The Only Way To Learn Mathematics

The only way to learn mathematics is to do mathematics. The legendary Paul Halmos said this and in this video we discuss it. Do you have any opinions or advice for others? If so, please leave a comment below.
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[douglasstrother]

"To use mathematics effectively in applications, you need not just knowledge but skill. Skill can only be obtained through practice.", Mary Boas in "To The Student" of her "Mathematical Methods in the Physical Sciences".

[noJobProgrammer]

Drawing that Q.E.D. at the end of a proof that you just did is the most satisfying thing

[MMAengineer]

your video where you talk about "you can get up to date within 2 weeks no matter how hard the course is" really motivated me to give 100% everyday man!

[guidichris]

My son is completing his doctorate in cello performance. One of his early teachers was a phenomenal player from Poland. His take was to be a great cello player you had to practice 6-8 hours a day. My son does indeed practice at least 4.

What does this have to do with learning mathematics? Like anything in life, actually doing the work is required to obtain mastery.

[martinhawrylkiewicz]

I highly recommend reading his autobiography "I Want to be a Mathematician"

[fSFan]

I see the thumbnail, read the title and immediately have this quote in my mind, I know that is gonna come up in the video, so before clicking on it, I repeat the quote several times loudly, even though I don't even know where I got it from, I just knew it instantly.
also worked on math problems for 10 hours today, sometimes I'm a little bit slow, but I think the time is worth it. Keep it up.

[ernststravoblofeld]

The really insidious thing is, watching videos can make you feel like you're getting it. But the next day, you don't have it.

[angleth]

only realized today that I wasn't subscribed, despite having watched countless of your videos
thank you!!

[AnishaSharma-ykox]

Indian student here, and Sir I really get lots of help from your channel .
Thank you ❤

[antinominianist]

Programmers know this intuitively. The only way to learn a new programming language or framework, is hands on. No amount of reading the documentation will help. Documentation is good for reference because it is hard to remember all of this. So you forget most of the material after hands on familiarity but retain the "knack" to look things up and do it again.

[saidneder]

Your camera quality it's crazy better! Thank you sorcerer

[TechR]

I'd argue that YouTube is for visual learners people who learn through videos, and it does help certain people. Certain people need their own pace(which a video provides, a video also provides you to go back and forth, and pause on each step of the math problem). But a video also sometimes simplifies complicated textbooks, personally I think videos are the simplest and easiest form of learning, I think reading a textbook is a lot harder. This also brings me to the teacher, the biggest benefit of a teacher is them being able to interpret the information in a much more simpler way, especially if its challenging to pick up somewhere else where, and them being in a video makes it easy I feel.

[ermiasawoke]

It took me a while to appreciate this. Once I practice on mathematical problem it was a game changer experience.

[AnnieMarie]

I think doing math is a great way to pass the time and better than doing puzzle books like Sudoku which I also like doing. I feel like I learn more from the problems I get wrong than the ones I get right I did 31 math problems last night and have done 10 so far today and there's still a lot of of hours left in this day

[kabirbhattacharyya]

Hi sir, I've been self studying mathematics and your videos have been really helpful to me. I've realised that even though I love the subject, I've had trouble with trying to score of it. I'm in my second year of college right now. In distant future, I hope to meet you. Gratitude from India. 🖤

[YassinYassin-jetr]

It's good to hear from you, and for quotes like this

[redfinance]

Im very excited to learn more mathematics this summer. Your channel has provided me with so much info on learning and truths of life; thanks for your amazing videos!!!

[t-qz]

You talk about practice but what if you are just stuck due to lack of explanation by the teacher or book? I feel many students get stuck im loops where they struggle to get out of

[douglasstrother]

"Mathematics is difficult, even for mathematicians." ~ Reinhold Böhme, quoted in Appendix A of "Vector Calculus" (2nd Edition) by Marsden & Tromba.

[ojas]

Thanks for invoking my reading of Ivan Niven's Booklet, where he says early on, that one learns Math by doing Math. At first glance a tautology, by an excellent strategy worth analyzing! I enjoyed Halmos Naive Set Theory and Measure Theory, those were all I could afford during my student days! 👍