The Only Way To Learn Mathematics
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- เผยแพร่เมื่อ 21 มิ.ย. 2024
- 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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"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".
Drawing that Q.E.D. at the end of a proof that you just did is the most satisfying thing
"that looks good! quick, draw the square! tap it! tap it! nice."
Oh yes
it's a little red square for me 😍
@@rudyj8948 why red ? )
@@noJobProgrammer I frequently switch between dark mode and light mode, and so my main color for writing on my iPad is a nice dark blue, and my color for comments and marks is a reddish pink. This is so they show up nicely in both modes, and have good contrast so the marks stand out. 😅😅
I highly recommend reading his autobiography "I Want to be a Mathematician"
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!
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.
Wow! That's an amazing level of dedication. I wish him the best
There is math in whole musical profess, it’s in abstract form
@@kamol901 As a cellist I totally agree!
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.
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.
Yup!
only realized today that I wasn't subscribed, despite having watched countless of your videos
thank you!!
Indian student here , and Sir I really get lots of help from your channel .
Thank you ❤
Great to see another Indian here too👋
Your camera quality it's crazy better! Thank you sorcerer
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!!!
It took me a while to appreciate this. Once I practice on mathematical problem it was a game changer experience.
Good point thank you!
It's good to hear from you, and for quotes like this
I greatly appreciated this video.. thank you 🙏💕
Thanks for the video
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
Math is the best way to invest your time
@@noJobProgrammerfunny handle name btw especially for JavaScript "programming" that alot of kids call that being a computer programmer, computer systems coordinator in the mid 90s n if u look up that job title it's like 6 different separate jobs wen it was all in a days work if you wanted a job
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.
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. 🖤
Thank you!!
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! 👍
What are the main difficulties in solving the Riemann Hypothesis? Or, is it unsolvable, something like too many variables with too few equations? Thank you
Very true for me, there is always a gulf between what I learn from a video and actually doing similar problems. By actually doing it for myself, I bridge the gap.
Isaac Newton is still alive
don't be fooled by appearances.
He looks more like Leibniz.
@@DavidVonR I've known many guys who physically resembled Jesus, but the were just hippies.
I'd argue that TH-cam 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.
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
Another good way to learn is to write a book on the subject matter (just for your own consumption if needs be). I've done this for set theory and logic. Many of the proofs in sources are often skeletal or non existent so it's quite challenging writing complete rigorous proofs.
i was solving calculas and getting all upset because i wasn't getting any of it right but then you posted this video Thankyou sincerely
This should be something we’re told in elementary school. You will not learn math unless you solve problems. It’s just a fact. Math is relevant in almost all stem fields. The more mathematically competent humanity is, the better we are for it.
Do math with the help of a great tutor is really great! 👍 ❤
Hey Math sorcerer do you have a course on Geometry?
Everything starts with passion and motivation to get through rough patches.
My professors would call just reading and not doing "learning by osmosis".
Which is rather worthless when it gets practical, I remember right wen ww2 ended the US grabbed every engineer that graduated from school n put them in the military
Hello Sir. I am seriously struggling with trigonometry. can you give me some advice
I had the honor of getting to know Dr Georg Berzsenyi when I was in high school. Hungary sure churned out some straight up geniuses
Edit: IS and WAS a great read. Paul Erdos was my hero as a teenager n a early 20s maths major n till this day n the traveling suitcase was a great read
can u make a video about discrete maths
Great vid! Prof. Halmos has been a true inspiration for me. He said" don't just read it.... Fight it!" and that is so true! Do the exercises on your own, try to figure things out, find interesting proofs or counterexamples. I do math daily (foundations like logic, set theory and math proofs from How to Prove it by Daniel Velleman and Book of Proof by Richard Hammack). Absolutely love it when I get to self study math without any deadlines, pressure to study for tests.
I`m reading the cool book right now. It is called "The Psychology of Money", author is Morgan Housel.
That’s true! ❤train, train, train…❤
What do you think of using LaTeX to do your math? Seen math majors on youtube doing it like that
Latex is the standard way to write the proofs, or any other mathematics
If you mean doing the math itself, there's a massive learning curve but it pays off. Your mind needs to think differently to spend a little longer in deciding exactly what to put down, when and how.
@@Overlord176 tbh im 3 days in and it doesn't seem super daunting at all, although I'm already used to different syntaxes in Programming
@@enriktigasna no like after you learn everything, it takes about a month to be able to do it as quick as writing the math on paper. My handwriting's trash so i made the jump my sophomore year of highschool, and now i write latex faster than i ever wrote on paper
@@Overlord176 I see, I currently use a lot of vim macros to get faster at writing since it's definitely very syntax dense
"Nobody develops muscles by reading workout books and manuals"!!!
hehe good point:)
You know you've mastered a math problem when you look at the problem and the answer makes sense.
The only way to learn is to do it, genius, who would have thought of that
Don't bend; don't water it down; don't try to make it logical; don't edit your own soul according to the fashion. Rather, follow your most intense obsessions mercilessly.
Franz Kafka
Ok
Damn good video!!
How many times does the average person need to tackle a difficult topic before they understand it? 3 or 4
Greatest pure mathematician of the 20th century was Paul Erdos m btw who has an Erdos number that they would erase for a trillion dollars --- noone ever
I am waiting for NeuraLink!😂
Lol hope you can live to be a thousand n get the info from proper sources n not Google n the swarthy lots
Paul Erdos.
Math is hard. Harder things are boring too. You come easier with it by doing.
Math, not maths.
POV : Sir Isaac Newton comes back from grave to give you a necessary reality check .
Sinric from Vikings! 🤗
Do you have any videos on the subject of AI and it's relationship to a motivation or lack of motivation to learning math? The reason for my question is that it would appear AI will make Learning math moot at some point. Agree? Disagree?
Solving problems by yourself
Regarding to integrals, you all the time perform U sub. I used new concept formulas that shortcut and give up U sub, compare both U sub is calculus garbage.
Ive ran through so many notebooks and pens just doing hundreds of practice problems 😅
why is this ripped wizard in the attic so insightful? i mean, I guess, what did I expect of a ripped wizard in an attic. I suppose all attic dwelling, gym going, math doing wizards are insightful? i dunno, you tell me.
We have chatGPT in 2024….knowing anything like mathematics is useless. I even quit my job as a programmer to become a truck driver because coding is becoming replaced by AI
Paul who? Could not catch the name.
Paul Halmos
I jumped the gun on my calculus exam smh nd I failed it. I failed you 😭