What Do You Do With a PhD in Math?
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- Опубліковано 19 чер 2024
- Watch the full episode: • Ben’s Brother (ft. Mat...
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did i understand anything he said at the end there? no absolutely not. but i love hearing people talk about stuff they're passionate about!
I kinda did and reminds me of how lonely stem students are lol
Same!
To understand that U probably have do at least masters in pure maths or higher because no body can make U understand that...not even a math professor can...to understand that U really have learn that by urself.
@@MicahRion so...did she get it?
@@pankajkumarbehera8169 not really man, you could understand it if you were given any sort of primer into the topic, having a masters in math doesnt make you understand it if you dont bump into it on your way there and not having a masters in math doesnt make you unable to understand it, you just need to familiarise yourself with the topic
When I was studying math, I came across what I think is an apt analogy for pure math as opposed to applied math. Pure mathematicians are like guys who love to build railroad tracks. They don't care where the tracks go. They don't care whether anyone will ever want to go where they have laid the tracks.
Then, one day, a physicist realizes he has to go to X location, but he doesn't know how to get there. He does some investigating and, whattaya know, there are already some tracks leading him right there.
That's an unbelievably harebrain analogy. 🤯
That is a pretty good analogy
That's a great analogy, I'll probably use that :)
As a mathematics undergrad currently in Number Theory, I definitely second the “all the numbers became letters” statement. I am literally studying integers, and the ONLY numbers that have shown up have been in the subscripts lol (and I guess the Euclidean algorithm but still)
my boyfriend (a poli sci/creative writing double major) would look at my abstract algebra homework and think he was having a stroke lol gotta love that theoretical stuff!
I didn't even major in math, but I took logic one semester as it filled a math/science requirement. They recommend it to the pre-law track, so I thought there would be a lot of debating. Nope. Lots of equations with no numbers nor signs of operation. A^B->C is what the statements looked like. I got a tutor for the class and took it as a P/F. I did pass, but man, it was hard. Translations were a little easier for me than proofs though.
@@SheilaDeBonis A AND B IMPLIES C
As a mathematics student too I disagree. Behind the letters are always numbers. It's just really inefficient to study one number after the other, and there are infinite amount of them.
@@mzg147 As a fellow mathematics students, I have no idea what you mean. Letters can represent anything from sets to functions to sequences to groups… Why would you say it’s always numbers?
I did a bachelors in math. I’m a PhD student in Econ now. I thought I was phenomenal at math until I got to the proof-based courses he mentioned in this video. Those courses are really what separates those who are good at math from everyone else.
I’m on that same track! I’m double majoring in Econ and Applied Math+ scientific computing. It’s actually really cool, I love to see the connections from my linear algebra, probability, and calculus classes to things like Econometrics and Intermediate Micro.
People that can do proofs amaze me. I can’t get my brain to “see” the path ahead. It’s all darkness whichever direction I shine my mental flashlight.
And yet at the last company I worked for, on projects we did at NASA, our executives would introduce me at meetings as the smartest guy in the company.
As a physics major I was usually the dumbest guy in each of my classes.
I have a graduate degree in econ and have been working as a professional economists for about 12 years now. I feel like a lot of people that have graduate degrees in economics studied math or physics in undergrad.
I was good at the proof-based stuff; it was part of my favorite mathematics courses, and I always enjoyed math for the “Dissecting” I did of it “Well, this and this, so it has to be that, yeah, it makes sense, cool.”
That was my inner monologue throughout any math lecture, and I always marveled at the inner workings of everything going on.
Similarly, my favorite courses were the explanatory and intellectually exploratory ones, rather than the rote-memorization ones.
Until I got to college, nobody else around me really gave a shit about any of the math in the classes I took. Lol. Probably a lot of people even in my Calculus courses just had it to fill a requirement in another degree too.
Kinda facts. But thats why applied maths is great. Undergrad in applied math and masters in “biochem” (doing chemical kinetics, math bio stuff)
I'm a maths grad and the moment he was asked "what's the best number" I was like "please say zero it's got to be zero", and then he said zero and I punched my fist in the air in celebration. what a moment.
😃 Indeed. Is there any material on ‘Zero for (absolute) Dummies’ that I might be able to read, please?
@@claudiamanta1943 as someone studying maths, wikipedia is a great place to start!
The first difficult math hurdle is long division. Then algebra. Then calculus. Then proofs. Then group theory. Then I don't know what else because I can't figure out group theory.
So, did you figure it out? Group Theory is such a beautiful topic, and it gets even more when you study Galois Theory and see that Group Theory solving problems you can actually explain to regular people (the reasons why you're not able to write down a formula to find out the roots of any polynomial of degree greater than or equal 5). It kinda feels like going on a long journey and coming back with an answer: "no".
The last line made me laugh.
Categories 😣
😂🤣
Calculus was always easy tbh
PhD Physicist here, hello! I am one of the two that understood the reference to tenors and topological space. Would actually love to hear more about it.
Tenors is not a thing
@@roybean9983 Tenors are a thing and they usually sing
@@roybean9983 You know (she?) was typing on her phone and meant tensors.
SAME
Me too! I can't find a reference for the fact that there are 14 unique tensor products of banach spaces modulo injective/projective associates
Matt can talk all day, I won't understand it, but I just want to listen
🤨
I am a medical doctor and I never seemed to understand why people didn't get my medical jokes, until this guy tried to explain his favourite number and now I see what it looks like on the other side haha
Ever heard of patients in a hospital bed?
They have [insert long and complicated medical jargon here]
What do nephrologists do in their free time?
Collecting ducks
I'm actually really glad they do these small clips because I am interesting in going to college for some sort of math, and I would have had no clue this podcast episode existed!!
Go for it! I just graduated with a bachelor’s degree in math and I’m happy I chose to do math.
@@kimtran6378 I used to hate math in my teens because it felt impossible for me to understand it. Now graduating from ICT-engineering and it's one of my favorites. Especially love its eloquence.
I just turned 29 and am working on my final year for a bachelors in math with a minor in computer science and I love it. My time management still kinda sucks though.
@@OCOCody This is one of the most relatable comments I've read on UA-cam. :)
Check out if you prefer applied math or pure math.
If you prefer applied math, check out actuarial science
I’m in 7th grade and I love math and want a math major at Stanford and Cristine inspires me to love school and want to go to college
sorry to be the bearer of bad news but...
math in university and math in middleschool/highschool are completely different.
But if you truly think u love math... u should look into proofs and see if youre interested in that!
You can watch some university lectures in math ocw.mit.edu/index.htm
So You get a feeling how university is like. It helped me a lot with physics back then :)
Yay!! You can do it.
shy_18, I am a PhD in math (my field is called topology, which is like stretchy geometry). I now actually teach Middle School (I was a college professor for about 5 years). And I want to encourage you to follow your dream. One thing people don't realize is that mathematics requires creativity. Mathematicians are always talking about how beautiful a particular proof is. I encourage you to follow channels like Vihart, 3blue1brown, Numberphile, and Standupmaths. Look up "recreational mathematics" Do logic puzzles. Learn origami. All of these things will help you learn more about math, and develop your math brain. Also, know that success in math has much more to do with effort and passion, admitting when you don't understand, asking questions, and being curious, than with "genius". Look up 'growth mid-set': that's what you want to cultivate in yourself. Have fun in your journey!
work hard and stay focused i’m rooting for you! that’s a great goal
It's true that all the numbers are gone and we only use letters. What they don't tell is that the letters don't signify numbers anymore. They signify a form of differential operators, a topological space, a limit set, or something completely different. Somewhere down there, beneath 4-7 layers of abstraction, there just might be numbers. Or there might not, as is the case in abstract algebra and topology.
I'm actually in Undergraduate School for my degree in Applied and Computational Mathematics. I plan on going on for my PhD as well. It's interesting to hear Matt talk about how isolating being in that high level of math can be because I am already feeling that as an undergrad. The only people I can talk about Math to is my classmates and even then I understand conceptual ideas better than some of them who are just taking the class as a prereq for either some engineering course or their math minor.
*edited: changed schoole to school lol
Melissa Wicks lol schoole
@@megandalessandro4290 yikes you got me lol. I may have typed all of that without my glasses on. Honestly surprised I didn't make more errors. 🤷♀️🤦♀️
@@junkyardjess9360 ahaha sadly I can only say it gets worse from there the higher you get. Wait until you get halfway through calculus 1 and your entire understanding of slope changes!
I tutor math at my university and it's always fun when an algebra student comes in needing help with slope and my brain goes directly to derivatives lol!
I’m on the other end. I’m not math illiterate by any means but my friends are just so much more passionate and better at the whole numbers and variables thing than I’ll ever be. Occasionally they’ll go into some deep math logical thinking puzzles and I’ll try my best to follow, only to tune it out afterwards. Makes me feel dumb sometimes, but I guess it also happens with other people in our group when I dive into physics or music theory.
@@junkyardjess9360 Lol imagine taking pre-calculus and thinking that it's advanced.
I actually am finishing up a PhD in abstract harmonic analysis, the same area as Matt (my supervisor is a former student of Matt's supervisor). Really interesting to listen to his perspective!
Cool! I always find it funny that people who do harmonic analysis say "abstract harmonic analysis", I suppose to distinguish from applied?
Do you happen to know a reference for the tensor product of Banach spaces theorem he mentioned at the end?
@@sebster100 Classical harmonic analysis is done on R^n, while abstract harmonic analysis is done on topological (typically locally compact) groups. I think of the word "abstract" here in the same sense as in "abstract algebra". I actually know very little about classical harmonic analysis, it really is a completely separate field.
And unfortunately I don't have a reference for the Banach space fact, I had actually never heard of it before myself either. Sorry!
@@UltraSwat That's really cool. I attend a small state university and the main areas of research for the math department are operator theory/operator algebras, number theory, and combinatorics. Even though I'm an undergrad, I have an interest in algebra and topological data analysis.
Beyyyyyynnnnns brother is a BABE
Yess
Definitely.
For anyone out there interested in the theorems he cited at the end about the number 14, they are Grothendieck Theorem and Kuratowski Closure-Complement Theorem. ;)
Thank you , Indeed very interesting.
I find it amazing how interesting your podcast is. Bringing this kind of guests and talk about math might feel totally unrelated to your channel, but it is extremly refreshing. I might not understand a thing about math, but the way he talks about it really makes me feel curious and want to keep listening ♥️.
I’m going into mathematics! This makes me really excited for what’s to come
As an Applied Math major, I definitely definitely fell in love with the analysis portion, there is beauty and exactness for most of the discovered and proved arguments
He's so fascinating!! Thanks for having him on!
Matt!! I would love to talk math with you! I am a physicist! All we use is variables all day long! I also get asked the question about what can you do with a physics PhD all the time. It is challenging to answer since those who can apply it become famous research scientists or work in industry and those who can't apply it, but know it teach. I suppose I fall into the latter category since I am currently teaching physics. It is incredibly isolating to be in such a small group of folks who truly understand your work that is so vital and personally important and yet somehow not practical (in a traditional sense)...
I have a BS, double majored in computer science and applied mathematics. For the AMS major, I did my thesis on theory related to Fibonacci and fractals (at least I can explain that part and even some non-math people understand).
To even delve into "pure" mathematics is something that gives me a headache. To make it simple for those reading this comment, mathematics major involves an obsession with proofs involving calculus level stuff in high dimensions.
That's correct. Pure math is the actual math major, everything else is baby talk. Most people think the math that engineers, computer scientists or the likes do is advanced as hell but that is nothing compared to the true, pure math that is 99% about proofs.
Almost no one finishes a pure math degree (especially not in the master or PhD variant).
The difference is night and day (exponentially).
"Math is like the mx+b stuff right? So hard, I can never think about that stuff."
[Discovers sheaf cohomology]
"I stand corrected"
@@ulzzangloverxD you think that the math that engineers use isn't real math? 🤦
@@benzemamumba It has nothing to do with the theory behind math. It's just application and a simple one at that. You don't even understand the logic behind it.
@@ulzzangloverxD only a smoothbrained dingbat would think that engineers don't do real mathematics. 🤡
I took functional analysis last year and it has tons of applications in quantum mechanics. The prof literally squeeze all the quantum mechanics I into the last 3 weeks of this course and we learned spectral integral in just one week which we would use it in many quantum mechanics questions, hardest one I've ever taken among all the physics, math and engineering courses I took in the past. Theoretical math doesn't mean it has no applications, actually, nothing I learned from a math class was nonapplicable, they usually have tons of applications in computer science and physics. If you think math is somewhat useless, either you don't understand math at all, or you are doing some boring and easy jobs which don't require you to use a lot math.
you sweet summer child
@@joshuaphillips8040 would love for you to elaborate on that 🙂
The distinction between theoretical* and pure is not really weather it has applications but in how much development is led by the applications. Case in point number theory I think is more often than not considered Pure mathematics even though it is central to cryptography.
Edit: this should read applied instead of theoretical. Hope that was clear enough.
@@andresfontalvo17 maybe, but what they said in the beginning of this video is not true, cuz theoretical math is not just purely disconnected from the reality
@@_Maxl344 to be fair I was refining your statement that theoretical mathematics doesn't mean it has no application.
There's not a strong line to divide applied from pure maths, but I reckon that what I gave is gonna point you in the right direction more often than not.
Also, minor point: all math is theoretical. Even when you are trying to solve a problem using math the first step is to abstract away as much real world as you think appropriate.
As a current math major, hoping to enter grad school next year, I enjoyed listening to this
I don’t understand but I want more theoretical math talks! Numberphile is a great UA-cam channel for that :)
Oh man I used to love topology and wanted to go into math, then we started doing the Very Long Proofs and I said Byeeeeeeeeeeee. Now I’m just trying to be a data scientist like everybody else 😂 It’s really cool to get to see a woman in an analytical-type field on UA-cam, especially when you’re thinking out loud on your podcast. That sort of personality in women is very underrepresented in this medium. Love it!!!! Hope you’re feeling better and thanks for your great content! 💛
@FriedIcecreamIsAReality bruh u define Homotopies in like the 1st course u take. The idea is not very hard to get and is essential for whatever u do after that(Fundamental Grps and all)
@FriedIcecreamIsAReality Their idea of topology is probably restricted to: coffee mug = doughnut.
I'm interested in what topology you actually studied as prerequisites and fields studied in tangent with topology are quite "proofy" areas of maths
You won't lose your virginity talking like that.
My undergrad degree is in math, and it feels so nice to hear the language of my people!!
Also mathematical modeling is huge in applied mathematics, especially right now with COVID-19 modeling! I just finished my first semester in an Applied Mathematics Ph.D. program and I hope to work for the Center for Disease Control or World Health Organization or some other organization where I can apply my knowledge of math to modeling diseases and how they spread. My very first research project (which, coincidentally convinced me to go to grad school) was in disease modeling. It’s super cool stuff! The fact that we can use mathematics to literally save lives blows my mind every day.
Yeah. THAT. 😡
That is great! I've taken Math modeling in the undergrad program and of course not nearly as rigorous as what you do in Ph.D. We used MATLAB and Python mostly to model our projects, I wonder what programming tools you use. Good luck.
I love these videos!!
Hats off man ❤️❤️❤️❤️
I am actually struggling with R4al Analysis and your doing PhD in Functional Analysis.. thats super awesome ❤
Oh wow, the last statement was actually interesting. I love the exercise about checking the fourteen results of combinations of interior and closure operators. It became my favorite topological exercise.
2 years late but the 14-set comment made me perk up a bit: in modal logic, using the negation and square operators (or the diamond), you can obtain exactly 14 distinct modalities and some people think that's also related to the closure-complement problem he mentioned (look up the mckinsey-tarski theorem) and also the comment about 14 tensor products.
That just made Matt even hotter. Brilliance is very attractive
I've never heard of your podcast before. But I am in graduate school for mathematics, trying to get my PhD. I actually want to do research in functional analysis. Maybe that is why your video was reccomended to me 😅
There's a common misunderstanding of imortance of maths. When I was going to study it, everyone around me thought I will end up as a teacher. That's a normal thing, most people don't know maths and are unable to imagine all its applications. Once you get into, you realize the benefits of having such background. I work now as a quant in a large bank, I'm not doing anything mathematically complicated, but I cannot imagine someone to do my job without deep understanding of basic math concepts and analytical mind set. I regularly interview candidates, it's sad how hard is to find a good one - there are very few graduates on the market and all have good jobs, so it got pretty tight, and salaries are pretty good. Strongly recommend to study it, if you have analytical mind set.
This comment is very helpful! I love love love math but as I research different careers it’s hard to find a job that actually uses a lot of math in day to day work. It seems like even data scientists don’t use a whole lot of math ( mostly just stats and programming). Do you feel like you get to use a lot of math as a quant and how are the hours and stress levels? I’ve heard that quants have to work lots of hours, that it can very stressful, and that most quant positions are only found in big cities like New York or the Bay Area
Quant is just one option, and it really depends on bank and departm. There's a front office where they do more or less what you would study on financial math studies (model fin instruments, option pricing etc, but it boils down usually to some programming). There are risk dep. (e.g. market or credit) where you balance between finance and different math models and statistics. There's validation with lots of coding, thinking and writing reports. Guys in NY and London tend to work long hours usually. I don't actually, my friends neither, but we may got lucky (it depends on the country and labour law). Besides quants, there are many other options. One of my friends e.g. work in game industry, analyzing behaviour of gamers, looking for weak spots in game. But I guess there's always some coding involved, and recently it leans towards machine learning more and more. Best
I'm doing research on modla logic and it's relation over a topological space this semester and was able to understand the back half :)
Lol I am not a math-oriented person at all, and actually do fall in the "I did calculus in high school... And that's it" camp... lol and although I am currently tired of my own struggles within Academia, I am so enamored with him. I loved this discourse!
Unless you work for the NSA, you’re probably overqualified for most non-academic jobs as a pure math PhD. But you generally do a PhD not because you want a job, but because you want to learn the material/do research, and doing a PhD is the easiest (some would say only) way to go about it.
as a science student i love this so much. We don´t get enough people talking about science and maths and all this cool stuff so thank you for giving him a platform
My relative has a PhD in maths and initially worked in encryption, eventually as a senior executive for a very large tech company, and has now returned to the same university he obtained his PhD from but in an academia-industry relationship role.
My husband was a math major and I sat in on one of his classes where he had to do proofs. It was so annoying to me because I just took the formula or whatever as it was... I didn't want it have to prove it.
For 18+
Sometimes I whisper math problems in his ears 🤣
Sorry but the last statement is probably false or you must be careful with the problems. Because if the problem is interesting enough your husband's blood will flow upwards.
For the poor mathematicians' partners out there. The secret is to ask an explanation of whatever the person is working on. Maybe you will have to hear a lot of unnecessary information but oh! You will see the flame in those eyes.
Ayo?!
Thanks for this👍🏽👍🏽
As a mathematics grad student interested in doing a PhD, thank you for posting this
That's so trueeee!!! I tell people the same thing. Once you get to a certain level in math becomes less about numbers
I love this I could listen to bro teach all day everyday
I am a Language and Literature Major and have a master in Politics, but this podecast episode was by far the most interesting I have ever been in Math (considering I also have an MBA in Finances). I really with to have more Matt with Math talk, if he was my teacher in high school I wouldn't be so "I hate Math" (most of my teacher seens to hate Math so why would I like it right?).
1/2 👋
I understood Kuratowski's closure complement, but don't really remember anything about tensor products. Still, pretty cool fact!
Huge respect to people who are this passionate about what they do.
If you can do pure math then you can do applied math. Despite Pure math not having applications it is certainly the more difficult as it requires you to think outside the box. I excelled quite easily in calculus, but pure math was quite the challenge for me, because my college didn't give us any prereqs before jumping into abstract. I luckily found external sources to undo my professor's failures. I took some applied courses as electives. Pure math can be absolute hell at times, but the bliss of discovering the complete structure of an idea is what makes it worth the suffering.
I beg to differ at the statement: "Pure math doesn't have applications". I would say it might not have direct applications but it do have applications in the real world. My masters project was entitled: "A survey of Robertson-Walker Spacetimes and Schwarzschild's Solution" which is related to general theory of relativity. To understand just the definition of spacetime, one requires a hell lot of pure mathematics like point set topology, theory of manifolds, Riemannian Geometry (parent of relativity). One of the very basic example is GPS, it could not have worked if there was no relativity and Einstein could not have developed that general theory without the theory of surfaces in higher dimensions (later called Manifolds). Similarly today quantum computing is not possible without pure mathematics.
100% agreed !!! The beauty of understanding even tidbits of pure math is a feeling nothing else can give you tbh. It's also 100x as hard as applied math.
So nice and I only found your podcast just today. Where to find the whole video
If you wonder if you'd be good at college-level pure math, I recommend the game Baba Is You (PC or mobile). I find that working through the most difficult levels feels just like trying to figure out how to prove a squirrely theorem, more so than any other puzzle game.
As an undergrad student in mayhs🎉i agree with him wholeheartedly
you're right, I did love that!
My undergrad degree was in Applied and Computational Math and I doubled in Econ. Believe it or not, it was hard to find a job immediately after graduating, since people don't see the value of math. My current job is a mix between library science, geography, and data science. The education I got is invaluable. No problem is too difficult for me to figure out. I work with a great team too.
Bro imma keep it a stack, I have absolutely ZERO clue what you were saying at the end but I 100% would like to hear more. Totally blew my mind.
Actuarial, computational chemisty, chemolytics, hedge fund/investment banking, etc.
Me also being a math major with the favorite number 14 because it’s my birthday. I have one more year of undergraduate, so I won’t take topology until next year (couldn’t fit it in with the chem and bio minors this semester), but I always find it interesting when someone pursues an education in math. Like as an undergraduate there’s only 5 of us in my graduating class that I know of, and even now no one understands what we’re doing, lol, so I feel the isolation already.
I am an undergrad for math at LSU. There are only 200 math majors in all of the 25,000 undergrad students. I totally relate
I work in AI and machine learning. I have several highly successful colleagues with PhD’s in math, EE, nuclear physics… you name it. We even had an intern a few years ago who was applying topology to real world data science.
Any advice on how someone with a geoscience degree can get into applied mathematics, I’m really curious
Interesting video! Functional analysis is an interesting area and will always be one of my favourites. After graduating my masters, I wanted pursue a Phd in operator K theory in the UK (continuing down the route of functional analysis and topology) but never ended up securing funding. However, recently I have just secured a scholarship to study Pure math for computer science (Birmingham uni) which looks very interesting to me and a nice challenge. If anyone has any questions about maths or anything related @ me and I'd be willing to help.
I did my early graduate research in novel solutions to the hypergeometric differential equation; to this day, aside from my math lecturers/professors, I have never physically met another person who even has even heard of the hypergeometric differential equation.
Interestingly, "Pure math" includes things like number theory and (as Matt did) functional analysis are fundamental to real applications - functional analysis covers a bunch of stuff related to AI and cryptography.
Matt is fiiiiiiiiiiiiiiiiiiiiiine!
Yeah I’ve gone up through ordinary differential equations and still have no idea what he’s talking about at the end there 😂. I have a massive amount of respect for someone who can remain that passionate and driven in their studies and achieve such a high level of knowledge that even other, similarly intelligent people can’t understand them.
4:05 isnt the nullset that from which one can construct the natural numbers? I guess as one defines 0 to be ths symbol for the nullset this works too.
It is amazing to see person who really thinks what i think too
I went to a great high school with an advanced academic program. I was able to go through calculus 3, got a separate semester of trig, and a year of stats. I had algebra in 7th grade, geometry in 8th Algebra 2 as a freshman, and a semester of trig as an elective. I joined the Army out of high school and earned a BS in mathematics. It was easy for me because I could ask the professor if I could take the midterm and final the first week, if I passed I didn’t have to attend class, if not I wouldn’t miss a class. I later earned a MS in information systems, and a PhD in electrical engineering. I retired from the military and started a engineering manufacturing business. What many miss about the study of mathematics is that it’s about problem solving and theory. I hire people now for my business and I always ask about their math skills. People good at math tend to be tenacious problem solvers. The US needs to change is math curriculum in schools. They need to narrow their focus and ground students in the base skills of arithmetic and then algebra. It doesn’t have to be fancy, just logically consistent.
Analysis is super useful in AI with the high-dimensional embeddings we use!
PhD physical organic chemistry here. applied math for me was Schrodinger field equations... really started to love maths at that point
when he started explaining why his fav number is 14 i was like 'yes i definitely understand everything you said down to the last bit"
Came back to this video :) I am now officially getting a BS in Statistics and MS in Applied Math.
That ending was great LOL!
I feel like Functional Analysis is probably the most useful of the pure maths fields. I mean ... knowledge about PDEs come out of Functional Analysis.
Omg the forget about the numbers thing is real. Yes there's the fact that that you mostly use letters, but also math is really interested in explaining everything, even the stuff that's obvious. Like he was saying about the - (-1) thing. In first year math I took a course where we couldn't assume anything until we proved it. We had to prove 2 existed 😂😂
Personally abstract algebra was the turning point regarding the use of variables and letters instead of numbers
My math knowledge stops at AP stats and college algebra. I teach math to 3rd graders, so I definitely don’t understand any of this.
That said, I love hearing people talk about things they love, even if I don’t understand.
I thought I was good at math when I was in high school. I got a perfect 800 on the math section of the SAT and tested out of the math classes required for freshman in college. Sophomore year I took a 300 level Linear Algebra class and it kicked my ass. Calculus came pretty naturally to me and felt intuitive but then dealing with matrices and vector spaces was a lot harder to wrap my head around. I ended up dropping out of school that semester for other reasons but it was definitely going to be an uphill battle to pass that class.
It's so strange to me when folks say linear algebra is hard. It was always the easier parts of math for me at least.
I mostly understood what he was saying. Also hes right that numbers less frequent because of Strings and Languages in set theory
My brother is doing a lot of math for his engineering degree and it is really funny having him explain his homework to me. It's like a different language and I was good at math in highschool
I think there comes a stage or rather a level of maths knowledge that becomes completely abstract that only gifted individuals can really understand...
After calc 3 at an engineering college i was sure glad to be done with doing math with letters
4:08 Me too! Apart from that, we have nothing in common.
I have a B.S. in math and yeah he stated it really well. I wasn’t really following what he said at the end. I know what tensor products are, but not really how to do them
" if you're good you go to tech , if you're evil you go to finance " love it 😂
It should be- if you’re evil you go to Finance. If you’re really evil you go to tech.
You can easy learn programming, learn physics , mechanics , you can do anything - this depends to man who practice mathematics - , like me i don’t have phd in mathematics, but i have to degrees in structural analysis and mechanics, and know i do programming, complex numbers, operating system programming,
And i have my personal project :
1. Theory on programming languages and human language.( here we study any kind of communication system, wave signal or visual signal, feeling signal)
2. Complex analysis - studying of inverse functions of gamma type -
As a high school student (graduating later this year) doing physics, philosophy, specialist mathematics, mathematical methods (South Australian Curriculum)+ two other subjs which i am not fond of but required to do but regardless after graduation i hope to actually complete the following books which i had for a while now but never dedicated time to read them
Naive Set Theory by Halmos, P. R.
A Book of Abstract Algebra by Pinter, C. C
Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus by Spivak, M. D.
Calculus: An Intuitive and Physical Approach by Kline, M.
‘I’m convinced there’s a connection between these two facts’ is the most mathematician thing to say.
This was funnier than it was informative, thanks!
Kuratowski closure... petty interesting construction...
Unfortunately as someone who studied computer science - it requires this crazy theoretical math. I hated it but I had to do it to graduate and now I don’t use any of it :P
I'm working towards Computer Science right now and wow surprisingly it turns out that learning math with minimal communication with your teachers, no access to study groups, unreliable access to tutoring, etc... is pretty hard.
@@yukikanegawa7470 crazy, isn't it? Who woulda guessed
My bf is a medical physicist and he was struggling in the first year of his Bachelor in Physics, bc of math. We came to the conclusion that math is a language you need to speak to actually get the hang of it. And we both don't speak the language. I'm a cultural anthropologist 😂
It's a context free language. You can generate words using a parse tree.
I was in the same boat as you thinking math is a language and was intrigued by it while being scared of it at the same time. After I got my bachelor's, I have no respect or desire in any proof based math or theoretical math because only 0.0001 people care about it. So, people say it teaches discipline and exercises the brain, so does other fields like philosophy, psychology etc. Now, I only respect and dedicate my time to applied and computational maths.
Simultaneous thoughts: wtf?
..but also, I love this lol
1:08 Bro's out here slinging Hilbert spaces and bounded operators left and right.
You calculate the x and y square spaces in order to be specific which opponent you're bound to go up against with whenever you enter a field of battle in pokemon
Amazing video as always! Question for you: what do you think about Yanis Varoufakis's thesis that we no longer live in capitalism but in a new form of feudalism, which he calls Technofeudalism. Yanis Varoufakis wrote a book with that title where he expands on this thesis. Saludos from Monterrey, México!
One reason People do math major is that it’s the only challenging stuff that is interesting enough. You can certainly try some grad analysis class and grad algebra classes at sophomore and that seems quite invigorating. Otherwise you just take business class and got free A and class high with 2hr weekly effort and go to trading firm working with brain dead people having no idea what they are doing and just running codes written by others
Damn .. too real 🥲
Reference to the second fact about the number 14 he mentions: en.wikipedia.org/wiki/Kuratowski's_closure-complement_problem
As someone with a math degree, this is very accurate. It becomes way more proofed based (which is a lot more fun) but also no one actually has a good idea of what gets learned in a math degree.
you had me at tensor....
How in the name of god is Matt still single?
I'm wondering the same thing!
He’s not, he said that in this podcast 😉
Thx. I haven't been able to listen to it all. Thw woes of being a math teacher in the USA right now
I had to look up projective and injective association of Banach spaces. He's talking about mapping in tensor operations. Projection is a concept that exists in vector spaces that you learn about in linear algebra... I'm not 100% sure that projection in the context of vector space implies the same idea as projection in vector space. I've, at least, heard of that. I have no idea what injective association is. All of this sounds like the stuff you'd learn if you were writing proofs involving the Einstein Field Equations that describe how space and time bend under the influence of gravity.