhype his own work. It's so inspiring to see a guy who has a legitimate claim to leading his field with respect to encouraging pure-math exploration that still values all that in the context of improving the world and helping young kids learn better.
It's inspiring to see how humble he manages to be despite the pressure his work quality and the feedback he gets must put towards inflating his pride. To the best I can tell, it seems genuine too.
100% agree with his take that programming is useful, but not just for computers. Learning to program, especially under the lens of software development, teaches you to think about problems and models in terms of layers of abstraction in order to manage complexity. That is an incredibly useful skill that can reframe how you view the world
100% agree, I can feel the difference between when I'm talking to someone about breaking down a problem (regardless of domain really) when its with a person who's experienced with programing vs a person who isn't
@@maythesciencebewithyouI don’t even think they have unique methodologies for doing so. What they do have is a lot of good problems to practice these skills in an integrated way that’s different from the mix in other subjects.
Funny story about mathematicians working in other fields. During graduate school for computational biology I focused on modeling agricultural systems. I found out during graduate school that I really liked farming. I'm a relatively talented mathematician, that was offered a job where I went to graduate school immediately upon graduating, a research position. I declined and asked if I could just be a mere lecturer, and they obliged. I have since started farming and sell at local markets. In about 10 years it is my intention to quit teaching mathematics and just farm. There is a lot of similarities in farming in mathematics, believe it or not.
I enjoy a conversation in which people are speaking genuinely and intellectually and happily. So much of the internet is out of context and mentally degrading.
High School Maths teacher here. Grand Sanderson stands out not only a great educator, but also a humble human being. He shows huge respect for teachers, and even though he's (apparently) never been a teacher himself, he's full of insights about teaching. I particularly appreciated his stance that excellent teachers should stay in the classroom to inspire students. I loved that Grand fancies going into teaching himself at some point for a while, and I'm sure that he'd be a wonderful and popular teacher.
SO glad I stumbled across your Podcast, it reminds me of all the things I loved about Lex Fridmans AI podcast back in the day. I hope you have the same success. And yes, I'll share with all my friends in Mathematics and the Sciences.
Grant has the approach that's needed in high school classes. His videos do a very good job of presenting math to people who aren't at a high level of mathematical maturity.
I have to shout out Kerbal Space Program as by far the finest educational game ever made. There is no better curriculum for building an intuitive understanding of orbital mechanics than spending a couple of weeks doing a mars program in KSP. I think the best educational games are games that *simulate* (in a fun-focused way) the process that the student is meant to understand, rather than trying to use a game framework to do traditional teaching.
Outside of financial transactions, a 24 hour clock leverages a more abstract understanding of numbers. Keeping track of time was a big motivation for early numerical developments. I also think back to those older society descriptions of measurements and its like "Take a square with 5 inch long edges..." wheras I can just think 5^2 = 25 sq inches or 5x5 square. More generally I think most people find it easier to think in terms of truncated real numbers rather than as q/p rational numbers.
Agree. And basing agricultural benchmarks on astronomical phenomena: "after [so many Moons] the river will flood. Then we will [ hunt/ plant/ fish / forage ...]"
on the issue reallocation of mathematical talent: i'm one of the guys that got duped by grant into doing a phd in pure math (haven't met him though), and i've been thinking about this issue one-and-off for a few years now. it's clear that there's a waste of talent at the phd+ level due to the undersupply of academic jobs. the training you get when studying math gives you a high level of insight for general problem-solving skills, but you lack the knowledge in any other field to make use of it. so effectively you're only good as a outside consultant, unless you want to dive into a whole new field. this (+ $$$) is why the two canonical non-academic paths are tech or finance, as those two fields have low barrier to entry in terms of content. if you can think well, you can float in those two fields much easier than e.g. biology
When you say tech and finance have a lower barrier of entry than biology, do you mean that mathematics is more applicable in those fields or that they’re outright easier to find jobs in? I’m considering a M.S. in biostatistics and would love to know how you think a field like that would compare to the usual tech and finance routes. My hope was that the job market would be better given fewer people go the biostatistics route, as I’ve heard many of my CS friends struggle to find jobs despite being considered a very “in demand” career.
I earned an applied math Ph.D. at the University of Arizona studying mathematical physics (soliton theory and integrable systems). Today, I am a Quantitative Medicine Scientist at a non-profit tackling "rare" diseases (neuro-degenerative, genetic, immuno-suppressant, etc) by integrating Digital Health Technologies into the drug development pipeline. I chose that my efforts contribute towards the general field of Public Health (stemming from family values). I see others with similar training going into Pharma, Tech, Defense, Economics, Environment, Government, NGO, Finance, Transportation, Startups - wherever their passions may lie.
That was great!!! On multiple times, I felt that Grant was questioning if a question was valid or not. Or at least giving an answer that you're not expecting. Anyway, you let the guest talk and explain his points. Multiple interviewers would interrupt and try to make their own points be heard. Glad to know your podcast!!
This interview is how I, a frequent TH-cam watcher who happened to benefit from Grant’s videos during school, find out that Grant does his own animations 😂 so inspiring
An AGI can self learn new things, come up with new thoughts/ideas without fine tunning and re-training, It needs to be beat me in all tasks, work, driving, thinking, ideas.
46:00 I feel like that the point mentioned there is one of the most overlooked. While preparing for upcoming exam phase we could do the old tests and there were huge differences between the difficulty of the single tests - like I remember rocking some of them and others felt impossible for me. And I was like wtf!? I talked to some friends and we generally felt the same - basically what happened was, that the Prof was totally detached from the common students. He was lecturing everything for so long, that he didn´t have any feeling left for what are hard concepts to follow when you hear them the first time.
Grant let me say on behalf of a lot of people I know studying engineering; You really helped us understand how to think about linear algebra,basis transformations and PDE´s in a way, that at least for me have made it so much more intuitive. In this way you have helped a lot of people become better engineers. Thank you. Great podcast.
one thing i keep thinking about as someone studying physics and maths to become a teacher is whether the university system where i live isnt backwards for making teachers basically its 50/50 regular maths and physics lectures (no watered down versions for teaching) for the bachelor and then 2 years of pedagogy/education training for the masters degree with basically no practical teaching parts during the bachelor when u now take what grant said about "remembering what its like to not understand" and "the best explanation being highly dependent on the individual" any ammount of unnecessary time spent / excess topics learned between being a student and being a teacher would be something that should be avoided at any costs i do tutoring and even the better students rarely have math questions that go beyond what you know after semester 1 or 2 of university but at the same time, im expected to attend analysis III and Linear Algebra II when the required level for highschool teaching and then some would be met by just hearing the Physics Math lectures for Physics of course its alright to dive a bit deeper, since most of what u need for an advanced physics lesson is basically university stuff with less math but i feel like raising the Bar for the Subject itself too much prevents a lot of good explainers from ever becoming teachers since they are expected to learn something that will have very little/possibly no benefit to their actual quality as a teacher
The anecdote at ~52:00 resonates with me so strongly. I remember cringing so much growing up at loose-lipped teachers who are all-too-ready to say something slightly demeaning to students who are struggling. The littlest things can matter so much to kids, especially when it's coming from an authority figure. I don't mean to undermine the frustration and erosion to mental fortitude that being an educator entails, but it's just really scary how massive those effects can be.
The reason mathematicians should go pair with people in other fields is not because mathematicians are better, they're just different, and that cross-pollination is always a good way to get novel ideas happening. I figure it's just as likely the mathematician comes away with something they learned in that foreign field that helps their work in math as the converse.
It's funny because I am 96% done with a math degree and I hit the brakes, thinking "is grad school or industry even what I want to do?" Lately I just.... don't want to partake in the slog of academia, worry about grants, student outcomes, CVs, activities to pad my CV,... etc. That shit just kills my soul and motivation to learn math. I love and admire what Grant did, I'd actually love to build an "open source and friendly" math community around me. Anyway some friendly advice... you've got a question for the professor but feeling like... "everyone is going to think I'm stupid for asking this." Then just hit up chatGPT, talk to it about it organically like you would a professor, and maybe rephrase your question in a way that doesn't make you feel anxious to ask it.
I forgot to mention, check the understanding you gained with chatGPT with a professor, because man that thing gets some stuff wrong, but it has just helped me, when I'm about to ask a dumb question, just gain a lot of insight into Mathematics.
It takes a lot of confidence to simply ask questions when you do not understand something. Many times asking a seemingly stupid question reveals that everybody in the room actually wanted to know it but were simply too shy to ask, too afraid to seem stupider than the rest.
Grant is genuinely someone who i see as a hero. A brilliant guy but with a lot of heart- all about the why of maths. Everyone who has done maths knows this feeling 4:15 😅
Lol did you even understand any of what he said or were you just desperately looking to find validation for your own biases? Grant explicitly says that it's weird to expect a discrete change of a nigh indeterminate variety before getting to label state of the art natural language models as "intelligent", given that there's already a large amount of generalization and astonishing strains of logical reasoning that they are capable of. His position runs totally contradictory to your mistaken interpretation of his words.
8:26 Ideally, "applied mathematicians" should be *anywhere and everywhere* because there's really no predicting when or how the next big applications are going to emerge. But that may not take PhD-level specialization, and even if it does, then specialization itself will probably be inadequate. The key therefore is to just elevate the mathematical sophistication of as many different people as possible and to combine specialized depth with generalized breadth. This would also make it easier for people with different educational and professional backgrounds to understand each other as they learn from each other. In effect, we may not see many more *applied mathematicians* (defined as PhD-level specialists), but we can instead still see more *applied mathematics.*
Regarding the "where should applied mathematicians go", I really think engineering firms should be more open to hiring math PhDs. So many employers just have the mindset "they must have an engineering degree". A math PhD might have fantastic modelling, simulation, programming skills. Fantastic problem solving ability. Better understanding of fluid mechanics, solid mechanics, thermodynamics than the engineers. And so on. I had this issue when I finished my PhD. Everyone wanted engineering degrees. And I would think "I literally taught fluid mechanics to third year engineering classes, how could you possibly think they're better equipped for a CFD role than me?".
on the halting problem, in my experience, ruminating on why computation runs up against that limit was instructive especially early on when programming. It helped me develop an intuition for the "perspective" of a computational machine which helped motivate filling in the details of an algorithm easier when otherwise i would have been stuck looking at an input and the desired output.
I wish I had Grant Sanderson's math videos (and TH-cam in general actually) when I was in school. I am a computer programmer now but I'm pretty bad at math. I had a substitute teacher in math class for over 2 years because my teacher was in a car accident.
Grant, I’ll have you know that something you said actually made me feel more at peace with NOT becoming a math PhD. It was one if your Q&A videos where you talked about Shannon and Lorenz, and how maybe it’s good to have math-y people in other applied fields. So, good job balancing it out in the other direction 😁.
Grant may have only a BA in math, but he knows as much as an average math MA I'm sure, and as much as many PhD students. I'm a fourth year math student, decently above average I'd say, and pretty wide-ranging and deep, but I know barely anything about functors between categories, or chaos theory, and I know nothing about information theory. His command of algebra, topology, number theory and combinatorics is well above mine. I probably match him in analysis, linear algebra, vector calculus and differential geometry, but that's it. He has what it takes to be a truly great mathematician.
I've been a great fan of 3Blue1Brown many times, and you seem charismatic enough; I wish you the best in your podcast journey and hope you get some big names coming your way soon. Not that having Grant on is bad though.
This was a superb interview! At 29:32 I can't resist suggesting that we need abstract numbers to cope with quantities that are too large to grasp intuitively: a video has 10 million views; my collaborator lives 5000 miles away; Jesus lived 2000 years ago; someone just won a $1.7 billion Powerball jackpot. Also at 55:04 the graduate student was George Dantzig.
@3Blue1Brown 13:26 : Yes, you did bridge your abstract problem solving skills to another field: To the field of didactics and how to pass knowledge to other people in a beautiful and efficient way! Thank your for that!
Grant mentioned "numeracy" multiple times in this video. There's a really interesting book called "Innumeracy" by J. Paulos which covers the exact thing he's talking about. It has a particular focus on how people tend to have skewed views of numbers and statistics.
28:46 I think it may be related to the demise of slide rules. They convert addition (which naturally works with linear scales) to multiplication by putting the numbers on the scale LOGARITHMICALLY! IMO everyone with any interest in or need to know math should learn to use a slide rule. I even wonder if a linear-scale slide rule should be introduced in first or second grade, along with the number line to help learn addition. Or maybe I'm projecting about what I think would have helped me. I went through standard high school math then electrical engineering where algebra, trig and complex numbers were just a repeat of high school, then a couple calculus courses. That was pretty much all the math I needed for that EE school, but I've always been interested in number theory and other mathy things, and feel like if I had different opportunities I would have gotten a math degree, which would require going to a different school.
I just want to remind everyone that "computer generated art" doesn't exist. Computer generated art has been fed a great number of human works. It's a synthesis of human creativity, not the invention of a creative robotic mind. Computers have learned chess and go from zero human input, not art or music.
The games of go and chess can be defined in a human-agnostic way. Art has no commonly accepted human-agnostic definition. Thus, it is trivially true that all computer generated art is meant to appeal to humans. If you or anybody else were to propose a standard definition for art, I could almost certainly optimize a network for that
Grant's novel idea about planting fake highschoolers actually seems kind of brilliant. I wouldn't be surprised if countries have already implemented it really inconspicuously. Your social network and desires really affects your interests more than anything else.
I agree as a self-learner after graduation, I stopped doing the calculations. I still want to learn more HEP-th, but without time for "homework" I know it's pretty useless to try.
Yes, it is a sad reality. Even though school education should be a utmost priority, school teachers are paid less compared to the work they do everyday. So, only a dedicated few find that as their career due to lots of other constraints. Grant created his own world around him bringing mathematics education to a different level. It's so amazing that he uses his own software to make those deep and profound animations that make so much more sense. Thanks Grants for doing all these.
I am super biased but I think MATLAB is this friction-free coding environment discussed around 17:00. I don’t have to look for packages anymore, now the syntax is second nature, and the extra stuff you can install is really so helpful and user-friendly. It has taken years but now I really feel like almost any simulation I want to do or see, I can plug into MATLAB, set up bounds, choose some parameters, debug for a few minutes and get the result in less than an hour! Thanks so much MATLAB!
@@warguy6474 people should be paid for their work, especially good work. The free + open source movement is a good idea but not sustainable for people who live in the world and have bills to pay
In my mind mathematical talent is in general more "generally applicable" in a problem solving sense because solving problems in the real world requires two things: observation and logic. All stem fields train both of these (even math), but math is special in that all of its observations can also be derived from logic (except for axioms of course). This truth makes math much more focused on the logic than the observation, which logic is much more difficult to use. TLDR logic is more difficult than observation in terms of thinking/effort and math simply focuses much more on the logic than observation. Thus making the study of math inherently better at training logical thinking (more time spent on it compared to other subjects).
His screen name is a reference to the abnormal coloring of his eyes. He has a blue eye and a half blue/half brown eye. So his eye color is 3 blue 1 brown. He often uses the brown pi creature to represent him, and the three blue pi creatures to represent his audience.
6:50 i think the thing that Grant is grasping for that would explain his intuition for why AI that gets gold at IMO is not a harbinger of every creative human endeavor being taken over is that all AI models are trained for /that/ task, even if they can be applied to other tasks on a general level, and that's just not the way human creativity works, or at least not all of it. a person who makes a podcast talking to Grant Sanderson and puts it up on TH-cam for others to watch is engaging a creative impulse that cuts across dozens of domains, and is doing so as a result of motivation that grows out of being a person in a community of other people. Dwarkesh recognizes such a conversation would be interesting to other humans to listen to because Dwarkesh is a human who also finds the conversation interesting. he manifests a creative product out of a cultural (and biological) context. change any aspect of Dwarkesh's life and he isn't making the podcast anymore. there are just too many other factors that go into why and how people do what they do and for whom they do it that an AI model has no access to.
1:00:00 This is the way I feel about the halting problem. Can we write a program that can determine whether any other program will halt? The answer is 'no', but the proof is just a diabolical counterexample. What's the solution to the soft halting problem?: "Given a program, an input, *and a big stick to deter evil geniuses* can you determine whether that program will halt?"
I'm pausing at the question "why is so much maths so new" because it had just occurred to me also, not least because I was googling for maths problems just prior to TH-cam recommending this video to me and I noticed this while clicking around on wikipedia and wondering how much "advanced" maths could have even been needed before sophisticated machinery and things like digital accounting/databases. The observation that most mathematicians prior to the 20th century were also something else, in addition to a latent ~dispassion I have toward the formal education system, makes me wonder if there's space for a more holistic model of education that does not differentiate subjects at the outset, but perhaps presents all learning in the context of the practicality of its genesis and sees any surrounding historical context as an optional but colorful mnemonic. That is, breaking down the typical taxonomy of "subjects" or recognizing the natural fractal-nature of academic knowledge/disciplines in a more explicit way, seems like a valuable project and prerequisite for distributed/decentralized education heralded by projects as large as e.g. Khan academy and as esoteric and broad as channels like Grant's. I'm sure what I've tried to articulate here isn't novel yet perhaps I'm reaching into the void at a future that nobody's adequately found a framework for steering yet. Fascinating conversation so far, resuming the video now!
It would be wild for high school kids to get this guy as a teacher. I hope he doesn't teach at a gifted school, rather, I hope he would teach at an ordinary public / state school.
He'd be wasted at a school full of poor people. Many of them come from cultures where learning academics (especially mathematics) isn't important, and often don't have sufficient IQs to benefit from even intensive instruction. This guy is best fit for those who are interested in learning, and intelligent enough to grasp abstract concepts.
What an utter waste it would be to have someone like him teach at a public school. He would be 100x more useful as a teacher for already gifted students from great families and good genetics, those who have the most potential. How selfish and idiotic is it to want his skills being wasted with public school kids just because you were once one of those? Coming from an ordinary guy someone who went to a public school himself.
I am so happy to have found the time to listen to the whole thing. I was very intrigued by the idea of a potential since I am currently experiencing a small-scale miracle myself. In my research I feel like I finally found a spot where I can perfectly apply the knowledge I build up the last months. Naturally I stopped reading about the subject completely. I'll probably try to allocate some time to reading, I don't want to get out of touch with my subject.
I went for my PhD and Masters in Math specifically to solve problems in chemical engineering & bionanotechnology: especially getting nonconsenting innocent animals out of biological testing, and out of factory farming & fur farms.
I have only a bachelors in chemical engineering and now work in technical sales. I don’t need higher education to make leaps and bounds in my career (maybe an MBA one day). I would like to go back to school for a math PhD for the merit of it one day
That's amazing I love how you took your skill set in Maths and were able to apply it to an important thing you care about and hopefully make the world a kinder place
Two things about the “get mathematicians into other fields” conversation. First, look at maybe the ultimate trump card you can play: Von Neumann. During the Manhattan Project, where basically everyone was an uber-genius and the leadership was filled with Nobel laureates and the like, there was near universal agreement on one thing. As smart and as competent as they were in their different fields, Von Neumann was on a different level. And his contributions range wide and far. From quantum mechanics to game theory to the explosion lenses for implosion-style nukes to how modern computers work to cellular automata to basically predicting DNA. I can keep going but I think the point is made. Being good at math and reaching into other fields can be done at the highest of levels. Second, let’s look at my favorite field of science: the science of complex systems. You can’t engage with this field from a purely mathematical way. You need to understand a wide range of fields to understand complex systems. And that’s how the science of complex systems was developed as well. You had economists and particle physicists and medical doctors (or at least people who went to med school) and computer scientists and bankers. The intersection of math with other fields is where a lot of interesting things happen
I'd love to know what you mean by "active cognitive models". Nobody I know has given a non arbitrary difference between our minds and LLMs for example. Prove to me your 'special human feature' makes you both 'general' / conscious and distinct from existing technologies. I agree that the discussion is framed wrong though. Perhaps I misunderstand what you mean by AGI. Could you elaborate on it?
@@voxelsilk8462 the differences aren't arbitrary, they're significant and nuanced. ML models are static for one, and only somewhat resemble *memory*, not thought processes.
Of you are given all the necessary tools to learn something you will learn it one way or another. If you are not then you get lost with everyone else. I think what helps him is that he had the tools to create the visualizations that allow him to explain complex subjects.
4:39 “Replacing Jobs”. It’s really about leverage. If it takes 10 people with shovels to dig a trench, but only two people with a backhole to dig a trench. That backhole is said to replace 8 people. So, if 20 CSR workers with AI support can support the same workload as 40 without. The AI has replaced 20 workers.
15:32 I'm inclined to disagree about that point about orders of magnitude. I is 1, X is 10, C is 100 and M is 1000. What do these represent if not orders of magnitude? The lack of decimals or orders of magnitude tells us more about what the romans used and what they didn't use math for, and how many order have necessary to think about in practise in roman society. In fact, I suspect a roman history scholar could probably speculate on the reason for why it made sense for them to think about thousands but not tens of thousands. Speaking of which, both chinese and japanese have a unique word for ten thousand ("wan" and "man", respectively), which implies that these societies might have had a broader span of magnitudes compared to Rome, which has had an impact on the language. Interesting stuff, this.
Solving math questions is hard. But asking the right questions is what requires genius (or intelligence). I wont be surprised if LLMs can solve lots of problems. I dont see them asking good questions. Because "good" is an anthropomorphic concept, that I do not believe is properly captured by any data set. Indeed the definition of "good" evolves over time.
I got a master'sin theoretical physics, however right after I finished I knew That I only went there because I was good enough in academics however I didn't enjoy it that much, and literally after finishing my master s I applied to a computer science master's because (migh as well just do that to find a job) and after a year of that I fell in love with academia again and now Im opting for a phD in computer science wheras I wanted to go out of that field (higher academia) like 2 years ago
Given that there will obviously be a lot of "math people" reading the comments, I've got some questions for anyone interested in engaging with me. I'm new to math, and came in with an interest in exploring base twelve geometry, so: 1) Is it an axiom that there is no difference between the bases? Has anyone considered that the size, or length, of the decimal places are different, and therefore perhaps there are patterns which exist which don't show up in base ten, but DO in base twelve. 2) With regard to irrational numbers, is it "against the rules" to assign a second variable to the total length of...say √2 ? The idea being that √2 emerges from the physical properties of matter, which ultimately has two aspects when you get down to the atomic and/or quantum realms - that of matter, and empty space. Ultimately it seems like a solid line needs to have empty space dispersed throughout its length, just as it is dispersed throughout everything we experience as solid in our everyday world. 3) More of a comment - seems like if there is a ratio between the "solid" and "empty" that permeates the Universe it would have something to do with Pi. Has anyone ever considered that there is a version of Pi in another base that might have different characteristics than what we are familiar with in base ten? Referring back to question 1 - working with different sized units to build a circle, perhaps another base would yield significantly different results? A simple example of what I am talking about is the decimal version of 1/3 In base ten = .33333333 - and so one might assume that therefore it is impossible to divide one by three and not have a remainder, and yet... In base twelve = .4 And then apply that same logic to the geometry of the circle.
replying to myself 10 months later - no one replied to my questions. My take away from the lack of response is that the level of interest, and/or awareness, of base-12 math, right now, sept 2024, is... on a scale of one to ten... zero.
Halting problem has major consequences for what kinds of programs are possible. Maybe its just more relevant for compiler programmers and that sort of thing. Also mathematicians dont care about Goedel because many are effectively Platonists. A priori there's no mathematical reason for Riemann hypothesis to be provable from zfc or whatever. If it turns out to be independent we'd have to reverse engineer some plausible axiom that implies it or just take it as its own axiom just because we want it to be true.
It turns out that you can often ignore the halting problem in practice (although you do have to remember it exists). This is primarily because most of the time, before you hit the halting problem, you run into NP-hard problems that are technically solvable, but practically unsolvable.
So, i think grant is mistaken about the AI stuff. Ai is not capable of any amount of thought whatsoever. The sophistication that goes beyond a tree searching alogarythm is displaying abstract thinking and problem solving, but it is being done by the human who made the code. The code that is written for a chess ai, is different than the code that is used for the GO ai, etc. This is because for any artificial intellgience thing, they are fine tuning different values and tolerances, A. and B. they are based on different factors, related to the specific thing. For instance, in chess they might give the ai some reward points for taking an enemy queen, but not losing their own queen as a result. That isn't translatable to go. There are also values that dictate how risky you want your ai to be, when you are training it. And many many other variables, that go into fine tuning any ai for any task. That is to say, none of what's going on in even the best ai out there, displays any thought whatsoever. And requires no thought whatsoever, other than by the creator. And so if an ai could do math proofs, and do them consistently correctly, without having seen the proof they are writing before, then A. the code itself would need to be able to generate novel and abstract thoughts, and B. that it would be doing soemthing fundementally different than what we see today. Grant might or might not be right, that because it can do this, does not neccesarily mean it can do some other thing, but in my view, if it can do this, it can do anything. Again, i am giving that I might be wrong about that conclusion, but defintely grants view is based on likely misunderstandings about currrent ai. Also, Also, the best and only definition of AGI would be to train it on something entirely different, like say a game like chess, and then have it be exceptionally good, without any training, on an arbitrary game you make up (any and all). Or, train it on a set of games, and then it is exceptionally good without training, on an arbitrary set of games. This would be the first rung in what should be defined as AGI, and of course the final rung is being able to be trained on one game, and being better than all humans for an arbitrary large amount time into the future at any game given to it, without training.
As an aside...Grant..you remind me of... David Gower...an elegant cricketer...from an earlier era...by the way..I teach physical chemistry... at high school..and I enjoy your videos ..utterly...
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If Grant becomes a high school teacher I'm going back to high school to learn from him.
I love that quote.
No you wouldn't
@@andherium You wouldn't know
@@stupidguy97
Probability is close to 0 as it gets.
Never heard of a grown man going back to school after already successfully finished.
maybe he should contribute to khan academy. then all of us can go back to school
Grant really stands out to me for staying grounded in the face of people trying to overhype his own work. It's so inspiring to see a guy who has a legitimate claim to leading his field with respect to encouraging pure-math exploration that still values all that in the context of improving the world and helping young kids learn better.
It's inspiring to see how humble he manages to be despite the pressure his work quality and the feedback he gets must put towards inflating his pride. To the best I can tell, it seems genuine too.
amazin.
He has an incredible ability to explain things clearly to people at all levels. He speaks with eloquence.
100% agree with his take that programming is useful, but not just for computers. Learning to program, especially under the lens of software development, teaches you to think about problems and models in terms of layers of abstraction in order to manage complexity. That is an incredibly useful skill that can reframe how you view the world
100% agree, I can feel the difference between when I'm talking to someone about breaking down a problem (regardless of domain really) when its with a person who's experienced with programing vs a person who isn't
@@qualia765 Programmers are not the only people who break down problems to solve them.
@@maythesciencebewithyouI don’t even think they have unique methodologies for doing so. What they do have is a lot of good problems to practice these skills in an integrated way that’s different from the mix in other subjects.
@@pookz3067 more so than math? I'm keen on math but would learn programming if it offers something more/different
Funny story about mathematicians working in other fields. During graduate school for computational biology I focused on modeling agricultural systems. I found out during graduate school that I really liked farming. I'm a relatively talented mathematician, that was offered a job where I went to graduate school immediately upon graduating, a research position. I declined and asked if I could just be a mere lecturer, and they obliged. I have since started farming and sell at local markets. In about 10 years it is my intention to quit teaching mathematics and just farm. There is a lot of similarities in farming in mathematics, believe it or not.
How farming = math?
I'd be really interested in how you apply math to farming!
can you please elaborate on this
@@harsheh What would you like to know?
Can you share the similarities? Really interested to know
I enjoy a conversation in which people are speaking genuinely and intellectually and happily. So much of the internet is out of context and mentally degrading.
He nailed this entire interview. I especially love the repetitions of calculations. That is 100% accurate, in my case.
High School Maths teacher here. Grand Sanderson stands out not only a great educator, but also a humble human being. He shows huge respect for teachers, and even though he's (apparently) never been a teacher himself, he's full of insights about teaching. I particularly appreciated his stance that excellent teachers should stay in the classroom to inspire students. I loved that Grand fancies going into teaching himself at some point for a while, and I'm sure that he'd be a wonderful and popular teacher.
Please share if you enjoyed! Really helps out a ton! 😎
SO glad I stumbled across your Podcast, it reminds me of all the things I loved about Lex Fridmans AI podcast back in the day. I hope you have the same success. And yes, I'll share with all my friends in Mathematics and the Sciences.
Grant has the approach that's needed in high school classes. His videos do a very good job of presenting math to people who aren't at a high level of mathematical maturity.
I have to shout out Kerbal Space Program as by far the finest educational game ever made. There is no better curriculum for building an intuitive understanding of orbital mechanics than spending a couple of weeks doing a mars program in KSP. I think the best educational games are games that *simulate* (in a fun-focused way) the process that the student is meant to understand, rather than trying to use a game framework to do traditional teaching.
Outside of financial transactions, a 24 hour clock leverages a more abstract understanding of numbers. Keeping track of time was a big motivation for early numerical developments. I also think back to those older society descriptions of measurements and its like "Take a square with 5 inch long edges..." wheras I can just think 5^2 = 25 sq inches or 5x5 square. More generally I think most people find it easier to think in terms of truncated real numbers rather than as q/p rational numbers.
Agree. And basing agricultural benchmarks on astronomical phenomena: "after [so many Moons] the river will flood. Then we will [ hunt/ plant/ fish / forage ...]"
I've seen a number of podcasts with Grant. This is by far one of the best, and all in all just a wonderful discussion.
on the issue reallocation of mathematical talent: i'm one of the guys that got duped by grant into doing a phd in pure math (haven't met him though), and i've been thinking about this issue one-and-off for a few years now. it's clear that there's a waste of talent at the phd+ level due to the undersupply of academic jobs. the training you get when studying math gives you a high level of insight for general problem-solving skills, but you lack the knowledge in any other field to make use of it. so effectively you're only good as a outside consultant, unless you want to dive into a whole new field. this (+ $$$) is why the two canonical non-academic paths are tech or finance, as those two fields have low barrier to entry in terms of content. if you can think well, you can float in those two fields much easier than e.g. biology
When you say tech and finance have a lower barrier of entry than biology, do you mean that mathematics is more applicable in those fields or that they’re outright easier to find jobs in?
I’m considering a M.S. in biostatistics and would love to know how you think a field like that would compare to the usual tech and finance routes. My hope was that the job market would be better given fewer people go the biostatistics route, as I’ve heard many of my CS friends struggle to find jobs despite being considered a very “in demand” career.
I earned an applied math Ph.D. at the University of Arizona studying mathematical physics (soliton theory and integrable systems). Today, I am a Quantitative Medicine Scientist at a non-profit tackling "rare" diseases (neuro-degenerative, genetic, immuno-suppressant, etc) by integrating Digital Health Technologies into the drug development pipeline. I chose that my efforts contribute towards the general field of Public Health (stemming from family values). I see others with similar training going into Pharma, Tech, Defense, Economics, Environment, Government, NGO, Finance, Transportation, Startups - wherever their passions may lie.
That was great!!! On multiple times, I felt that Grant was questioning if a question was valid or not. Or at least giving an answer that you're not expecting. Anyway, you let the guest talk and explain his points. Multiple interviewers would interrupt and try to make their own points be heard.
Glad to know your podcast!!
This interview is how I, a frequent TH-cam watcher who happened to benefit from Grant’s videos during school, find out that Grant does his own animations 😂 so inspiring
He made programming library he uses public. It is called manim and is a Python library.
An AGI can self learn new things, come up with new thoughts/ideas without fine tunning and re-training, It needs to be beat me in all tasks, work, driving, thinking, ideas.
46:00 I feel like that the point mentioned there is one of the most overlooked. While preparing for upcoming exam phase we could do the old tests and there were huge differences between the difficulty of the single tests - like I remember rocking some of them and others felt impossible for me. And I was like wtf!? I talked to some friends and we generally felt the same - basically what happened was, that the Prof was totally detached from the common students. He was lecturing everything for so long, that he didn´t have any feeling left for what are hard concepts to follow when you hear them the first time.
Grant let me say on behalf of a lot of people I know studying engineering; You really helped us understand how to think about linear algebra,basis transformations and PDE´s in a way, that at least for me have made it so much more intuitive. In this way you have helped a lot of people become better engineers. Thank you. Great podcast.
A true modern hero. I respect this man a lot.
Guests just keep getting better and better
one thing i keep thinking about as someone studying physics and maths to become a teacher is whether the university system where i live isnt backwards for making teachers
basically its 50/50 regular maths and physics lectures (no watered down versions for teaching) for the bachelor and then 2 years of pedagogy/education training for the masters degree with basically no practical teaching parts during the bachelor
when u now take what grant said about "remembering what its like to not understand" and "the best explanation being highly dependent on the individual"
any ammount of unnecessary time spent / excess topics learned between being a student and being a teacher would be something that should be avoided at any costs
i do tutoring and even the better students rarely have math questions that go beyond what you know after semester 1 or 2 of university
but at the same time, im expected to attend analysis III and Linear Algebra II when the required level for highschool teaching and then some would be met by just hearing the Physics Math lectures
for Physics of course its alright to dive a bit deeper, since most of what u need for an advanced physics lesson is basically university stuff with less math
but i feel like raising the Bar for the Subject itself too much prevents a lot of good explainers from ever becoming teachers since they are expected to learn something that will have very little/possibly no benefit to their actual quality as a teacher
Wow 🤩 the future of education section truly blew me away. He is completely right.
The anecdote at ~52:00 resonates with me so strongly. I remember cringing so much growing up at loose-lipped teachers who are all-too-ready to say something slightly demeaning to students who are struggling. The littlest things can matter so much to kids, especially when it's coming from an authority figure. I don't mean to undermine the frustration and erosion to mental fortitude that being an educator entails, but it's just really scary how massive those effects can be.
The reason mathematicians should go pair with people in other fields is not because mathematicians are better, they're just different, and that cross-pollination is always a good way to get novel ideas happening. I figure it's just as likely the mathematician comes away with something they learned in that foreign field that helps their work in math as the converse.
It's funny because I am 96% done with a math degree and I hit the brakes, thinking "is grad school or industry even what I want to do?" Lately I just.... don't want to partake in the slog of academia, worry about grants, student outcomes, CVs, activities to pad my CV,... etc. That shit just kills my soul and motivation to learn math. I love and admire what Grant did, I'd actually love to build an "open source and friendly" math community around me. Anyway some friendly advice... you've got a question for the professor but feeling like... "everyone is going to think I'm stupid for asking this." Then just hit up chatGPT, talk to it about it organically like you would a professor, and maybe rephrase your question in a way that doesn't make you feel anxious to ask it.
I forgot to mention, check the understanding you gained with chatGPT with a professor, because man that thing gets some stuff wrong, but it has just helped me, when I'm about to ask a dumb question, just gain a lot of insight into Mathematics.
It takes a lot of confidence to simply ask questions when you do not understand something. Many times asking a seemingly stupid question reveals that everybody in the room actually wanted to know it but were simply too shy to ask, too afraid to seem stupider than the rest.
Grant is genuinely someone who i see as a hero. A brilliant guy but with a lot of heart- all about the why of maths.
Everyone who has done maths knows this feeling 4:15 😅
It's amazing to hear him talking without seeing animation.
This interview been in my recommendations for a while, but that clip you posted recently is what got me to watch. Good work
Breaking Math Podcast here - sir, this interview is *chef’s kiss*
People calling machine learning programs "intelligence" just shows they don't understand it at all. Grant seems to get that a lot more than Patel.
Why would machine learning not be intelligence?
@@newwaveinfantry8362 Look up the Chinese Room thought experiment.
Lol did you even understand any of what he said or were you just desperately looking to find validation for your own biases? Grant explicitly says that it's weird to expect a discrete change of a nigh indeterminate variety before getting to label state of the art natural language models as "intelligent", given that there's already a large amount of generalization and astonishing strains of logical reasoning that they are capable of.
His position runs totally contradictory to your mistaken interpretation of his words.
8:26 Ideally, "applied mathematicians" should be *anywhere and everywhere* because there's really no predicting when or how the next big applications are going to emerge. But that may not take PhD-level specialization, and even if it does, then specialization itself will probably be inadequate.
The key therefore is to just elevate the mathematical sophistication of as many different people as possible and to combine specialized depth with generalized breadth. This would also make it easier for people with different educational and professional backgrounds to understand each other as they learn from each other. In effect, we may not see many more *applied mathematicians* (defined as PhD-level specialists), but we can instead still see more *applied mathematics.*
Regarding the "where should applied mathematicians go", I really think engineering firms should be more open to hiring math PhDs. So many employers just have the mindset "they must have an engineering degree". A math PhD might have fantastic modelling, simulation, programming skills. Fantastic problem solving ability. Better understanding of fluid mechanics, solid mechanics, thermodynamics than the engineers. And so on.
I had this issue when I finished my PhD. Everyone wanted engineering degrees. And I would think "I literally taught fluid mechanics to third year engineering classes, how could you possibly think they're better equipped for a CFD role than me?".
on the halting problem, in my experience, ruminating on why computation runs up against that limit was instructive especially early on when programming. It helped me develop an intuition for the "perspective" of a computational machine which helped motivate filling in the details of an algorithm easier when otherwise i would have been stuck looking at an input and the desired output.
I wish I had Grant Sanderson's math videos (and TH-cam in general actually) when I was in school. I am a computer programmer now but I'm pretty bad at math. I had a substitute teacher in math class for over 2 years because my teacher was in a car accident.
You can still learn it now. Internet provides everything you need, but maybe you are less interested than you suggest.
29:00 This reflection on whether linearity is natural or unnatural to human cognition is fascinating.
Grant, I’ll have you know that something you said actually made me feel more at peace with NOT becoming a math PhD. It was one if your Q&A videos where you talked about Shannon and Lorenz, and how maybe it’s good to have math-y people in other applied fields. So, good job balancing it out in the other direction 😁.
Link?
Source
Yes!!! I’m going into psychology research… big replication issue, hoping I can find some statistics-related problems
One of the best interviews I’ve ever heard
Really? It was all over the place! He answered very well, but it was as if it was randomly generated.
His TH-cam videos in Linear Algebra and calculus serve as a necessary refresher for machine learning programs at Berkeley and Stanford.
Grant may have only a BA in math, but he knows as much as an average math MA I'm sure, and as much as many PhD students. I'm a fourth year math student, decently above average I'd say, and pretty wide-ranging and deep, but I know barely anything about functors between categories, or chaos theory, and I know nothing about information theory. His command of algebra, topology, number theory and combinatorics is well above mine. I probably match him in analysis, linear algebra, vector calculus and differential geometry, but that's it. He has what it takes to be a truly great mathematician.
I've been a great fan of 3Blue1Brown many times, and you seem charismatic enough; I wish you the best in your podcast journey and hope you get some big names coming your way soon. Not that having Grant on is bad though.
This was a great conversation. I really enjoyed it.
He is such a good person. I would give so much just to have one conversation with him!
Great guest, looking forward to listening to this episode!
This was a superb interview! At 29:32 I can't resist suggesting that we need abstract numbers to cope with quantities that are too large to grasp intuitively: a video has 10 million views; my collaborator lives 5000 miles away; Jesus lived 2000 years ago; someone just won a $1.7 billion Powerball jackpot. Also at 55:04 the graduate student was George Dantzig.
Can't go a day without seeing a reference to Jesus😂
@@andrewcameron5495 hmm 🤔, wonder why?
@@joshuawallwork6678 "cUz He'S ReAL!!!!"
@3Blue1Brown
13:26 : Yes, you did bridge your abstract problem solving skills to another field: To the field of didactics and how to pass knowledge to other people in a beautiful and efficient way! Thank your for that!
I see Grant Sanderson, I click the like button.
Grant mentioned "numeracy" multiple times in this video. There's a really interesting book called "Innumeracy" by J. Paulos which covers the exact thing he's talking about. It has a particular focus on how people tend to have skewed views of numbers and statistics.
Phenomenal podcast! Well done Dwarkesh!
A little summary on who these people are for those of us who don't know would be helpful IMHO. Great interview
28:46 I think it may be related to the demise of slide rules. They convert addition (which naturally works with linear scales) to multiplication by putting the numbers on the scale LOGARITHMICALLY! IMO everyone with any interest in or need to know math should learn to use a slide rule. I even wonder if a linear-scale slide rule should be introduced in first or second grade, along with the number line to help learn addition. Or maybe I'm projecting about what I think would have helped me. I went through standard high school math then electrical engineering where algebra, trig and complex numbers were just a repeat of high school, then a couple calculus courses. That was pretty much all the math I needed for that EE school, but I've always been interested in number theory and other mathy things, and feel like if I had different opportunities I would have gotten a math degree, which would require going to a different school.
TH-cam algo gods blessed me today. Great video and glad to have discovered your channel
I just want to remind everyone that "computer generated art" doesn't exist. Computer generated art has been fed a great number of human works. It's a synthesis of human creativity, not the invention of a creative robotic mind. Computers have learned chess and go from zero human input, not art or music.
The games of go and chess can be defined in a human-agnostic way. Art has no commonly accepted human-agnostic definition. Thus, it is trivially true that all computer generated art is meant to appeal to humans. If you or anybody else were to propose a standard definition for art, I could almost certainly optimize a network for that
Grant's novel idea about planting fake highschoolers actually seems kind of brilliant. I wouldn't be surprised if countries have already implemented it really inconspicuously. Your social network and desires really affects your interests more than anything else.
I thoroughly enjoyed this interview. It was just so much fun, you're both great! =D
Saw the video was with Grant, liked it, and now I watch it
Always thankful to 3blue1brown for all the amazing content ❤
I really wanted to be a match teacher but ended up in tech. This video is so spot on
That last point about getting an attractive classmate interested in a subject as a means of teaching was gold 😂
Thank you for this podcast, I really enjoyed listening. Many great questions and a lot of insight.
I agree as a self-learner after graduation, I stopped doing the calculations. I still want to learn more HEP-th, but without time for "homework" I know it's pretty useless to try.
Yes, it is a sad reality. Even though school education should be a utmost priority, school teachers are paid less compared to the work they do everyday. So, only a dedicated few find that as their career due to lots of other constraints. Grant created his own world around him bringing mathematics education to a different level. It's so amazing that he uses his own software to make those deep and profound animations that make so much more sense. Thanks Grants for doing all these.
I am super biased but I think MATLAB is this friction-free coding environment discussed around 17:00. I don’t have to look for packages anymore, now the syntax is second nature, and the extra stuff you can install is really so helpful and user-friendly. It has taken years but now I really feel like almost any simulation I want to do or see, I can plug into MATLAB, set up bounds, choose some parameters, debug for a few minutes and get the result in less than an hour! Thanks so much MATLAB!
closed source ick
@@warguy6474 people should be paid for their work, especially good work. The free + open source movement is a good idea but not sustainable for people who live in the world and have bills to pay
Grant is superb mathematician
Wow! I was surprised to hear the reference to Lars. I knew him in college. Will definitely watch your interview with him.
Wow, thanks for this. He is al down to earth 🌍🌎 and inspiring. 😊
Love your channel about AI 🤖! Nice to see you here. :)
Really like your talks Dwarkesh. Keep it up 👍
In my mind mathematical talent is in general more "generally applicable" in a problem solving sense because solving problems in the real world requires two things: observation and logic. All stem fields train both of these (even math), but math is special in that all of its observations can also be derived from logic (except for axioms of course). This truth makes math much more focused on the logic than the observation, which logic is much more difficult to use.
TLDR logic is more difficult than observation in terms of thinking/effort and math simply focuses much more on the logic than observation. Thus making the study of math inherently better at training logical thinking (more time spent on it compared to other subjects).
1White1Brown
LMAO
1White1Brown : 2Interesting.
His screen name is a reference to the abnormal coloring of his eyes. He has a blue eye and a half blue/half brown eye. So his eye color is 3 blue 1 brown. He often uses the brown pi creature to represent him, and the three blue pi creatures to represent his audience.
@@carultch Well, I guess anybody reading this comment thread knows that, so why restating it ?
@@R_V_I didn’t know
6:50 i think the thing that Grant is grasping for that would explain his intuition for why AI that gets gold at IMO is not a harbinger of every creative human endeavor being taken over is that all AI models are trained for /that/ task, even if they can be applied to other tasks on a general level, and that's just not the way human creativity works, or at least not all of it. a person who makes a podcast talking to Grant Sanderson and puts it up on TH-cam for others to watch is engaging a creative impulse that cuts across dozens of domains, and is doing so as a result of motivation that grows out of being a person in a community of other people. Dwarkesh recognizes such a conversation would be interesting to other humans to listen to because Dwarkesh is a human who also finds the conversation interesting. he manifests a creative product out of a cultural (and biological) context. change any aspect of Dwarkesh's life and he isn't making the podcast anymore. there are just too many other factors that go into why and how people do what they do and for whom they do it that an AI model has no access to.
1:00:00 This is the way I feel about the halting problem.
Can we write a program that can determine whether any other program will halt? The answer is 'no', but the proof is just a diabolical counterexample.
What's the solution to the soft halting problem?: "Given a program, an input, *and a big stick to deter evil geniuses* can you determine whether that program will halt?"
Hey Grant, my sister went to MIT as math major and became a lawyer. Fwiw
I'm pausing at the question "why is so much maths so new" because it had just occurred to me also, not least because I was googling for maths problems just prior to TH-cam recommending this video to me and I noticed this while clicking around on wikipedia and wondering how much "advanced" maths could have even been needed before sophisticated machinery and things like digital accounting/databases.
The observation that most mathematicians prior to the 20th century were also something else, in addition to a latent ~dispassion I have toward the formal education system, makes me wonder if there's space for a more holistic model of education that does not differentiate subjects at the outset, but perhaps presents all learning in the context of the practicality of its genesis and sees any surrounding historical context as an optional but colorful mnemonic. That is, breaking down the typical taxonomy of "subjects" or recognizing the natural fractal-nature of academic knowledge/disciplines in a more explicit way, seems like a valuable project and prerequisite for distributed/decentralized education heralded by projects as large as e.g. Khan academy and as esoteric and broad as channels like Grant's. I'm sure what I've tried to articulate here isn't novel yet perhaps I'm reaching into the void at a future that nobody's adequately found a framework for steering yet. Fascinating conversation so far, resuming the video now!
It would be wild for high school kids to get this guy as a teacher. I hope he doesn't teach at a gifted school, rather, I hope he would teach at an ordinary public / state school.
unfortunately him working at a public school is very very very unlikely, he's probably just going to benefit rich kids
@@Kishblockprokids at regular schools often don’t want to learn away - trust me I work at one
He'd be wasted at a school full of poor people. Many of them come from cultures where learning academics (especially mathematics) isn't important, and often don't have sufficient IQs to benefit from even intensive instruction.
This guy is best fit for those who are interested in learning, and intelligent enough to grasp abstract concepts.
What an utter waste it would be to have someone like him teach at a public school. He would be 100x more useful as a teacher for already gifted students from great families and good genetics, those who have the most potential.
How selfish and idiotic is it to want his skills being wasted with public school kids just because you were once one of those?
Coming from an ordinary guy someone who went to a public school himself.
Really like all the topics you brought up. Great interview!
I am so happy to have found the time to listen to the whole thing. I was very intrigued by the idea of a potential since I am currently experiencing a small-scale miracle myself. In my research I feel like I finally found a spot where I can perfectly apply the knowledge I build up the last months. Naturally I stopped reading about the subject completely. I'll probably try to allocate some time to reading, I don't want to get out of touch with my subject.
I went for my PhD and Masters in Math specifically to solve problems in chemical engineering & bionanotechnology: especially getting nonconsenting innocent animals out of biological testing, and out of factory farming & fur farms.
I have only a bachelors in chemical engineering and now work in technical sales. I don’t need higher education to make leaps and bounds in my career (maybe an MBA one day). I would like to go back to school for a math PhD for the merit of it one day
No one cares.
That's amazing I love how you took your skill set in Maths and were able to apply it to an important thing you care about and hopefully make the world a kinder place
I’m applying to math grad school as I’m watching this
Two things about the “get mathematicians into other fields” conversation.
First, look at maybe the ultimate trump card you can play: Von Neumann. During the Manhattan Project, where basically everyone was an uber-genius and the leadership was filled with Nobel laureates and the like, there was near universal agreement on one thing. As smart and as competent as they were in their different fields, Von Neumann was on a different level. And his contributions range wide and far. From quantum mechanics to game theory to the explosion lenses for implosion-style nukes to how modern computers work to cellular automata to basically predicting DNA. I can keep going but I think the point is made. Being good at math and reaching into other fields can be done at the highest of levels.
Second, let’s look at my favorite field of science: the science of complex systems. You can’t engage with this field from a purely mathematical way. You need to understand a wide range of fields to understand complex systems. And that’s how the science of complex systems was developed as well. You had economists and particle physicists and medical doctors (or at least people who went to med school) and computer scientists and bankers. The intersection of math with other fields is where a lot of interesting things happen
AGI isn't about being "better" than any particular thing, it's having active cognitive models, which no "AI" has at all.
I'm genuinely disappointed in the framing of this discussion.
If you asked 10 people you'd get 10 different answers.
I'd love to know what you mean by "active cognitive models". Nobody I know has given a non arbitrary difference between our minds and LLMs for example. Prove to me your 'special human feature' makes you both 'general' / conscious and distinct from existing technologies.
I agree that the discussion is framed wrong though. Perhaps I misunderstand what you mean by AGI. Could you elaborate on it?
@@voxelsilk8462 the differences aren't arbitrary, they're significant and nuanced. ML models are static for one, and only somewhat resemble *memory*, not thought processes.
Of you are given all the necessary tools to learn something you will learn it one way or another. If you are not then you get lost with everyone else. I think what helps him is that he had the tools to create the visualizations that allow him to explain complex subjects.
Correction: He invented the animation tools.
I love how grant is explaining the plot to good will hunting @56 min
Are you referring to Scott Aaronson at 56:34? Answered at 58 minutes. Fascinating interview.
Random Georgism plug. What an interview!
it's amazing that Grant almost exactly predicted the way that Google got silver on the IMO
4:39 “Replacing Jobs”. It’s really about leverage. If it takes 10 people with shovels to dig a trench, but only two people with a backhole to dig a trench. That backhole is said to replace 8 people. So, if 20 CSR workers with AI support can support the same workload as 40 without. The AI has replaced 20 workers.
15:32 I'm inclined to disagree about that point about orders of magnitude. I is 1, X is 10, C is 100 and M is 1000. What do these represent if not orders of magnitude? The lack of decimals or orders of magnitude tells us more about what the romans used and what they didn't use math for, and how many order have necessary to think about in practise in roman society.
In fact, I suspect a roman history scholar could probably speculate on the reason for why it made sense for them to think about thousands but not tens of thousands. Speaking of which, both chinese and japanese have a unique word for ten thousand ("wan" and "man", respectively), which implies that these societies might have had a broader span of magnitudes compared to Rome, which has had an impact on the language. Interesting stuff, this.
Great interview, thanks! Small note: Euler is about 200 years ago not 2000 years
1:26:54 is such a fun premise. I would watch the hell out of this drama
Solving math questions is hard. But asking the right questions is what requires genius (or intelligence). I wont be surprised if LLMs can solve lots of problems. I dont see them asking good questions. Because "good" is an anthropomorphic concept, that I do not believe is properly captured by any data set. Indeed the definition of "good" evolves over time.
Holy shit homeboy was so kind to this interviewer
I got a master'sin theoretical physics, however right after I finished I knew That I only went there because I was good enough in academics however I didn't enjoy it that much, and literally after finishing my master s I applied to a computer science master's because (migh as well just do that to find a job) and after a year of that I fell in love with academia again and now Im opting for a phD in computer science wheras I wanted to go out of that field (higher academia) like 2 years ago
automatic like for Grant
Given that there will obviously be a lot of "math people" reading the comments, I've got some questions for anyone interested in engaging with me. I'm new to math, and came in with an interest in exploring base twelve geometry, so:
1) Is it an axiom that there is no difference between the bases? Has anyone considered that the size, or length, of the decimal places are different, and therefore perhaps there are patterns which exist which don't show up in base ten, but DO in base twelve.
2) With regard to irrational numbers, is it "against the rules" to assign a second variable to the total length of...say √2 ? The idea being that √2 emerges from the physical properties of matter, which ultimately has two aspects when you get down to the atomic and/or quantum realms - that of matter, and empty space. Ultimately it seems like a solid line needs to have empty space dispersed throughout its length, just as it is dispersed throughout everything we experience as solid in our everyday world.
3) More of a comment - seems like if there is a ratio between the "solid" and "empty" that permeates the Universe it would have something to do with Pi. Has anyone ever considered that there is a version of Pi in another base that might have different characteristics than what we are familiar with in base ten? Referring back to question 1 - working with different sized units to build a circle, perhaps another base would yield significantly different results?
A simple example of what I am talking about is the decimal version of 1/3
In base ten = .33333333 - and so one might assume that therefore it is impossible to divide one by three and not have a remainder, and yet...
In base twelve = .4
And then apply that same logic to the geometry of the circle.
replying to myself 10 months later - no one replied to my questions. My take away from the lack of response is that the level of interest, and/or awareness, of base-12 math, right now, sept 2024, is... on a scale of one to ten... zero.
Great podcast!
Halting problem has major consequences for what kinds of programs are possible. Maybe its just more relevant for compiler programmers and that sort of thing. Also mathematicians dont care about Goedel because many are effectively Platonists. A priori there's no mathematical reason for Riemann hypothesis to be provable from zfc or whatever. If it turns out to be independent we'd have to reverse engineer some plausible axiom that implies it or just take it as its own axiom just because we want it to be true.
It turns out that you can often ignore the halting problem in practice (although you do have to remember it exists). This is primarily because most of the time, before you hit the halting problem, you run into NP-hard problems that are technically solvable, but practically unsolvable.
I like the freedom knowlege gives us.
So, i think grant is mistaken about the AI stuff. Ai is not capable of any amount of thought whatsoever. The sophistication that goes beyond a tree searching alogarythm is displaying abstract thinking and problem solving, but it is being done by the human who made the code.
The code that is written for a chess ai, is different than the code that is used for the GO ai, etc.
This is because for any artificial intellgience thing, they are fine tuning different values and tolerances, A.
and B. they are based on different factors, related to the specific thing.
For instance, in chess they might give the ai some reward points for taking an enemy queen, but not losing their own queen as a result. That isn't translatable to go. There are also values that dictate how risky you want your ai to be, when you are training it. And many many other variables, that go into fine tuning any ai for any task.
That is to say, none of what's going on in even the best ai out there, displays any thought whatsoever. And requires no thought whatsoever, other than by the creator. And so if an ai could do math proofs, and do them consistently correctly, without having seen the proof they are writing before, then A.
the code itself would need to be able to generate novel and abstract thoughts, and
B. that it would be doing soemthing fundementally different than what we see today.
Grant might or might not be right, that because it can do this, does not neccesarily mean it can do some other thing, but in my view, if it can do this, it can do anything. Again, i am giving that I might be wrong about that conclusion, but defintely grants view is based on likely misunderstandings about currrent ai.
Also, Also, the best and only definition of AGI would be to train it on something entirely different, like say a game like chess, and then have it be exceptionally good, without any training, on an arbitrary game you make up (any and all). Or, train it on a set of games, and then it is exceptionally good without training, on an arbitrary set of games. This would be the first rung in what should be defined as AGI, and of course the final rung is being able to be trained on one game, and being better than all humans for an arbitrary large amount time into the future at any game given to it, without training.
As an aside...Grant..you remind me of... David Gower...an elegant cricketer...from an earlier era...by the way..I teach physical chemistry... at high school..and I enjoy your videos ..utterly...