Anyone Can Be a Math Person Once They Know the Best Learning Techniques | Po-Shen Loh | Big Think
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- เผยแพร่เมื่อ 9 ก.พ. 2025
- Anyone Can Be a Math Person Once They Know the Best Learning Techniques
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Po-Shen Loh is a Hertz Foundation Fellow and Carnegie Mellon mathematics professor who thinks that history is a much harder subject than math. Do you agree? Well, your position on that might change before and after this video. Loh illuminates the invisible ladders within the world of math, and shows that it isn't about memorizing formulas-it's about processing reason and logic. With the support of the Fannie and John Hertz Foundation, Po-Shen Loh pursued a PhD in combinatorics at the Pure Math Department at Princeton University.
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PO-SHEN LOH:
Po-Shen Loh, PhD, is associate professor of mathematics at Carnegie Mellon University, which he joined, in 2010, as an assistant professor in the Department of Mathematical Sciences. As a Hertz Fellow, Professor Loh received his PhD in combinatorics of the Pure Math Department at Princeton University. His thesis discussed several original results that he discovered during his graduate study in joint projects with his advisor and other collaborators. Professor Loh studies questions that lie at the intersection of two branches of mathematics: combinatorics (the study of discrete systems) and probability theory.
Prior to his work at Princeton, Loh received the equivalent of a master's degree in mathematics from the University of Cambridge (United Kingdom) in 2005, where he was supported by a Winston Churchill Foundation Scholarship. He received his undergraduate degree in mathematics from Caltech in 2004, graduating first in his class, and his undergraduate thesis later received the Honorable Mention for the 2004 AMS-MAA-SIAM Morgan Prize.
In his spare time, Loh has maintained his involvement with the United States Mathematical Olympiad program. He is now the head coach of the national delegation, as well as a lead fundraiser for the organization. As a high school student, he won a silver medal at the 1999 International Mathematical Olympiad (IMO), and following his win continued to be active in the training of high school students at the U.S. national Math Olympiad Summer Program. In 2004, he served as the deputy leader for the U.S. team at the IMO in Athens, Greece, where our national team placed second. After completing his PhD, Loh again, served as deputy team leader for the United States at the International Mathematical Olympiad from 2010 to 2013. Afterwards Professor Loh was promoted to national head coach of the U.S.A. IMO team, and on his second attempt, Team U.S.A. won first place, in a competition with teams from over 100 countries represented.
Earlier this year, Loh received an NSF CAREER award, the most prestigious NSF award for junior faculty, which honors outstanding research combined with a commitment to teaching. Professor Loh is the founder of the educational technology startup expii.com, a crowd-sourced platform for the world to share interactive lessons in math and science.
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TRANSCRIPT:
Po-Shen Lo: I think that everyone in the world could be a math person if they wanted to. The keyword though, I want to say, is if they wanted to. That said, I do think that everyone in America could benefit from having that mathematical background in reasoning just to help everyone make very good decisions. And here I'm distinguishing already between math as people usually conceive of it, and decision making and analysis, which is actually what I think math is.
So, for example, I don't think that being a math person means that you can recite the formulas between the sines, cosines, tangents and to use logarithms and exponentials interchangeably. That's not necessarily what I think everyone should try to concentrate to understand. The main things to concentrate to understand are the mathematical principles of reasoning.
But let me go back to these sines, cosines and logarithms. Well actually they do have value. What they are is that they are ways to show you how these basic building blocks of reasoning can be used to deduce surprising things or difficult things. In some sense they're like the historical coverages of the triumphs of mathematics, so one cannot just talk abstractly about “yes let's talk about mathematical logic”, it's actually quite useful to have case studies or stories, which are these famous theorems.
Now, I actually think that these are accessible to everyone. I think that actually one reason mathematics is difficult to understand is actua...
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I failed math GCSE I on the other appreciate game theory, I think it needs in education to be treated as a separate subject within its teaching, that is more methodical that appreciates different learning styles.🤯🤯🤯
I really want to thank the team and all professors. I am from rural area and I am getting such a pure knowledge at my fingertip. I really from heart thank all of you. Please bring more knowledge on this. We will be very thankful
I agree history is more difficult than mathematics.
Absolutely sir I experience it
Would you please suggest what are those prerequisites are?
This is so true. When I was younger, I was so bad at maths until I got a teacher who sat down with me and started from scratch and fully explained and taught me what I didn't know. She saved my life because if I moved forward without a basic understanding of mathematical concepts, I would have continued to fail for the rest of my life
That is one good teacher!
You are so lucky....i wish if I also got such teacher
Absolute BS! There are PLENTY of people who haven't 'failed' in life who are bad at math. Who told you it was a life failure to struggle at math?
You have hit a great truth. A good teacher is key.
What are those basic concepts i need to know?
I like this argument. I was never good at math until I started taking my math classes online. I'm a slow note taker and it takes me a while to understand concepts, so in a traditional classroom setting I fall behind the curve really easy. But with online classes, I can rewind the lectures, pause them to catch up, and use multiple sources of learning to figure out a concept rather than just depending on the professors way of learning which may or may not work for me. There are some downsides to learning purely online, but in regards to math online for me, the benefits outweigh the costs.
khanacademy , coursera etc....youre welcome
I'm taking them at a local community college, but I use Kahn Academy or other math channels on youtube to figure things out/refresh my memory
Chris Wise I too use internet a lot to understand math, I find it much easier to sift through many sources and find the one I'm most comfortable with, than relying completely on lectures and my professor's notes
Chris Wise same here!
Chris Wise what program do u use??
I absolutely love how he's hyped about maths. You can literally see it in his eyes.
There is a professor in Oxford who once said that Maths is just another language we can understand the world through. It really changed my perspective about maths. It's not just about numbers and statistics and geometry and trigonometry, but rather it's a language. A language through which we can communicate with the universe itself.
that was really beautifully put.
What a beautiful answer i agree. And for math is the language of the universe,it is complete itself, Math is perfect. Some say we Invented math, i Say no we Discover Math.
@@Rejee-wq5om I will say the fundamental of math that is numbers are discovered. But the symbols and methods to do math are more likely invented.
I felt in love in Mathematics because i have practiced it excessively.
Per day 4-5 hrs of question solving made me so confident that my approach to solve questions is completely changed and became efficient
I'm learning Mathematics, any advices?
(Sorry for my bad English)
Has it shown positive effects? Jus asking.
I'm really bad at maths, and also I never practice it. I thought the difference might be in practicing or others....
@@lly_09 it's definitely practice and having the right mindset
Absolutely agree. I have been studying the likes of calculus and other stuff to prepare for physics because physics was interesting. I then just started loving the maths itself (still love physics but preparing using the maths made me love it more was my point)
Khan acadamy
I completely agree, I was getting under 50% in every maths test. I then was introduced to physics (maths with an apparent purpose). I approached maths with an I love it attitude for the next two years because I loved physics. I also ignored people saying "don't worry you did poorly, maths is hard." I stopped messing around in my free time and decided to learn maths to a point where I was average. my view of average increased as I got better. Now there is the dreaded b+ . This was simply due to a change in mind set, hard work and replacing peoples opinions with difficult goals. " if you don't sacrifice for what you want, what you want will be the sacrifice."
Preach!
anonymous john I hate physics but I love maths
who said the phrase in quotes?
Saint Frank L. No just curious
same for me but i got into programming so i wad forced to learn maths :d
math requires lots of practice and everyone gets better at various pace. At universities there isn't time for practice, topic are taught for a week and moved on to the next
He who must not be named
Yes but was rejected first by mankind and mathematical society for years before acceptance.
He who must not be named I agree with you, I had very less marks in Mathematical Physics, so much that if I show it to someone in my current field of research they will judge me to be incompetent, but currently I work in the field of Theoretical Physics. I had a lot of time after my M.Sc to cope and improve on my previous failures, what helped me was that I started working on a research project and understood a lot of intricacies and understood it works on just simple concepts related to Linear Algebra. On the way I learnt that Maths works a lot by intuition, there are infact books written by the greats like Hilbert's "Geometry and Imagination" which underlines the ideas which led him to innovate things like Hilbert Space etc.
I got my degree by starting at algebra in my college.
There is time to practice.
You may fail a few times but there is time if you study and forget about life.
Smith Smitherson '' FORGET ABOUT LIFE '' I CRY 😂 😂 😂 😂 😂 😂
Maths doesn't require practice
This is so true. My dad is basically a math genius and he explained to me that 'all smart mathematicians are not aware of the maths itself, but rather the *principles* of the maths'. Since then I have never failed a test.
Wow that's awesome.
Can you please elaborate on being aware of the principles of math?
@@PeppaTheCutestdid you find the answer for your question? I am also curious of what “understand the principles of math” means.
I was the worst in math but I needed to learn computer science. So I went on and started learning online from youtube khan academy etc and now I feel like a pro. From simple addition to integrals, probability and logic and It really opened my mind. My thinking process changed. I really recommend learning math. Its not just for school
Hey can you tell what you started with? Like for basic to get better?
@@devenderkhanna8517 I started from the basics. Addition multiplication negation and division. Just to warm up. Khan Academy provides a great roadmap just check the math section and start from the beginning because math is a chain. You will never understand second grade equations if you dont understand the simple ones. Or you will never understand derivatives if you first don't understand the slope of a line or even the very equation of a line. You need to keep consistent and determined. Good luck
How much time any did it took you to master till calculus
and nay tips, like note taking, practice sessions, any tips, it would be really helpful
I havent master calculus yet but my gameplan is to understand the concept very well and understand the relationships between them. Understanding relationships between mathematical concepts usually brings you "Ohhh, thats why" or "Damn bro this is incredible" moment
and only there, actually solving problem till it became automatic
same here, I am learning Machine Learning and it requires me to know calculus. I'm auditing a course on Coursera but i'll definitely check out Khan Academy.
I badly needed this since I'm bad at Mathematics that is why I'm starting to study the basics again. It's one of my dreams to be good at Math. Thank you for this inspiring video.
Same, we can do this!
Are you there yet??
Absolutely spot on. Math is pure reasoning and analysis, it always makes me laugh when people think that being good at math means being able to multiply insane numbers in your head in just seconds. People who can do things like that are certainly talented but there's a lot more to mathematics than ridiculous computations lol
Interesting how projection works. They think being good at math means being exceptionally good at where the hole in their tracks was, when in reality they just didn’t have that hole and kept moving forward.
Arithmetic is NOT maths but it is one of three areas especially in the early years. So competence & confidence are important in determining future performance. Fractions are a great area to reinforce previous learning and to refresh & relearn these skills but in a new way which can open up new insights about numbers. Finally a good grasp of arithmetic can provide a great foundation for algebra. Students are often taught the mechanics without understanding the why and this understanding should be encouraged. Today with computers students can draw down other explanations and then ways of testing their understanding. Key is encouraging curiosity & willingness to explore and play around with problems. We miss a great opportunity by not presenting mathematics alongside the footsteps of the mathematicians who first wrestled with these problems. A sense of history would go along way.
@@sharonjuniorchess wow you're absolutely right actually, we do this with physics, why not with math?, In physics it always helped me to understand these things deeply, I remember wondering about this too in high school
Kinda as long as you have accurate axioms but humans can get weird about that
Aaaaaaaaa
This dude is insane. He was educated in Caltech, Cambridge Part III and later Princeton, those are best schools for theoretical physics and maths in the world.
i see why he didn't have time to brush his teeth
Lmao!!!@@haritinasakova4327
@@haritinasakova4327dude.
What a wonderful breakdown! Thanks professor Loh
Thank u too sir
God commentent
thats loh
Oh my god you are there bprp
OMG..
BiG fan sir...💖💗💖❣from ..🇵🇰.
I Love the way you solve Calculus problems...😇💖❣.
Plz. Have some focus on "Probability and statistics"😥
YES, exactly I have been telling students that if they miss one concept they will miss part of the chain. If you miss the class on the quadratic equation there goes your whole understanding of what to do when the teacher ask simplify using the quadratic formula. Good to know professors are teaching that it is important not to miss math class. :)
0:23 Math and Decision Making
0:50 Reasoning/Logic
1:35 Chain of Deduction (miss a part, you can be lost)
3:18 Learn at your own pace
Hey, I like your way of structuring the things. I am not aware if you remembered the structure with conscious effort or not but, I found your way of thinking, given the fact I surmise about your thinking based on this comment, to be very similar to that if Bill Gates. Would be great if we can talk more! Share any of your social channels(if you are ok)
Dhanush Mendu ok boomer
In 1:35(the reson math makes me angry)
Thanks
I skipped the video to 1:35. I'm completely lost!
"if you miss one link in the chain, you will end up lost"
Yep. I know it first hand.
🤣 seconded
Thirded
Fourthed
One problem of the way that schools teach mathematics is that they focus too much on calculations and memorization of formulas and algorithms. Computers can do the calculations billions of times faster and they can store every single textbook you'll ever need. Schools should focus more on translating important, everyday problems into mathematics, the construction of mathematical proofs, and the ability to spot errors in arguments. They also should test students' abilities to intuitively explain their results. A simple 1 hr test doesn't allow enough time for thinking in order to show understanding.
nyx211
You should learn some usefull skills, if it includes math so be it, and learn that then.
if schools started teaching analysis rather than calculus no one will ever be interested in mathematics.
U are right according to me
instead geometry can i learn the laws of my country
You are absolutely right, agree 100%. I feel like this is my issue I have been encountering
I was always bad at math but I saw this video a year ago (around December 2022 and January 2023) and decided to challenge this belief of his that everyone is a math person. So I started learning math from scratch, I did take some breaks here and then but one year later I'm now on algebra and I'm SO much better at math that I ever was in school. And what's crazy is that I also enjoy doing it. So I can say he is right
please do tell where to start from is there resource that explain the concept behind math or what?
This is why I love math and computer science!! You can deduce a lot from knowledge you already have and figure it out yourself by using logic.
I was not really good at math throughout middle school and high school, but still made it into Engineering school. So to prepare myself for college, I was able to develop a study method to review all my deficiencies before the start. I learned that being put in an accelerated class in middle school may have resulted in me picking up those deficiencies. I really do agree with Po-Shen Loh, and by using these principles my math reasoning in my Mechanical Engineering courses has become a powerful beneficial tool. I am also taking my final math course, Differential Equations and happy to say I've become more of a math person.
May i ask, where can i start?
U can just telle more about how u started maybe i can get i hint of where i lost track of mathematical thinking..
It would be nice if schools could take this man's approach to learning math, and let students learn such a fundamental subject at their own pace.
Interesting, I came to a similar conclusion when I started delving into Advance maths and used Khan academy to catch up. It was amazing to see what I had a a weak grasp in and how, at my own pace, if could strengthen them.
Lead me to believe that math is simply a poorly structured subject in our school systems, rather than something nefarious.
same!!
Bro How can i join khan Academy to learn Math
I completely agree. I think he nailed down the problem exactly. The most upsetting thing for me, is that the link that most people seem to be missing in their mathematical thinking is somewhere around second grade. I TA for undergraduate math, and one of the difficulties I have noticed most often is that students have a poor understanding of fractions and ratios, which goes back to second grade. This is something I have noticed throughout my education at every level. Without an intuitive sense for fractions and ratios, higher level mathematics becomes just a manipulation game that is more akin to how a computer works than to real understanding.
I agree on individualized education. It would help for other subjects as well. It is especially helpful for students with special mental/ health/ situational needs, like those with dyslexia, teenagers rehabilitated from weeds and drugs, or just didn't have a chance to access school on time.
Wow! I wish I had known this.
A good teacher makes all the difference!
I finally understand some trig when I had a teacher who SPOKE NO ENGLISH, but illustrated the concepts with such clarity and enthusiasm that my brain caught on. I went on to take a theoretical calculus course and loved it, then I got lost in the mire again.
This is such crucial information!
Thank you!
too bad universities have their own schedule.
I think universities and tests are more based one answers based exam, what method you used are not important, in fact the numerical answer is more important than the technique used
yes, but if you do this before hand and get really into it, ,then you might consider doing a university course on it once you're more confident and interested in it all
Haha yea right?
Universities teach you why the maths works the way it does. It's up to you to use those concepts to create solutions to questions.
Teh Yong Lip not here in Germany depending on your class.
One of the most valuable things I learned at university was "The order in which to learn each topic". Exactly as is described in this video, you need to know about certain concepts before you can grasp some others. Even having all the right books won't help you if you don't know in what order to read them.
I flunked out of calc 2 at one point (two actually). I then went 3 years without doing math at all. Then I got a job tutoring at a community college while I got an electrical certificate. I learned from other tutors and also from helping other students. This filled in the missing links described here. I am in my last two semesters of a physics and applied math degree, and I do very well. It’s not easy by any stretch of the imagination, but I still give most of the credit to my tutoring experiences. We need to allow people to discover math at their own time and pace. Math should be explored, not force fed. I really enjoyed this professors insight.
I feel lucky on having a great teacher who introduced *common sense* in math and made it enjoyable in 7th grade. I always took my time on my homework and would work on a question till’ 12am if I did not understand it. Math was something I liked because I could be in my own little bubble and problem solve. The flexibility of math due to its connections gives me freedom in learning. To see results after working hard and pushing my brain is amazing. Now math comes easy to me and I have A’s in all my math courses in my time in high school.
This is very true. From my experience, In high school I got D for basic maths but later one when I went to college and I started to understand the basic concept better. I struggled and failed twice before I scored an A for Concept of Calculus than on Cal I and Cal II were easier for me to master.
The thumbnail is all chemistry not math😂😂😂
xGrinch101 just noticed
Mathematics is the basis and everything else is built on top.
Have you ever taken a chemistry course? Stochiometry, Molar ratios, Equilibrium, etc. It might as well just be called an applied math.
It may not be arithmatic, but it uses it.
might have well*
i completely agree with you. you just spit facts. this is also my thoughts about math.
"if you miss one link in the chain, you will end up lost" this is what i say to everyone else.
This is a great insight. Here in Spain when I was studying for my written driving exam the classes were actually circular. You had one book with every chapter you need and a few teachers who would cycle through the book. You could join the class any time you wanted, start with any chapter, and stay for as long as you need. You can repeat the chapters as many times as you need before the test just by waiting for the class to cycle back to them.
It seems like this would be a good model for teaching maths. I wish I could have a teacher like this for maths, but I am older now and it's hard to find tutors for people my age.
KHAN ACADEMY
"Everyone should learn with their own pace" love it
THIS IS GOLD!!
Been wondering about this all years in school and college.
Wonder why no one step in and make the changes
Tell me one thing
If it's about math then why is the thumbnail salts?
@@goditian2526 yeah it's full of chemical equations. They just chose something "sciencey" for the thumbnail.
I completely agree with you. The strange thing in math is its so deep and interlinked, hence it turns to be fragile. If the link in the chain is lost the whole chain is lost. Match math with your pace, then maths comes into your pace
I'm just now taking Discrete Structures, my first proofs course, and what I am learning gives me a deeper understanding of even addition! I wish a simpler version of Discrete Structures was integrated into Elementary School curriculums.
Totally agree, when I was lost in math, i had to learn the basics first, and only after that learn the actual subject that I was studying
This is so true.. i missed just 2 weeks worth of classes and could not catch up for the rest of the year . I did not get what I was doing wrong , why I was unable to understand anything. But now I know , I missed the basics and without a solid foundation, any building is doomed to fall.
I just went through two years of struggle with a level maths because I missed the most of the content for the first year (we had a teacher that was always absent) and then had to try and fill in those holes in the second year whilst learning new stuff and it turned out to be a complete disaster. Then Corona struck and i got bad grades. I still have the feeling that I can really understand maths if i break everything down and build up again with the basics and this video has made everything so much clearer as to why i struggled so much!
My current 7th grade math teacher literally said "All you need to do is know the formulas". It may sound a bit like "All you need to do is understand the formulas and why they work" but considering how he gives us the formulas without explaining anything, I don't think that's what he means.
Yup that's pre-college math in a nutshell. Then that student who was amazing at remembering formulas goes on to become a math major and is unpleasantly surprised at the reality.
Thank you, sir. I can completely agree with this statement. I, for all of my early life, felt I was just doomed to be bad at math. As I learned, I learned every subject I love comes back to math. I finally decided to at least learn some math. I went in not expecting anything and came out thinking about everything. Once you have the connection with math click, and I do believe everyone can with the right approach, it almost becomes easy. I am saying this as someone who originally thought I could never, ever be good at math. Math is actually really cool, once it starts to click.
Interesting video. I liked the contrast between learning history and math. After a career in industry, I taught high school chemistry and physics for several years in the city of Chicago. I was very dismayed by the level of math knowledge in general.
What I would like to add to the discussion are two points: first, because a student is "bad" at math, doesn't = they are "stupid" or unable to learn it. They need to see and understand the importance of knowing the subject. Second, education does not need to be torture. For anyone interested, a great book on education is "The Smartest Kids in the World and how they got that way" by Amanda Ripley. Last thought: find a reason to learn. The future belongs to you.
I skipped preschool because of my age and didn't speak any English in my 1st grade class. I remember doing math in 2nd grade and it being very difficult for me. I was too slow. I still struggled in 3rd grade, but fortunately in the 4th grade we just repeated what we learned in the 3rd grade. It was the same stuff on repeat. That allowed me to catch up and I eventually ended up taking math courses one grade above me. For much of the same reason as described in this video.
can agree personally! did history for my degree and did some math on the side, math became really easy once i gave myself time to digest it all
This would have helped me so much if they had taught us this at school! This is the foundation of how to really master the subject of maths!
This video is very useful. I would add one more thing. math is beautiful, and very challenging, so enjoy the challenge! See it as taking a difficult hike, playing Chopin, or learning a new language (which it is, in a way). There is much pleasure to be gained in tackling a challenge meticulously, gradually, and with dedication, and seeing the slow but gradual progress that takes place, until one day you see that you finally reached the top.
I have learned much math on my own, and at my own pace, and it gives me great pride and confidence to be able to do it. No matter what your particular case is, try to be able to enjoy this wonderful challenge!
“Everything builds on what to already know” - David Eagleman
I totally agree with him! During school, I lost my way by missing certain key links in my chain. So recently, at the age of 28, I started to teach myself basic Pre-Algebraic Mathematics. A month ago, I didn't know how to do really basic Arithmetic like long division or my 7 times table, but now I'm working through arithmetic operations with ease! Fractions have started making a lot more sense for me too! Hopefully I'll keep this up and eventually get good at Algebra, Trigonometry and maybe even Calculus! 😁
Lovely to watch. It has been 1 week since I decided to learn math from scratch. Cause i'm bad at math when I was in school.
I wish you the best of success throughout your journey 📈
Most of maths teachers are stupid pedagogues. As far as we keep victimizing the victim (in this case the student) we are doomed. The reality is: bad pedagogy is a recipe for failure, for if a blind man guides another (blind man) both go into the abysm.
My mind blew when I started doing math my self with the help of online vides . It’s like my iq went from 90 to 140 in a few months . I suddenly started to get top marks in my class and even started understanding other very hard topics easily .
How was you're math level before and now how is it going? is there any advice you can give me? because i really don't believe myself... (╯︵╰,)
well, one of the best things about stem in general, is that you dont have to worry about bias from the professor, or arbitrary metrics for grading, etc. its nice to deal with objectivity.