Allow me to clarify one thing, I said "... he [Leslie Lamport] is the one stating programmers need more math" but this is inaccurate. Leslie Lamport never said that. He is advocating for mathematical thinking and to broaden familiarity of logical operations since many programmers are intimidated by them even though they are no more complex than "two plus two equals four", just less familiar. What I intended was to use the hook to say "programmers need more math according to Leslie Lamport", then segue into saying "well actually, what he was really saying is programmers need more mathematical thinking." But in doing so, I made a false statement. So just wanted to clear that up.
i think basic mat like: +, -, * is at needed as a beginner to understand coding when you start out. But if you wanna develope better like in machine learning math can help you to know what is going on and understand calculatios better. i always try to make before i start learn to code to try a little math before coding.
Why is this vid up when the thumbnail and first minute is completely misleading. Thanks for the clarifying comment but I think YT is already plagued with a lack of nuance and misquotes.
The main subject of the video is really interesting, It's the same as Why physicists need mathematics, But I don't think that computer science is a subfield of mathematics, I think mathematics is a tool computer scientist use to describe Theory and logic, But still mathematics remain a tool, It's like learning electronics or computer architecture we need to understand them to program them, Which mean they are a tool for us to apply what we learn, So mathematics is the language we use to describe theory, But that doesn't mean Theory is a part of mathematics, This is my view point Thanks for the video.
As someone who spent lots of hours studying math, I may say that the only way to fully acquire mathematical thinking is by learning math in the "hard way". Nothing teaches you more than some hours of frustration to understand a simple example.
@@vorladeththepphavongsa9029 its the same for programming , its just most people these days use chatgpt or forums with understanding what theyre copying .
@@vorladeththepphavongsa9029 It's less about solving math equations themselves and more... understanding the process of solving an equation (and the order of operations for solving an equation). And long study sessions don't really work unless you're really engrossed in the work, too. "The Hard Way" is learning concepts from the ground up, that way you gain an intuitive understanding of the problem's building blocks. You may not be able to solve an equation or problem immediately, so you go back and build the understanding up until you reach that equation. The more equations you solve, the faster you'll get at this. Math outcomes (and most logical pursuits) have been way too obsessed with end results, issues be damned. It leads to unnecessary bloat and difficulty down the road.
Just doing math teaches you how to organize and structure systems of logic. So even if you’re not necessarily solving equations (or whatever you think “math” is), it fundamentally changes the way you approach a problem. As a mathematician who codes a lot, I found I often write better code than the actual CS majors, largely because of all the time I’ve spent organizing mathematical arguments on paper. There is something to be said about mathematicians who don’t invest in learning to code well too tho.
Did you mean self-taught software developers? Or maybe developers with a business focused IT degree? A Bachelor of Science CS degree from a reputable university requires a lot of math.
@@madallas_mons That's mostly irrelevant. A CS degree requires so much math that a CS grad is generally assured to be good at math. Obviously there will be some exceptions. I once worked with a software developer who had a math degree yet couldn't mentally calculate the 15% tip when our group would go out for lunch.
@@DemPilafian Most mathematicians are bad at arithmetic. Fast calculation is a skill that needs to be maintained and most people lose it when they learn higher math. I was much faster at it when I was 12 than I am now at 23. All you need in terms speed for higher math is fast algebra
He's absolutely right, I have an engineering degree and I've been working as a software engineer for about two and a half years, but the more serious I get about this, the more I realize the importance of abstraction and formality, giving a small example, I can solve difficult LeetCode problems with my trained logic, but sometimes I do it by intuition and God help me come up with the proof of correctness for the algorithm, I believe I'm good at programming because I'm decent at mathematical thinking (although I don't really know much), for me, the base of all we do is abstraction, logic, and analysis, which math does formally. I'm doing good in my career, but as I realize this, I've gotten to the point in which I firmly believe I need to go back to a formal training in math (maybe another degree), because most of what we do is simple practical mathematics.
@@gandhisFlipFlops I mean, it's well established that you can make software more time and space efficient. And with a good understanding of math some simulations become constant.
Structured and logical thinking, abstraction, and analysis (math) are useful for anything that requires you to think, it takes a very ignorant/dumb person not to realize this. But well, "common" sense and logical thinking don't actually seem to be that common among people
It’s not useless, but its usefulness is debatable. Architectural patterns, microservice design, meta programming, UIUX, devops, infosec, product etc have very little maths involved. If you’re a student, sure you’ll learn your algorithms. But the longer you work in software engineering the less important maths becomes
@@bonquaviusdingle5720 Everything you wrote has to do with maths, more or less. Often time understanding of proof writing, formal logic, statistics etc is what makes a difference between average developer and great developer. The reason why we don't care about maths in programming is that we have gone through massive boom, or shall I say two massive booms. First one being massive demands for software, and second being massive hardware gains. But those booms are coming to an end, and with them there will be more and more emphasis on programmers being able to deliver their paid value. Because of that my prediction is people who understand how computer works, and can deliver actual good performance while leveraging modern abstractions like ADTs. Will be the ones who remain well paid. The rest will have to accept pay cuts. Gone will be the days where "developer time" were the biggest expense, and CRUD apps were in massive demand. And we have massive over-saturation of developers who lack understanding of algorithms, and rely on glued premade solutions.
I can testify to this. As someone who barely got math in highschool and teached herself programming first. I was able to program (and even on paper figured out some things that turned out to be basic mathemathical statements myself way before learning about them) to then suddenly having revelation after revelation when i did start to properly study math. That improved my programming and understanding of what was going on so much and solved many issues i had before when just trying to do it without some basic math skills. This turned into me going to university for physics and i can say the way i learned to think still helps me today as a developer more than the college for applied information technologies ever did.
I am not someone who tons of experience with programming with latest and greatest programming languages and frameworks, but I concur with Lamport's opinions: writing the algorithm of solving a problem for typing it out in some language leads to fundamentally better programs in comparison to those which are just typed out and "hacked" together. Donald Knuth also promotes the use of mathematics to define problems and algorithms to solve them, and intersperse code chunks with commentary, making them easier to read. He calls this "literate programming". I am a big fan of this approach as it makes programming easier (though big codes can be difficult to maintain unless strict guidelines are there). Jupyter Notebooks is a pseudo-literate programming tool which is popular in experimental physics and data science. Just imagine, the whole source code of popular projects, say the Linux kernel, or ffmpeg, written in literate programming style, with a table of contents, index and hyperlinks telling a newbie where to look. It would be amazing!! Like I said before in your video on Linux and history of Unix, nice video! Nice to the point, something which is rare these days.
Great video. I love this format of exploring topics on the intersect between software engineering and academics. When I was in school I thought it was all pointless. The more time I spend as a professional the more time I spend brushing up on math concepts that I really wish I would've nailed down when I was actually in school.
Ah yes, the holyTrinity of computers: Hardware, Mathematical analysis, and dealing with requirements that have nothing to do with the high level goals of the organization without losing it
I think a better approach is to learn the basics of logic, formal logic and to practice critical thinking, something i did before i took an interest to programming. These two fields complement each other very well. But learning math can also help in broadening your ability to think abstractly and tackle programming problems.
I completely agree with this. I have a degree in both computer science and pure mathematics . Breaking down complex software engineering problems in smaller less complicated ones is the same logic we used to prove complex theorems and solve complicated problems in maths . In first year of university we only wrote pseudo code to write algorithms , the focus was on solving the problem not the language syntax .
That's an impressive resume. I have a question for you (if you don't mind). I'm building a website which will take in a huge amount of text-based data and store it into a back-end db. Would you recommend adding a sorting function prior to a search function for querying? What I don't want are huge delays as it's written in Python anyway. If you don't want to respond, no worries. If you do, thank you very much!
I couldn't tell you how many times I've had to revise or throw out plans. I understand where Lamport is coming from, when I worked on control systems and distributed systems, most of my time was spent planning + testing + verifying but if you're working on complete applications the sheer bulk of code makes insuring correctness ahead of time very difficult. Formally specified UI would be cool I guess but you'll have to 3x your dev time to do it well, good luck getting stakeholders on board with that.
@@paulsingh11 teaching standards are very low this is the real problem. When simple boolean operations are taught in the most painful and distasteful way possible there is nothing you can do to incorporate more stuff and get a good result
It’s a shame. Honestly, looking back I think I wasted more time with the annoying algebra reducing in math than the actual subject and the application in CS. I mean.. we program the stuff not solve by hand. Statistics was another issue. I asked my professor if I can turn assignments in Python but we had to use the Ti-84 which I never owned in college
@@tom901ful we had to take Calc 2 before our class where we learned about Big O notation. Seeing integrals in the textbook suddenly made Calc more interesting, but since it was taught with no practical application it left a bad taste
I failed maths so many times because of my teacher, then I got a good teacher and I got 86% subject score and actually understood a ton of the material.
The value of pseudo-code is you learn to reason logically. After that, the specific language isn't as important. You UNDERSTAND the logic, the steps, the patterns, below that.
@@Aurora-bv1ys you think I'm going to run some DFT calculations without knowing what they do and what each computation means? Not at all. If you don't understand the meaning of each line of code in the things you make or the things you use, you're not handling your code correctly. It's a dated way of approaching computational work, but it has stuck around for good reason.
Spending hours on math problems without dedicating time to programming tasks is not a good way to become a software engineer. However, focusing heavily on both can easily provoke burnout.
The process is, requirements lead to a high level design when outputs pseudocode and high level objects. This is then implemented as the low level details. If a problem if found during implementation, you go back to the design to see if they represent the requirements or if the requirements are not sound. Then you determine if the implementation can be traced to statements and structures in the design. I have an mscs degree. What I noticed in the computer labs at school is that many students immediately started writing code. I think this was because there were afraid they were not going to finish the project. The process I learned in school I still do today.
IMHO mathematical thinking is core to establishing / understanding the correctness of a program. We don't have to go as far as formally proving everything but familiarity with how such proofs work and common "idioms" like induction and invariants can go a LONG way. When discussing code with other software engineers...even if they really know their programming language well, that only helps clarify what the code is doing, but only some engineers are able to communicate effectively about why their code is correct. I'm just guessing but I suppose this is correlated with how comfortable they are with mathematical thinking.
Unfortunately, I have been asked to do things in a bespoke, cloud-based CRM. So I am building a dashboard and reports for it. I clustered the so-called opportunities in sets of (2^x)*100, only to find that there is no negative number space in this thing. All negative numbers are grouped in the bottom cluster.
I love how the myth continues. "Do I need to know math to code?" -> "Well it depends." No it does not depend. Programming and math are very intertwined. Learn actual modern CSS and try to do something cool and fun in it using nothing more than HTML and CSS and come back and tell me you weren't using a combination of Arithmetic, Algebra, Geometry, and Trigonometry. The fact that the myth that math is not necessary is used to beat around the fact that most people are just not interested in math and telling them that math is needed sparks all sorts of immediate issues. This adversity towards math needs to end. It's just as important as grammar, biology, chemistry, or anything else. It all uses math in one way or another. Math is one of the major pillars of all science. Without it, you'll be lost.
Agreed. We also need to read more fundemantal (math) papers. The more I learn about old papers, the more I'm amazed at how advanced the math already was in the 60s-70s. It was simply the hardware that was lagging (even though that improved by leaps and bounds as well over the years). I've read the original paper describing the Relational Model. The foundation of the relational database, and by doing so, I now more deeply understand SQL. I am now less confused by data manipulations and I wish the same for other devs as well.
I don’t necessarily disagree with Turing, but I think how urgent the need to know it upfront depends on what you are coding. With the way HR departments are nowadays, they will look at this and start requiring people have taken calculus two for Junior level positions Mathematical thinking can be learned on the job even. And from talking from my many tech grey beard friends, they used to know that
100% programmers need to understand more math. I hate all the r/Programming and r/learnprogramming post of users saying "why I'm learning DSA at uni instead of React?"
Explain then why DSA is more important for people trying to get jobs than just learning react. There are infinite programming concepts that won't help you to get paid.
If you have solid principles you can learn React (or basically any other library/language) in 1/2 weeks, if you just know React, you just know React. To be clear I’m not against it, for a lot of jobs it is enough, but if you want this type of education you can just attend a bootcamp
@@lobiqpidol818 learning complex/deep CS concepts is hard, learning react is easy and doesn't require a professor or loads of resources to learn. I would want a refund if a university was teaching me web and app frameworks
@@lobiqpidol818I had a friend that "knew Python" but he didn't have a formal STEM background, he was flabbergasted by the most basic algorithms/solutions required in a real project, his code was honestly repulsive. Any mentally competent person can realize why structured and logical thinking, abstraction, and analysis (this is all math) is crucial for any task that requires you to think, it's dumbfounding when people ask why. You can learn any library/framework in a couple of weeks when you are smart enough. Maybe this is more of a discussion on why people on the USA need to go into life-crippling debt to get a degree which leaves them feeling unsatisfied when they can't get a job, but honestly, you are basically asking "why is it important that I think" 😢 Mathematical thinking is absolutely fundamental for any intelectual endeavor, it's as simple as that.
i agree with you. last year, i reviewed some mathematical courses like calculus, linear algebra, probability, statistics . and i found those maths are very useful when i want to shift to machine learning and computer graphics .
More Math is fine and good but unfortunately universities do not to teach it with an emphasis on computation and implementation and the theory is too much far away from the practice, They should mix the theory with the practice from the start, And yes I agree… For WebDev no need for math at all, The most math heavy field in my opinion is GameDev. Also there is some newer cool programming languages with cool paradigms such as Proof Oriented Programming (F*, ATS, Lean4 and others) which I hope will further help mixing the theory with the practice and blurring the line between them
i have good understanding of programming fundamentals specifically with python, and i wanna dive into ML and data science, should i start learning Math??
I read some papers from Leslie Lamport and I think programmers should read them too, at least to get acquinted with principles of distributed computing. But I am not sure if he is familiar with the everday challanges of 95% programmers. Besides, he is working at Microsoft where quality comes after other priorities, maybe his comment was aimed at his fellow programmers at MS?
the problem sometimes is that math is more rigid than code , yeah if you are writing a sorting algorithm or a ray tracer or something math is very much needed but most of the time it's more valuable to have code that can be quickly changed also you don't know how correct your math is until you write your code
Yeah, quite a bit. 😉 I'm an Agda fan myself, but I also think that dependently-typed programming is still far from its final form. A few transformations need to happen before it can realize its full potential. Maybe ATS was an attempt of a step in the right direction, but an unsuccessful attempt.
Program machine code on a commodore 64 with data statements... Try that without writing out what you're trying to do first, that is what I've stuck with since I was a kid...
Isnt this what we do basically do in dsa? Writing pseudocode, analysing algorithmic complexity, seeing if it works with given constraints and then implementing it?
I highly recommend you learn to mathematically solve your problems. Because if you provide a proven piece of math to an LLM it can print you out any code sub second. But if your prompting is sloppy even the best LLM can't understand what the heck you are up to. When i look at the monstrosity of a modern age browser just to display me view lines of text, an image or a video i sure wish people in that field would grind there minds more so my CPU would have to grind less.
Knuth made TeX, the Turing-complete language and its virtual machine. What we know today as LaTeX, is like an "operating system" for this virtual machine, written in TeX. That was what Lamport created. TeX knows how to draw symbols, words, and mathematical notation. LaTeX lets you talk about "document classes", "chapters", "tables", "references", and more.
i never understood the point of pseudocode. and i still don't. if i write low level pseudocode, i might as well write real code. if it's high level, how does it help to write "def solve(problem)"?
My biggest error was not getting a dual BS (CS & Math) rather than a CS with minors in math and business. For a master's, I could/should have gotten an MS in math rather than yet another CS program.
I agree with the premise: We all need more math, especially those people that implement systems based on them but a small quick neurotic caveat only 15 seconds in. LaTex is Donald Knuth's project. Not Lesse Lamort even though he too would agree with the premise and should sell more of his legendary programming bibles (The Art of Computer Programming by Don Knuth). Ok watching through this I should redact but I won't ... I was wrong and he (Lesse Lamort) did work on Tex and put the La in LaTex.
As someone who work with and manage software developers, math is the difference between a good and a great dev. Ok, I work in industrial robotics, so the linear algebra, trigonometry, and the likes are pretty common. I don't know many ppl who learned calculus without being forced to do so in school.
Yes, I have dropped out of what is basically college because I got 5/10 in math and had to be left one year behind and said "fck this I can't do more of this nonsense". But now, I have invented (probably invented because I haven't found other examples) an interesting data structure, and I had to do some pretty interesting math to make it work. I initially thought of it as a kind of linked list, but I program in javascript and it would innately just take waay too much memory. I just recently understood what math I neeed for a very juicy abstrction that will make it better than 2d arrays and at the same time much better than a linked list could ever be, because I don't have to traverse anything, it's just math.
Literally everyone could benefit from learning more math and mathematical thinking. The way schools teach math ruins it for everyone in a way nothing else could.
math is the fundamental of computer science.Especially old days,nowadays we tend to meet such script kiddies that are clueless about math and claims that programmers don't need math.Logic is already math,softwares like 3d graphic,simulation,dsp,cgi in general need a advanced level of math of course.
I say this as a math major who’s a professional programmer. You need a lot less math than you think, especially if you’re going to be a web developer. Learning Big-O notation is important. If you study SQL and Typescript you’ll pick up enough set theory to get by. Beyond that I wouldn’t sweat it. Just focus on well thought out maintainable code.
I think I it’s true… in my current program the math only goes up to linear algebra and discrete math after taking only two calculus classes… I think we should have the whole math sequence from college algebra to differential equations. Not because I feel I need it but because problem solving and math maturity enough to tackle complex problems should be the foundation I want to have. After all CS is applied math. Still the CS degree is hard as it is especially at the junior and senior level. But I feel it should be more math intensive than it already is. Kinda like computer engineering… doesn’t matter if you never use it… what matters is that we reach a level of thinking and problem solving that makes everything a little bit easier.
Ok so I originally read that as "meth" in the title, so obviously I had to know. A bit disappointing honestly, but in hindsight this makes a whole lot more sense...
I don't really think that's a useful starting point. Modeling a software program using category theory seems a bit overkill. There are things like UML and ERD that are more accessible to developers, and better at displaying more explicit properties, which Is very important. If you're designing algorithms, or doing functional programming, then I would suggest it however.
Sir I just want to ask you about I am leaned Java but I have no idea what is spring Framework but still I am learning spring boot Can you help or anyone
Programmers vs coders; so many people believe they are the same. Is a SWE the same as a coder. The basic math you need is discrete mathematics. That is the basic logic of programming.
I don't want to hurt his feeling but software development is often called software engineering for a good reason y we use math as all engineers but usually we don't invent formulas. I think I have a good basic understanding of math but what I saw on university level on the peak math for software dev 99% failed because it included for Hoar and full induction proof you need know how to write a proof as well for this a wide knowledge of formulas the whole mathematical background is missing . I don't want to go into much details but I also done some AI stuff where I swear math prof would scream what that this even mean(mathematically) ? Me : I just wing it and it works...
As a statistician watching software engineers build ML/AI solutions with easy to develop tools like OpenAI, I strongly believe software engineers in the US need more math 😂
Allow me to clarify one thing, I said "... he [Leslie Lamport] is the one stating programmers need more math" but this is inaccurate. Leslie Lamport never said that. He is advocating for mathematical thinking and to broaden familiarity of logical operations since many programmers are intimidated by them even though they are no more complex than "two plus two equals four", just less familiar.
What I intended was to use the hook to say "programmers need more math according to Leslie Lamport", then segue into saying "well actually, what he was really saying is programmers need more mathematical thinking." But in doing so, I made a false statement. So just wanted to clear that up.
i think basic mat like: +, -, * is at needed as a beginner to understand coding when you start out. But if you wanna develope better like in machine learning math can help you to know what is going on and understand calculatios better. i always try to make before i start learn to code to try a little math before coding.
I think you should pin this.
A massive oversight imo given how vapid most viewers are, although somewhat (viewers to fewer readers) compensated with this errata.
Why is this vid up when the thumbnail and first minute is completely misleading.
Thanks for the clarifying comment but I think YT is already plagued with a lack of nuance and misquotes.
The main subject of the video is really interesting, It's the same as Why physicists need mathematics, But I don't think that computer science is a subfield of mathematics, I think mathematics is a tool computer scientist use to describe Theory and logic, But still mathematics remain a tool, It's like learning electronics or computer architecture we need to understand them to program them, Which mean they are a tool for us to apply what we learn, So mathematics is the language we use to describe theory, But that doesn't mean Theory is a part of mathematics, This is my view point Thanks for the video.
As someone who spent lots of hours studying math, I may say that the only way to fully acquire mathematical thinking is by learning math in the "hard way". Nothing teaches you more than some hours of frustration to understand a simple example.
Agree, but how would you say learning math the "hard way" is ? Does it mean studying for a long amount of time consistently each day.
@@vorladeththepphavongsa9029 its the same for programming , its just most people these days use chatgpt or forums with understanding what theyre copying .
@@vorladeththepphavongsa9029 It's less about solving math equations themselves and more... understanding the process of solving an equation (and the order of operations for solving an equation). And long study sessions don't really work unless you're really engrossed in the work, too.
"The Hard Way" is learning concepts from the ground up, that way you gain an intuitive understanding of the problem's building blocks. You may not be able to solve an equation or problem immediately, so you go back and build the understanding up until you reach that equation. The more equations you solve, the faster you'll get at this.
Math outcomes (and most logical pursuits) have been way too obsessed with end results, issues be damned. It leads to unnecessary bloat and difficulty down the road.
that way of learning math made me hate it
Yup, it's called mathematically maturity.
It would help many many people if they spent some time learning proofs in and out
Just doing math teaches you how to organize and structure systems of logic. So even if you’re not necessarily solving equations (or whatever you think “math” is), it fundamentally changes the way you approach a problem.
As a mathematician who codes a lot, I found I often write better code than the actual CS majors, largely because of all the time I’ve spent organizing mathematical arguments on paper. There is something to be said about mathematicians who don’t invest in learning to code well too tho.
Did you mean self-taught software developers? Or maybe developers with a business focused IT degree?
A Bachelor of Science CS degree from a reputable university requires a lot of math.
@@DemPilafian a CS degree even from a disreputable requires a lot of math. It's not up to the university. The syllabus is quite standardised.
DemPilafianYes but a math degree from the same university requires yet even more rigorous math
@@madallas_mons That's mostly irrelevant. A CS degree requires so much math that a CS grad is generally assured to be good at math. Obviously there will be some exceptions.
I once worked with a software developer who had a math degree yet couldn't mentally calculate the 15% tip when our group would go out for lunch.
@@DemPilafian Most mathematicians are bad at arithmetic. Fast calculation is a skill that needs to be maintained and most people lose it when they learn higher math. I was much faster at it when I was 12 than I am now at 23. All you need in terms speed for higher math is fast algebra
He's absolutely right, I have an engineering degree and I've been working as a software engineer for about two and a half years, but the more serious I get about this, the more I realize the importance of abstraction and formality, giving a small example, I can solve difficult LeetCode problems with my trained logic, but sometimes I do it by intuition and God help me come up with the proof of correctness for the algorithm, I believe I'm good at programming because I'm decent at mathematical thinking (although I don't really know much), for me, the base of all we do is abstraction, logic, and analysis, which math does formally. I'm doing good in my career, but as I realize this, I've gotten to the point in which I firmly believe I need to go back to a formal training in math (maybe another degree), because most of what we do is simple practical mathematics.
how do we know one is good at mathematical thinking?
I think what he's actually trying to say while being diplomatic is that software has become overengineered and unnecessarily complex.
Bloatware, baby!
It may be overengineered and unnecessarily complex but it is nevertheless complex.
Bold claim, which insinuates there is a way to create software in a simpler way. I would like to hear how if we are to believe this claim.
@@gandhisFlipFlops I mean, it's well established that you can make software more time and space efficient. And with a good understanding of math some simulations become constant.
@@gandhisFlipFlops By your logic, you're insinuating that it can't be done.
Truth, I am so tired of people pretending that math is useless in programming.
Structured and logical thinking, abstraction, and analysis (math) are useful for anything that requires you to think, it takes a very ignorant/dumb person not to realize this. But well, "common" sense and logical thinking don't actually seem to be that common among people
Maths is the subject that creeps its way into almost everything whether one would like it or not... I dunno why people hate on it 🤷♂️
It’s not useless, but its usefulness is debatable. Architectural patterns, microservice design, meta programming, UIUX, devops, infosec, product etc have very little maths involved. If you’re a student, sure you’ll learn your algorithms. But the longer you work in software engineering the less important maths becomes
@@bonquaviusdingle5720 Everything you wrote has to do with maths, more or less. Often time understanding of proof writing, formal logic, statistics etc is what makes a difference between average developer and great developer.
The reason why we don't care about maths in programming is that we have gone through massive boom, or shall I say two massive booms.
First one being massive demands for software, and second being massive hardware gains.
But those booms are coming to an end, and with them there will be more and more emphasis on programmers being able to deliver their paid value.
Because of that my prediction is people who understand how computer works, and can deliver actual good performance while leveraging modern abstractions like ADTs. Will be the ones who remain well paid. The rest will have to accept pay cuts.
Gone will be the days where "developer time" were the biggest expense, and CRUD apps were in massive demand.
And we have massive over-saturation of developers who lack understanding of algorithms, and rely on glued premade solutions.
@@bonquaviusdingle5720cap
I can testify to this. As someone who barely got math in highschool and teached herself programming first. I was able to program (and even on paper figured out some things that turned out to be basic mathemathical statements myself way before learning about them) to then suddenly having revelation after revelation when i did start to properly study math. That improved my programming and understanding of what was going on so much and solved many issues i had before when just trying to do it without some basic math skills. This turned into me going to university for physics and i can say the way i learned to think still helps me today as a developer more than the college for applied information technologies ever did.
i read that as "programmers need more meth" and now i'm disappointed that it wasn't the title
I read it as that, then saw math in the thumbnail, and now im startled as to how I saw meth so clearly in the title before
why not both?
Its like a difference between a guitarist and a musician. All programmers code but not all coders program.
I am not someone who tons of experience with programming with latest and greatest programming languages and frameworks, but I concur with Lamport's opinions: writing the algorithm of solving a problem for typing it out in some language leads to fundamentally better programs in comparison to those which are just typed out and "hacked" together. Donald Knuth also promotes the use of mathematics to define problems and algorithms to solve them, and intersperse code chunks with commentary, making them easier to read. He calls this "literate programming". I am a big fan of this approach as it makes programming easier (though big codes can be difficult to maintain unless strict guidelines are there). Jupyter Notebooks is a pseudo-literate programming tool which is popular in experimental physics and data science. Just imagine, the whole source code of popular projects, say the Linux kernel, or ffmpeg, written in literate programming style, with a table of contents, index and hyperlinks telling a newbie where to look. It would be amazing!!
Like I said before in your video on Linux and history of Unix, nice video! Nice to the point, something which is rare these days.
Great video. I love this format of exploring topics on the intersect between software engineering and academics. When I was in school I thought it was all pointless. The more time I spend as a professional the more time I spend brushing up on math concepts that I really wish I would've nailed down when I was actually in school.
Ah yes, the holyTrinity of computers:
Hardware, Mathematical analysis, and dealing with requirements that have nothing to do with the high level goals of the organization without losing it
Leslie Lamport: my favorite Computer Scientist.
Math is the bridge between average developer and 10x developer
How so?
I think a better approach is to learn the basics of logic, formal logic and to practice critical thinking, something i did before i took an interest to programming. These two fields complement each other very well. But learning math can also help in broadening your ability to think abstractly and tackle programming problems.
I completely agree with this. I have a degree in both computer science and pure mathematics . Breaking down complex software engineering problems in smaller less complicated ones is the same logic we used to prove complex theorems and solve complicated problems in maths . In first year of university we only wrote pseudo code to write algorithms , the focus was on solving the problem not the language syntax .
That's an impressive resume. I have a question for you (if you don't mind). I'm building a website which will take in a huge amount of text-based data and store it into a back-end db. Would you recommend adding a sorting function prior to a search function for querying? What I don't want are huge delays as it's written in Python anyway. If you don't want to respond, no worries. If you do, thank you very much!
I couldn't tell you how many times I've had to revise or throw out plans. I understand where Lamport is coming from, when I worked on control systems and distributed systems, most of my time was spent planning + testing + verifying but if you're working on complete applications the sheer bulk of code makes insuring correctness ahead of time very difficult. Formally specified UI would be cool I guess but you'll have to 3x your dev time to do it well, good luck getting stakeholders on board with that.
My personal problem was in college they taught all this math in CS without direct application to CS itself.
Maybe it was just my university
Just yours? I would say this happens on 95% of colleges.
@@paulsingh11 teaching standards are very low this is the real problem. When simple boolean operations are taught in the most painful and distasteful way possible there is nothing you can do to incorporate more stuff and get a good result
It’s a shame.
Honestly, looking back I think I wasted more time with the annoying algebra reducing in math than the actual subject and the application in CS. I mean.. we program the stuff not solve by hand.
Statistics was another issue. I asked my professor if I can turn assignments in Python but we had to use the Ti-84 which I never owned in college
@@tom901ful we had to take Calc 2 before our class where we learned about Big O notation.
Seeing integrals in the textbook suddenly made Calc more interesting, but since it was taught with no practical application it left a bad taste
@@paulsingh11 the price of modern calculators is a crime
I failed maths so many times because of my teacher, then I got a good teacher and I got 86% subject score and actually understood a ton of the material.
The value of pseudo-code is you learn to reason logically. After that, the specific language isn't as important. You UNDERSTAND the logic, the steps, the patterns, below that.
4:35 there is no dot cache or dot distribute unless you write it yourself.
I'm biased on this one. A good portion of my work revolves around computational chemistry and physics, so I HAVE to be good at math for the work I do.
Chemistry?
@@Aurora-bv1ys you think I'm going to run some DFT calculations without knowing what they do and what each computation means? Not at all. If you don't understand the meaning of each line of code in the things you make or the things you use, you're not handling your code correctly. It's a dated way of approaching computational work, but it has stuck around for good reason.
Dream job. I wish I Was able to earn money doing computational mathematics
Spending hours on math problems without dedicating time to programming tasks is not a good way to become a software engineer. However, focusing heavily on both can easily provoke burnout.
Mathematics helps to find and analyze the computational complexity of Algorithms.
The process is, requirements lead to a high level design when outputs pseudocode and high level objects. This is then implemented as the low level details. If a problem if found during implementation, you go back to the design to see if they represent the requirements or if the requirements are not sound. Then you determine if the implementation can be traced to statements and structures in the design. I have an mscs degree. What I noticed in the computer labs at school is that many students immediately started writing code. I think this was because there were afraid they were not going to finish the project. The process I learned in school I still do today.
Interesting topic to bring up. I like it when I am given new perspectives and topic to think and learn about, subbed 👍
IMHO mathematical thinking is core to establishing / understanding the correctness of a program. We don't have to go as far as formally proving everything but familiarity with how such proofs work and common "idioms" like induction and invariants can go a LONG way.
When discussing code with other software engineers...even if they really know their programming language well, that only helps clarify what the code is doing, but only some engineers are able to communicate effectively about why their code is correct. I'm just guessing but I suppose this is correlated with how comfortable they are with mathematical thinking.
Working hours on math problems without hours on programming tasks is not a good way to become a software engineer
Unfortunately, I have been asked to do things in a bespoke, cloud-based CRM. So I am building a dashboard and reports for it. I clustered the so-called opportunities in sets of (2^x)*100, only to find that there is no negative number space in this thing. All negative numbers are grouped in the bottom cluster.
In the golden era of computer science was rampant with math majors in the haydays of yesterday
I love how the myth continues. "Do I need to know math to code?" -> "Well it depends." No it does not depend. Programming and math are very intertwined. Learn actual modern CSS and try to do something cool and fun in it using nothing more than HTML and CSS and come back and tell me you weren't using a combination of Arithmetic, Algebra, Geometry, and Trigonometry. The fact that the myth that math is not necessary is used to beat around the fact that most people are just not interested in math and telling them that math is needed sparks all sorts of immediate issues. This adversity towards math needs to end. It's just as important as grammar, biology, chemistry, or anything else. It all uses math in one way or another. Math is one of the major pillars of all science. Without it, you'll be lost.
I agree with what you said. I stand by your stance on this topic :)
Agreed. We also need to read more fundemantal (math) papers. The more I learn about old papers, the more I'm amazed at how advanced the math already was in the 60s-70s. It was simply the hardware that was lagging (even though that improved by leaps and bounds as well over the years).
I've read the original paper describing the Relational Model. The foundation of the relational database, and by doing so, I now more deeply understand SQL. I am now less confused by data manipulations and I wish the same for other devs as well.
I don’t necessarily disagree with Turing, but I think how urgent the need to know it upfront depends on what you are coding.
With the way HR departments are nowadays, they will look at this and start requiring people have taken calculus two for Junior level positions
Mathematical thinking can be learned on the job even. And from talking from my many tech grey beard friends, they used to know that
Did you leave the link to those articles? I'm not seeing them.
I don’t think I agree with this for the average developer. But at the top end, and e.g for language creators, then yes.
100% programmers need to understand more math. I hate all the r/Programming and r/learnprogramming post of users saying "why I'm learning DSA at uni instead of React?"
Explain then why DSA is more important for people trying to get jobs than just learning react. There are infinite programming concepts that won't help you to get paid.
If you have solid principles you can learn React (or basically any other library/language) in 1/2 weeks, if you just know React, you just know React. To be clear I’m not against it, for a lot of jobs it is enough, but if you want this type of education you can just attend a bootcamp
@@lobiqpidol818 learning complex/deep CS concepts is hard, learning react is easy and doesn't require a professor or loads of resources to learn. I would want a refund if a university was teaching me web and app frameworks
@@lobiqpidol818I had a friend that "knew Python" but he didn't have a formal STEM background, he was flabbergasted by the most basic algorithms/solutions required in a real project, his code was honestly repulsive. Any mentally competent person can realize why structured and logical thinking, abstraction, and analysis (this is all math) is crucial for any task that requires you to think, it's dumbfounding when people ask why. You can learn any library/framework in a couple of weeks when you are smart enough.
Maybe this is more of a discussion on why people on the USA need to go into life-crippling debt to get a degree which leaves them feeling unsatisfied when they can't get a job, but honestly, you are basically asking "why is it important that I think" 😢
Mathematical thinking is absolutely fundamental for any intelectual endeavor, it's as simple as that.
@@Janoww in 1/2 week 😂, really things are that easy ?😂
i agree with you. last year, i reviewed some mathematical courses like calculus, linear algebra, probability, statistics . and i found those maths are very useful when i want to shift to machine learning and computer graphics .
More Math is fine and good but unfortunately universities do not to teach it with an emphasis on computation and implementation and the theory is too much far away from the practice, They should mix the theory with the practice from the start, And yes I agree… For WebDev no need for math at all, The most math heavy field in my opinion is GameDev. Also there is some newer cool programming languages with cool paradigms such as Proof Oriented Programming (F*, ATS, Lean4 and others) which I hope will further help mixing the theory with the practice and blurring the line between them
i have good understanding of programming fundamentals specifically with python, and i wanna dive into ML and data science, should i start learning Math??
Yes. ML and data science are very math heavy
Linear algebra, stats and Calculus. Coursera should be a good Startin point for these 3. You can do this🎉
no, learn Klingon instead, you'll become very good at ML and data science with this alone
yeah , you need a lot of math there
Math is the most important skill in ML.
I read some papers from Leslie Lamport and I think programmers should read them too, at least to get acquinted with principles of distributed computing. But I am not sure if he is familiar with the everday challanges of 95% programmers. Besides, he is working at Microsoft where quality comes after other priorities, maybe his comment was aimed at his fellow programmers at MS?
This may be a very weak question. Where could I find all of the math that I would need to know?
Khan academy
the problem sometimes is that math is more rigid than code , yeah if you are writing a sorting algorithm or a ray tracer or something math is very much needed but most of the time it's more valuable to have code that can be quickly changed
also you don't know how correct your math is until you write your code
Do a video about the job market pls
I program in Coq, I guess I need a bit of math :')
Yeah, quite a bit. 😉
I'm an Agda fan myself, but I also think that dependently-typed programming is still far from its final form. A few transformations need to happen before it can realize its full potential. Maybe ATS was an attempt of a step in the right direction, but an unsuccessful attempt.
What they need is less time on youtube.
"Algorithm" may refer to that function's internal you wrote doing all kinds of crud, filtering and logical branching.
Appreciate this line of thought, but I majored in math and I think that it is a fundamentally different domain.
Am learning c++ but weak in math should i focus on math first 💁♂️
just focus on building really good projects. (almost) everything else will fall into place.
No
Program machine code on a commodore 64 with data statements...
Try that without writing out what you're trying to do first, that is what I've stuck with since I was a kid...
Computer Science initially derived as a branch of math!
whats your keyboard? looks really nice
Isnt this what we do basically do in dsa? Writing pseudocode, analysing algorithmic complexity, seeing if it works with given constraints and then implementing it?
Finally someone made a video on Leslie
I really like this video thank you
clear explanation of your point, direct and useful
completely agree with your point. i just wish i could tell you why exactly
100% agree, but investors dont care... just get some sh*t out to sell
I highly recommend you learn to mathematically solve your problems. Because if you provide a proven piece of math to an LLM it can print you out any code sub second. But if your prompting is sloppy even the best LLM can't understand what the heck you are up to.
When i look at the monstrosity of a modern age browser just to display me view lines of text, an image or a video i sure wish people in that field would grind there minds more so my CPU would have to grind less.
Knuth developed Latex.
Knuth made TeX, the Turing-complete language and its virtual machine.
What we know today as LaTeX, is like an "operating system" for this virtual machine, written in TeX. That was what Lamport created.
TeX knows how to draw symbols, words, and mathematical notation. LaTeX lets you talk about "document classes", "chapters", "tables", "references", and more.
i never understood the point of pseudocode.
and i still don't. if i write low level pseudocode, i might as well write real code. if it's high level, how does it help to write "def solve(problem)"?
I really hate math in coding, even though I know I should consider getting better...
Same
Programmers need more category theory
My biggest error was not getting a dual BS (CS & Math) rather than a CS with minors in math and business. For a master's, I could/should have gotten an MS in math rather than yet another CS program.
I've always found it a shame that Americans only have one math, here in the UK we have lots.
Grace Hopper was a Math PHD
I agree with the premise: We all need more math, especially those people that implement systems based on them but a small quick neurotic caveat only 15 seconds in. LaTex is Donald Knuth's project. Not Lesse Lamort even though he too would agree with the premise and should sell more of his legendary programming bibles (The Art of Computer Programming by Don Knuth). Ok watching through this I should redact but I won't ... I was wrong and he (Lesse Lamort) did work on Tex and put the La in LaTex.
Linear algebra and calculus are the ‘basics’ the question is, do you know more?
As someone who work with and manage software developers, math is the difference between a good and a great dev.
Ok, I work in industrial robotics, so the linear algebra, trigonometry, and the likes are pretty common.
I don't know many ppl who learned calculus without being forced to do so in school.
You didn't leave the links below ;c
Yeah I don't think it's the math per se that helps but the thinking around it. It's doable for sure to program without using advanced math but harder
I always start with psuedo code logic. My scripts start as a bunch of comments, then I implement each.
Yes, I have dropped out of what is basically college because I got 5/10 in math and had to be left one year behind and said "fck this I can't do more of this nonsense".
But now, I have invented (probably invented because I haven't found other examples) an interesting data structure, and I had to do some pretty interesting math to make it work. I initially thought of it as a kind of linked list, but I program in javascript and it would innately just take waay too much memory. I just recently understood what math I neeed for a very juicy abstrction that will make it better than 2d arrays and at the same time much better than a linked list could ever be, because I don't have to traverse anything, it's just math.
Programmer need more problem solving, and math is pure problem solving
Literally everyone could benefit from learning more math and mathematical thinking. The way schools teach math ruins it for everyone in a way nothing else could.
Are mathematicians good coders?
I have to saw for DSA (data structures and algorithms) problems math is invaluable.
Definitely food for thought
math is the fundamental of computer science.Especially old days,nowadays we tend to meet such script kiddies that are clueless about math and claims that programmers don't need math.Logic is already math,softwares like 3d graphic,simulation,dsp,cgi in general need a advanced level of math of course.
Came for the content, stayed for the Mustache
Cant paint all programming under the same brush. Some need math, some will be extremely successful selling CRUD.
I say this as a math major who’s a professional programmer. You need a lot less math than you think, especially if you’re going to be a web developer.
Learning Big-O notation is important. If you study SQL and Typescript you’ll pick up enough set theory to get by. Beyond that I wouldn’t sweat it. Just focus on well thought out maintainable code.
I think I it’s true… in my current program the math only goes up to linear algebra and discrete math after taking only two calculus classes… I think we should have the whole math sequence from college algebra to differential equations. Not because I feel I need it but because problem solving and math maturity enough to tackle complex problems should be the foundation I want to have. After all CS is applied math. Still the CS degree is hard as it is especially at the junior and senior level. But I feel it should be more math intensive than it already is. Kinda like computer engineering… doesn’t matter if you never use it… what matters is that we reach a level of thinking and problem solving that makes everything a little bit easier.
True, but a small margin tends to think mathematically/ Most of them are on the spectrum.
Ok so I originally read that as "meth" in the title, so obviously I had to know.
A bit disappointing honestly, but in hindsight this makes a whole lot more sense...
Programming is solving Problems
Mathematics is Problem solving.
I'm just gonna say start with category theory. Modeling software is going to be the biggest challenge and CT is the best tool we have right now.
I don't really think that's a useful starting point. Modeling a software program using category theory seems a bit overkill. There are things like UML and ERD that are more accessible to developers, and better at displaying more explicit properties, which Is very important.
If you're designing algorithms, or doing functional programming, then I would suggest it however.
And then "don't learn to code " 😂
But not many programming languages can present mathematical expressions nicely
Sir I just want to ask you about I am leaned Java but I have no idea what is spring Framework but still I am learning spring boot
Can you help or anyone
Programming is mathematical inductions in a way
Games and graphics needs a ton of math
Absolutely Agree
Programmers vs coders; so many people believe they are the same. Is a SWE the same as a coder.
The basic math you need is discrete mathematics. That is the basic logic of programming.
I don't want to hurt his feeling but software development is often called software engineering for a good reason y we use math as all engineers but usually we don't invent formulas. I think I have a good basic understanding of math but what I saw on university level on the peak math for software dev 99% failed because it included for Hoar and full induction proof you need know how to write a proof as well for this a wide knowledge of formulas the whole mathematical background is missing . I don't want to go into much details but I also done some AI stuff where I swear math prof would scream what that this even mean(mathematically) ? Me : I just wing it and it works...
Yes i agree maths gelp with problem solving and general life
Dyslexic and tired… read this as “Meth”… I’ll take a nap and come back.
What you said is totally true, however, I think doing math is important to get and improve your analytical thinking.
@@FranciscoZapata-s2f YES! Obviously, it's exercising your logic, abstraction and analysis skills, how people don't realize this is beyond me.
As a statistician watching software engineers build ML/AI solutions with easy to develop tools like OpenAI, I strongly believe software engineers in the US need more math 😂
“Programmers Need More Meth”
Not even high level mathy things, if u don't know DSA idk how u could call urself software "engineer". Layman programmer, maybe.
Language is math if you use it proper.