The Video EVERY Math Student Should Watch

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In this video I interview a wonderful mathematician and author. He discusses learning to write proofs, advice for math students, career advice, his research area, why he became a mathematician, his new book, etc.
His name is Thomas Garrity and he has just written a new book: amzn.to/3jiHSBd
(note this is my affiliate link)
Here are his other videos which I liked
Part 1: • On Mathematical Maturi...
Part 2: • On Mathematical Maturi...
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28 июн 2024

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Комментарии : 479

@theophrastusvonhoenheim4022 2 года назад

I am a 28 year old high school drop out, I started doing math as a hobby while I was in my early 20's and I am 2 years into a math degree in college now. I wish there were more interviews about people who do math who didn't start when they were 14. I haven't ever seen one.

@TheMathSorcerer 2 года назад

👍

@baseballMMAgames 2 года назад

@@theophrastusvonhoenheim4022 Good for you and your hard work. You got this!

@worldshaper1723 2 года назад

Brother, your story is very similar to mine.

@CB-dy1he 2 года назад

I'm also a hs drop out and atm I'm 31 and studying math to sit exams that will hopefully get me into college. I feel like I'm starting my life again, in a way.

@atlasbailly5439 2 года назад

Theres a series that has a bunch of people who found math in different ways! I think it is called Paths to Math

@atonurc 2 года назад

"Math is really hard, but I think most things that are worthwhile are hard."

@caiosiqueira6138 2 года назад

I'm a engineering student but every single video of yours I watch I'm more interested in go deeper and deeper in math

@anonexplorer8211 2 года назад

Lol same

@caiosiqueira6138 2 года назад

@Fre Joorfelgen sim kkk acho que meu nome entregou

@edmel144 2 года назад

I did Chem Engineering 25 years ago. I would always suggest if your as described to a Maths major then an Engineering masters.

@thushankathimira9587 2 года назад

Same here!

@helbitkelbit1790 2 года назад

Maybe you should quit the fraternity , lose the horse head , and put the bottle down.....

@user-lf6kg4sg8o 2 года назад

"the ultimate description of reality" "I'm Not a young person and I still learn math everyday" Most great what said..👍🏻👌🏻🌹

@jlopez47 2 года назад

Dr. Garrity's experience is a lot like mine in that it seemed instantaneous when the math you're reading finally makes sense, but he doesn't articulate the "why" completely which might lead some to believe it's miraculous when it's not. He immersed himself in the subject and was subconciously working out problems in his head. Most of use know what that's like when we've crammed for an upcoming exam. Becoming mathematically mature happens like that when you immerse your self in whatever books you're trying to read and internalize. It's your brain working overtime because you're oversaturating it with math. This is how we math people conquer new areas of mathematics. Just immerse yourself in it. You'll never learn it if you give a shallow attempt at it every once in a while.

@CrisOnTheInternet 2 года назад

The similarity with learning languages is big.

@aneeqaahmad6927 2 года назад

@@CrisOnTheInternet you mean like it could be just like learning a language ??

@aneeqaahmad6927 2 года назад

is there a certain algorithm for the immersion you are talking about? because I am trying to understand proofs right now. But so far I just do not grasp the whole concept of how this system of proofs is interlocked.

@CrisOnTheInternet 2 года назад

@@aneeqaahmad6927 I mean that a language makes more sense when you inmerse and understand the whys

@jlopez47 2 года назад

@FlyingMonkies325 I didn’t mean cramming, per se, though sometimes that’s when it can happen. Keep a study schedule and be consistent about it. Read many books of the content you are interesting in learning to get more than one perspective.

@ripperduck 2 года назад

When I saw the Roman aqueducts for the first time, it gave me a huge insight. Those structures are physical examples of hydrostatics, fluid dynamics, gravity as a source of energy and as a force, civil and mechanical engineering, architecture, and craftsmanship. None of the people who did any of that work had a college degree, never took any STEM courses. Yet, they created a system of water delivery that functions thousands of years later. The insight was that you must understand concepts before ever taking on problems. As Dr. Garriity points out, why is any of this necessary. For the Romans, a way of getting water where it needed to be was why they needed to know all aspects of aqueduct building. They learned as they went, trial and error, until they saw how the physical world works. Centuries later, Bernoulli codified the math, but the Romans didn't need any of that to get things done. That underscored that anyone put aside the theorems, formulas, proofs, and calculations aside until the concepts and the "why" were understood...

@katydid5088 Год назад

They had schools for engineering and rhetoric you know. It's not true that they never attended school, just that something approaching our university programs didn't quite exist yet. You would learn counting maths for arithmetic and cencus/business math separately from your rhetoric as a poor person but the builders and engineers of Rome would have learned that and started some sort of apprenticeship anywhere from 7 to 8 years of age. It's a heuristic loop most anti-college pro trade school/self teaching types like to trot out without realizing or recognizing the depth and relative similarities and simplicity with which people recieve all different kinds of education nowadays. This is not to say self directed learning is bad or that causal experience and trial and error weren't part of the Roman school/engineering experience but it's a survivorship bias as well that makes us look at one schools or truly apprenticeship skilled method of building aqueducts that then leads people to assume "no schooling was required and they still did a better job. " At best, we can infer that they may or may not have attended a trade school with some basic Euclidean geometry with "string theory " (and by that I mean, conjecturing and measuring alignments using basic geometry derived from triangulation and measurement with string,compass, plumb bob, and angles) to figure out alignment, standard cuts,lengths, and building material quality. Things like checking cement materials, density,and setting time alongside local geography, means of what survives, they either got lucky, planned the building site well, and only slightly avoided material pillaging or earthquakes. Back then for all the engineering robustness they still attributed earthquakes to gods getting angry and turning the world around like a snow globe. The concept of thermodynamics and geology and chemistry certainly wasn't possible with the type of knowledge and models they had back then.

@newsgo1876 Год назад

0:39 Self-Intro 1:20 Why did you decide to study math? 3:01 What's single most important thing that a math major should focus on? 4:06 Tell us about the book "All the Math You Missed" 6:45 How to write proofs (to be mathematically mature, not a linear process but like a stepping function, keep pounding your head against it and you will be there, some wonderful moment! Here's another link on this topic by Prof. Thomas Garrity ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-zHU1xH6Ogs4.html) 12:10 General advices for math students 13:32 What's your research area and why did you choose it? (multi-dimensional continued fraction: another way to express real numbers besides decimal expansion, it is really cool! And it turns some junk form in decimal expansion like a square root into a pretty pattern. So what about cube roots? It mixes all kinds of areas of mathematics.) 20:49 Career advice for math students (pragmatic concerns should never stop your math development.) 22:19 Anything to share with the RU-vid audience? (Two different kinds of mathematicians: theorem builder (the story) and problem solver (the craft). High school overwhelmingly focus on problem solving. But the story is not there. Try to both find the stories and work on the craft. 23:56 Wrap up. 24:24 BUY THE BOOK! :) I am too sleepy and will fill out the rest tmr. --- Now done!

@christophermuller5700 Год назад

Thank You!

@NicoVeenkamp 2 года назад

I’m now almost 65 years old and always was kinda interested in math. Used to be good at it, but never studied it seriously. Been following you for some time and recently ordered the book you mentioned. Now that I saw this interview I’m really going to spend one or two hours every day to read and study the book. Especially Fournier analysis intrigued me, so I may end up studying that in more detail. Thank you for taking the time to make this very interesting and entertaining video. Also special thanks to professor Garrity to take the time for this interview.

@MCJSA Год назад

This epiphany that Garrity is talking about around 11:30 is common in learning complex systems. I'm a linguist, not a mathematician, and this sudden convergence of understanding is pretty common in language learning. At some point, you suddenly realize that you have entered the language and you are operating in it without reference to your first or habitual language - you get a glimpse of the world of the native speaker. It's a liminal experience, but a very significant event in the learning process. It cannot be taught. Mathematics is very similar to natural language as a rule-based, closed, self-referential system that is rooted in human creativitiy and also emerges from the natural world.

@monissiddiqui6559 2 года назад

This was so amazing! I love the way he presents everything. The bit about the continued fractions and the way he was saying "OOOOOVER" over and over again legitimately made me laugh out loud 🤣🤣

@ikalopsia5140 2 года назад

As a lost physics major, I found this video so inspiring and enlightening. Thank you.

@magnoliazone6 Год назад

I'm a non traditional mathematics student. Work full time and come home to spend hours sitting on a chair doing problems over and over again for hours on end. Have a few classes left. Most stress I've ever experience but will tell you that I am up for challenges in my career and life. My approach to problems and coming up with better ways has improved dramatically. This is a great video. It is refreshing to hear someone's take on the subject. Will look for this book. Thank you for sharing!

@fluffurbia3501 2 года назад

I hope you will do more interviews with mathematicians like this one with Thomas. It was fun hearing about his mathematical Eureka moment triggered by Rebel, Rebel, his adventures with continued fractions and just his sheer joy immersing himself in mathematics. And thank you for always talking about the reality of the process of becoming a mathematician in your videos. Many mathematicians give the impression that they floated up to the pinnacle of mathematical understanding sitting on a feather due to their innate gifts. But you’ve always been honest about the blood, sweat and tears involved for everyone, as well as the excitement and satisfaction. By the way, your lighting conditions, whether through choice or happenstance, are exquisite. You look ethereal, like Salvator Mundi by Leonardo da Vinci, just without the orb.

@TheMathSorcerer 2 года назад

😀😀

@ShadaeMastersAstrology 2 года назад

Such a beautiful and encouraging comment:)

@something2doTV 2 года назад

Omg you got Thomas!? My all time favorite lecture is his talk about mathematical maturity! Got waay too exited when you announced it.

@ollielon5926 Год назад

I like the end where he talked about the need for both the story and the craft of doing mathematics. Humans are inherently creatures that love stories, and there is a lot to be told in mathematics. When math is presented in such a way, with both the story and the craft of it, it becomes beautiful.

@TheMathSorcerer Год назад

Yes!

@ceramicsky14 2 года назад

MathSorcerer, you are the gift that keeps on giving! You helped me get into graduate school, and now as I’m starting grad school you post this amazing video! You’re always one step ahead of me, you really are a sorcerer!

@randoomly39484 Год назад

What he said at the end about us neglecting the "story" side of math, made me smile, I'm the type of person who like to know the story behind the evolution of something before getting deeper into it. Thank u so much for this amazing interview.

@intdivisionbyzero 2 года назад

Mathematics truely unlocked so much of my knowledge in the computer science field of which I study, without mathetics, tech is useless. The logical foundation is priceless.

@thoriqakbar 2 года назад

His enthusiasm is contagious!

@framemaxxer 2 года назад

wow hes so humble, and i can relate to that assignment struggle at the start

@nickschmitt8594 2 года назад

"Why isn't everybody? It's the ultimate structure of reality." This is why I want to learn math. My math is so poor, I took the easiest classes in high school and I'm now deeply regretting it. Hoping to find time as an adult through basic high school math to more advanced topics. Not sure how I'm going to do it, kind of discouraged, but I would really love to be a confident mathematician.

@celeste3100 17 дней назад

Dude, you're singin' my song 🤧But here I am trying to get into the USAF so I can have school paid for after I'm out. I want to be an Aerospace Engineer either working on F-35s or on the F-135 engines. Wishing you the best 🙏

@divyanshupandey4728 2 года назад

that "something happens" at 11:43 is the keyword here. For me it was a ankle fracture which made me read the only book i had at high school and after that there was no going back

@kufena 2 года назад

This is a great interview - thanks. I have the first edition of his book and, despite not being a mathematician, have found it interesting and useful. I loved maths, but didn't study it because I was told I wasn't good enough - I did computer science instead, and my undergrad college didn't teach much maths. I then did a phd in type theory and really struggled, and no one really wanted to help or tell me what I needed to do. That was early 90s. I regret not doing maths or physics at undergrad now, although I enjoyed the computing side of things - 80s - it was all new. Last few years, you tube has given me a new interest in maths, which I'm really enjoying.

@sayujyabhandari1933 2 года назад

Okay. I have to say this. This video was absolutely awesome. These are the things no one ever talks about and before finding your channel I was in the dark about a whole lot of mathematics. Thank you very much :)

@TheMathSorcerer 2 года назад

👍

@mrheng562 2 года назад

This is dope!!! I really enjoyed his energy and enthusiasm for math!!! Although I don’t teach it anymore, I plan to continually be a problem solver and hopefully become good enough to be a “storyteller.” 😁👍 Do more of these interviews!!!

@vivgm5776 2 года назад

I found about this book on this video and just bought it. As a former physics student and starting a phd in mathematical physics, it helps fillings those holes in my education and made me understand the ideas of categories very quickly. I recommend to every person in a situation similar to mine.

@carlosvargas2907 2 года назад

This is just what I needed these days. Great, man!

@Nico-ef7bt 2 года назад

I really love the part where he got the enlightenment to write proof.This shows how maths develops our brain and make it powerful. Now i understand the 'my brain is open' by paul erdos.

@peterbenoit5886 11 месяцев назад

I have Professor Garrity's book and concur with his veneration of Spivak Calculus. Your discussion of the transition to theorem-proof mathematics was especially interesting because I completed my undergraduate degree in times far enough removed that courses designed to help students learn to write proofs were not yet in vogue. Consequently, I had no such course. However, I was doggedly persistent in extracting the gist of it from the textbooks, and I made the transition to group theory, real analysis, topology, and the rest with little stress. In fact, despite the dire warnings from my faculty advisor that real analysis was a "watershed course," I finished with a straight 100 average for the semester despite struggling with a protracted case of mononucleosis. The more "abstract math" courses were actually to my liking, though I admit a continued fondness for solving Putnam Exam and IMO questions recreationally even now, at age 68. A life spent with mathematics is one richly lived.

@bagzhansadvakassov1093 Год назад

He is so passionate about this. What an upstanding man.

@marshallsweatherhiking1820 2 года назад

The thing I remember with proofs is the way I thought about them was rarely the way they were written down in on the page. There's always a conversion process in my head going between a visual heuristic that makes intuitive sense as the main "trick" to complete the proof, and the more rigorous logic that ties all the loose ends together on paper. That's how it was with real analysis anyways. I'm very visual/spatial, and more advanced texts don't usually take up valuable space with pictures, which is intimidating at first when you don't even have a firm grasp on what the definitions mean in a more concrete context. The general notion of topological spaces defined by how unions and intersections of open and closed sets behave is cool to me and gives a useful pattern of how limit proofs can work in general, in a very abstract bare-bones way, but I always go back to visualizing open/closed intervals on the real line (or balls on the 2D plane) for guidance.

@treyhull8424 2 года назад

This is literally the book I've been looking for for the past two years! I can hardly wait for it to get here so I can dive in.

@rachindrahemarathne6482 Год назад

This is one of the most useful videos for Math Students on RU-vid.

@massipiero2974 2 года назад

Former physics student, now math student here (undergraduate). Just 3 minutes in, and his steps to get on the glorious path of mathematics are exactly mine. Wow, I guess mathematicians are born that way 😄

@xecon4368 2 года назад

I literally bought this book after watching your review of it, figured it would be essential. Glad to see a video with the author.

@LordZombieZanetta Год назад

That epiphany that I get when realize something that i've been crunching in my brain for days, is why I am working on being a mathematician. I have found very few things that I get a sense of passion for. Math has been one of those few things. I'm glad I found your videos.

@complexlogic8634 2 года назад

This is exactly how I would describe my approach to math and proofs...continuously pounding my head until suddenly it all makes sense. Also, I absolutely agree with what he said at the end that we should strive to not just know the craft and but also the story, as I think that provides a ton of inspiration when actually doing the craft.

@Gabzz96 2 года назад

This was awesome thank you for these videos. I actually disliked math quite a bit when I was younger but the past few months I’ve been studying on my own and watching your videos which has been a great experience

@JB-su7lm 2 года назад

He's back in the game! - and omg did he say category theory?! For the record, I've gone from freakin' college algebra to way beyond because of the Math Sorcer support system, if you will. Thanks fellas!

@TheMathSorcerer 2 года назад

@anshumansahoo7568 2 года назад

I came to know about your channel from my friend and I can't believe how I was sitting so long without knowing you !.❤️

@ShadaeMastersAstrology 2 года назад

This interview is an incredible watch. I can feel the passion through the screen and I admire the sense of mathematical optimism in both of you gentlemen. Thank you for sharing your insights and experiences with us ❤️

@whyyes6554 2 года назад

Thank you for the DESCRIPTIVE TITLE. Of course every math student will watch YOU'RE THE MATH SORCERER!

@buffendene9996 2 года назад

I haven’t watched all of it yet but so far your questions are really good. You should do more interviews!

@ass09tube 2 года назад

This video is like experiencing mathematical heritage. 👌. Loved it. Advice, guidance from a veteran, senior Mathematics scholar/learner is to be chewed n chewed, it tastes same...sweet. Very exciting to watch. Thank you.

@sanwellbeatz1630 2 года назад

Was struggling with Riemann...but after watching this video i got motivated and starting reading and doing Qs even if i didnt understand anything.Then suddenly everything has started falling in place just like he said....Thank you sooo much

@DocBree13 Год назад

That’s awesome and inspires me to tackle Riemann again

@markring40 Год назад

Great interview!! You do an excellent job of asking concise questions!!👍

@bronjo9343 2 года назад

The story part makes maths more interesting, like Thomas said, there is lack of story lower grades and too much craft. Thank you for the wonderful interview!

@nickgibson3451 Год назад

Just came into an engineering PhD as a pure biology background and this was exactly what I needed! Thank you.

@sanwellbeatz1630 2 года назад

Struggling with real analysis your vids give me hope n motivation and results

@danielgarrison7463 2 года назад

This video has been beyond inspiring, love these type of videos!

@ivantamayoromero1668 2 года назад

🙌🏾 Love his book and it was you who convinced me to get it! 🙌🏾

@mathsandsciencechannel 2 года назад

Yeah great

@jamez34 2 года назад

Hello! I am new to this CH and I just subscribed because i'm 27, I have 3 lil one that push me to become a better for them. I've been chipping away at general ed in college and now I am facing the math part of it. I am completely nervous but determined to learn math as it will get me into a career that I will be fulfilled with be a part of. Thanks for this video as it gives me some motivation to learn math and keep learning what math is all about! thank you!!!

@TheMathSorcerer 2 года назад

Welcome!! That is awesome that you are back in school. Great stuff, thank you for your comment!!

@Wandering_Horse 2 года назад

Thanks for doing this very cool interview format video, I think you should reach out to other influential figures in the realm of mathmatica and continue on this theme. I also wanted to say thanks to you personally, you have truly inspired me on my recent math journey. I am just getting into intermediate Algebra at age 51 and I find myself enjoying it and I am at the tutoring center several days a week just to stay on top of my game. Also you had done some videos on book reviews and extolled the virtues of building a math book collection....I know have 6 math books. One of them a very cool book on statistics from the late 50's with a students hand written notes and formulas throughout, super cool book to have in any collection. Thanks for all the time you spend making these videos, very much grateful...

@gradientO 2 года назад

Watching this as a computer science student, because, you know, computing

@imbreakingdown2683 2 года назад

Great video! I would love to see another interview with a mathematician.

@zerocks2294 2 года назад

I bought the book after you made the video and now it’s my favorite book.

@terrylewis5786 Год назад

I just donated to your site. I enjoy your videos and I watch them with my teen kids (one in college). I enjoyed this interview and I purchased the book. TY for the links and your passion.

@cdkslakkend5742 Год назад

Great interview. Honest outlook, which I appreciate.

@TheMathSorcerer Год назад

👍👍

@knw-seeker6836 2 года назад

Thank you for the interview

@musicalADD_theband Год назад

I’ve been looking for a term for this. I’ve been teaching math for the better part of 15 years and I think the biggest issue students have with solving problems is the approach that they’re taking to them. Everybody’s trying to remember the steps or the formula how to do a specific type of question. They’re not trying to understand what’s being asked in order to try to figure that out based on what they’re given. Ive been calling it “thinking THROUGH the question”. He’s describing exactly what I’m talking about

@joshuapowens 2 года назад

I bought this book after your review and watching Dr. Garrity's "On Mathematical Maturity" video on RU-vid. Love this interview.

@turboDout 2 года назад

This was an excellent video! I like this format and would recommend you trying this more often (given the opportunity!)

@uncwprojects2053 2 года назад

thank you for your wonderful way of making math easier and interesting

@Anythingforfreedom 2 года назад

Coool. Just bought his new book. I’m surprised he didn’t have more to say about career advice, but I’m glad he was honest (rather than just making something up).

@CarolynFahm 2 года назад

Great interview. A pleasure to watch it. I have the first edition which I purchased after seeing your review.

@PriDrummond 2 года назад

What an amazing interview!!

@Martin-mt4bo 2 года назад

Amazing video, really made my day! Would love to see more interview-style videos in the future. Gotta check out his book now 😄

@michaelmcgee335 7 месяцев назад

This was great and what an honest guy.

@vinayseth5899 2 года назад

Thanks a lot! Was surprisingly deeply insightful.

@byronrogers4489 2 года назад

The greatest teachers are storytellers.

@Enigma758 2 года назад

Wonderful, thank you!

@lorenzobarbano8022 2 года назад

Wow, both of those guys are AMAZING!

@ivantamayoromero1668 2 года назад

You have sold me in quite a few books. This is one of them. My bank account is smaller because of you.

@TheMathSorcerer 2 года назад

rofl!

@ripperduck 2 года назад

He's a hell of a great professor!!

@bernardofitzpatrick5403 2 года назад

Absorbing 👏🔥 yas. Story is so often missing ! Will buy the book!

@hedge_in 2 года назад

this was gold, thank you!

@TheMathSorcerer 2 года назад

Glad you enjoyed it!

@baseballMMAgames 2 года назад

As a guy who has a successful career in a non-math field, this channel has been wonderful. I am now in the process of going back for a computer science degree and understanding math better has been so helpful. Thank you!

@fredsandford2292 2 года назад

I love math I admire individuals that love math as well. I had a great math teacher in college.

@TrackopGaming 2 года назад

Wow. What a great video. It's extremely inspiring.

@jessehudson7036 2 года назад

Immediately bought the new edition of this great book!

@yash1152 Год назад

22:39 super super thanks a lot for the following part. I am a "story behind" person as well. And i didnt know this way of categorisation. But it was bugging me, i knew something was missing. Thanks for highlighting that high schools/colleges put more attention of "the craft" and people get turned off by it. Definitely resonated with me. Here's a techer who just uttered formulae in 2 lectures, without any story, and finished multivariable calculus _and_ vector calculus just like that - in total two lectures/3 hours (one lecture/1.5 hours each). I was very discouraged. But thanks, you words of recognition helped me. Also thanks for reminding that both are important. I used to do both when in school, but since in college, there has been just Sooooo much to do and learn, that i cant really manage to keep up. I am trying hard to keep up, to manage stuff, but it just doesnt seem to be adding up.

@wizz_wuzz 2 года назад

awesome and inspiring interview !

@nueythepyasuwan 2 года назад

Thank you. Interesting and informative. Would be great if you interviewed other mathematicians too.

@nathanhemenway4710 2 года назад

I could listen to this guy all day, he's great hahaha

@MB-ue2rf Год назад

So Inspiring, thank you

@stephenmaharaj5230 Год назад

Great book, great channel. Thankyou Sorcerer.

@meteor8076 2 года назад

Amazing interview !

@franzfischer3631 2 года назад

The Math sorcerer really looks like Albrecht Dürer, especially his hairs shimmering in the light

@cambridgebreaths3581 2 года назад

Wonderful. Thank you.

@trenza2566 Год назад

thank you so much Thomas Garrity, my left ear appreaciated it

@mathsandsciencechannel 2 года назад

Great man. He has bless our generation with is talent and skills. He has really inspired me a lot to start my maths and science channel.

@mobileuser453 2 года назад

hey man you have inspired me so much thank you love you

@aaronwong7340 9 месяцев назад

Great interview!

@hakimled4300 Год назад

I wish I had all those books behind you thank you Sir for sharing knowledge

@nguoikechuyenlichsu6472 2 года назад

Thank you for your great video. I also got big challenge in writing proof in first year at university. I wish I could watch this video many years ago.

@eeemuse Год назад

I highly agree that most math education in schools is all about the method, they so shyly run over the story of things. So you find yourself have to solve equations over equations without knowing the 'WHY?'