Math People Are Elitist 

I failed my first math class in university five times, then barely passed. I then spent a whole year (from May to September) studying math non-stop, 4 or so hours daily to pass my second math class, which was mostly calc 2. After that, the next two math classes I had I breezed through, calc 3 and tons of probability etc. hard work pays off.

If you were an "elitist" before, these books will put you in your place. Try doing ALL the problems in the mentioned texts and you'll become humble or you're a genius. Whenever I feel really knowledegable, I simply get humbled rapidly after trying to understand and work problems in the books. There's always something much more to learn.

I failed college algebra 3 times, I got a D in Algebra 2 in highschool. I went to the basics and relearned math, now I am a math major going into senior year. I studied so much, to understand what math was trying to convey to me. So worth it.

Although there is a certain degree of elitism among mathematicians, it's not necessarily the case for the most part. The problem in mathematics, however, is the lack of good exposition. Yes, you may convey lots of interesting stuff in a rigorous text, but you don't have to let rigor get in the way of clarity and good exposition.

I think elitism is the wrong word, but it's an underlying challenge in maths education (particularly at the early level), where you spend quite a lot of time "learning the language" without really doing anything with it. To take an analogy I read in an excellent book (I believe one of Jordan Ellenberg's books?) - it's like if an English class was focused entirely on things like spelling, grammar, proper sentence structure and so on, but you never read any books or never wrote anything of your own. Or if you had a PE class where you did nothing but drills and conditioning, without ever playing a game. It's like how people who've stopped studying maths at school often see it as mechanical and rigid, whereas people who go study maths degrees or do further research treat it as an art and see it as something really creative - because they get more chances to play the game, even if they have to do more drills along the way. Rigour in math is important because it *allows* you to explore more of the landscape and be more creative, just as a wider vocabulary and a stronger understand of grammar can help you become more eloquent and make your writing more impactful. But the way maths is presented as an early level makes rigour feel arbitrary and mysterious, because you stop before you get to the fun stuff - there's no payoff for all that rigour, so to speak.

A powerful opening sentence: "This is undoubtedly the most important function in mathematics." I thought it was an especially audacious statement the first time I opened this book, but I quickly came to agree

My father, a university math professor wouldn't consider me as a person until I got my BSc in computer science. My next one was a psychology BA. Now I am a child psychologist. Go figure.

I remember talking to a med student and telling her that the lecture notes I had to study for a 1 semester course were around 80 pages long. She laughed mockingly. However, I explained to her that I could only get through 2 pages an hour, on average. Her jaw dropped.

What I've realized is that your success with math very much depends on your confidence. I have some anxiety issues regarding math that made it harder to learn. I'd end up crying even thinking about doing math. At it's peak when I was younger, I failed pre algebra 4 times. Since you might learn at a slower pace or have trouble with a concept, you come to the conclusion that you're just stupid, and you're not a math person- which in turn makes it more difficult to learn the math because you grow to resent it, because you always feel like an idiot and that really holds you back. I still greatly have trouble with my confidence in myself but once I thought of math as more of a skill to be worked upon then some concrete determination of intelligence, I began to understand concepts way better than previously. When your mind is clouded with self doubt, it's hard to focus, and you immediately assume you're going to fail because you're "too stupid." A change in mindset and a boost in much needed confidence is the most important thing to becoming better at math in my opinion and it is so depressing our schools fail to ever do this. I think that the kids that feel stupid that observe the kids who excel in math and play a great deal into giving math this elitist idea where only the naturally gifted can enter, and you never will. Math skill is so often tied to the ego and we write it off as some kind of natural ability when in reality that couldnt be farther from the truth. Seeing math as inaccessible for some people by design is an anti intellectual idea for everyone involved and yet our society, parents, and children believe this and the effects are destructive.

I’ve met with elitism in many fields and the critical factor (since it’s necessary to form some definition of the word) is how willing people are to put their ego aside as they assist other people into their world. Mathematics is notorious for removing the scaffolding. Time and time again I’ve spent hours trying to get from step 1 to step 2 when texts could easily have spelt out intermediate steps. I got the impression it was displaying some form of weakness to explain the reasoning the author or teacher went through when they first set eyes upon the subject. It’s easy to see how musicians or visual artists or chefs could be elitist, and it’s just as easy to see how they can make it easy and enjoyable to welcome others into the fold. Mathematicians have a lot to learn in that respect, if even they care.

The problem I've faced with math during the middle part of school, was that we were only taught HOW and not WHY. I started school loving math and slowly turned into hating it, for me, the why, the story on how that was discovered and what problem does it solve, is very important. Then after that, practice, of course, but without the why, it's soulless.

I feel like knowing a lot of math definitely makes one susceptible to "elitism". I am just barely breaking into undergraduate math and I can already feel that "wow, I'm pretty smart!" feeling creeping in when I finally understand some results. The key is to just have fun with it, make some fellow math friends, but don't look down on people who don't know math. It's a blessing to have the time to be able to study math for a living! I used to get annoyed at "less than clear" expositions, but then later I realized...that's exactly what you want once you get to a higher level. It's like boom, boom, boom, let's get to the next result. There's an exposition out there for literally everyone at every level. That's why I love your channel because you really help people find the resources they need (and all the encouragement is awesome too!).

When I think of elitism in mathematics, I think of the pedigree books where people trace their PhD mentor lineage back to Euler or Newton to validate their self-importance, or people who explicitly state "if x-proof isn't immediately self-evident to you, you have no future in math." Deliberately discouraging people from pursuing math is definitely a destructive form of elitism.

I think you misunderstand what people mean when they say someone is elitist. Elite and elitist are not the same. If you are elite in the math world, that is fine in my book. The issue lies with elitist people. Here is a definition: a person, P, is elitist if they belittle, mock, or make fun of those who are not as skilled as them, if they insist that the other person is not a math person because they haven't reached P's level of skillfulness, and/or if they try to exclude other people from discussions who they see as lesser to them because of a perceived inherent mathiness quality, rather than encouraging other people to improve their skills so they can make substantive contributions to a discussion. So an elitist isn't just someone who is good at something or renowned for a thing, but decides to be an asshole about it. Elitist as an adjective usually refers to the attitudes of such people. One can be skilled without being an ass. I hope that helps.

If the most notable (supposedly positive) features of a book is that its "really tough" and "not for the faint of heart" and "takes a lot of effort" to read, perhaps the elitism criticism isn't very far off… We live in a culture where being challenging and unapproachable is apparently a positive feature. These are not the goals of education. They're the goals of elitism.

One thing I consider very elitist in math is that a lot of content is hidden behind paywalls that regular people just wouldn't be able to afford. Especially if they don't know what to necessarily look for. Without having access to books from my library (and sometimes just doing plain piracy out of laziness), there is simply no way I could have completed my PhD. Sometimes I just needed to check one or two pages from a specific book/article and I'd have to pay like 30$ for having access to those said pages. I'd say though this is a problem with academia in general: a lot of science gets mystified because the sources are made inaccessible by publishers due to extravagant fees. Don't even get me started on undergrad college text books which is a scam on its own.

The trouble with math(ematics) on the whole, is that "scalability" of the field has never been considered meaningfully. By "scalable", I mean that difficult elements of the field are not intentionally simplified for wider distribution of acceptance. Mathematics, as a culture, seems to have an inbuilt desire to maintain it's historical levels of unapproachable abstraction. The cultural behavior within Mathematics of naming methods and algorithms after the people who discover/invent them is a good example of dirty architecture presenting itself. It is very difficult to mnemonically comprehend systems if the nomenclature of the objects within the system is based on something which is completely disconnected from the conceptualization of what said object does/is/behaves/acts as/is related to/is for/etc. In my mind, Mathematicians aren't "elitists" exactly, but most of them just not clever/smart/wise/courageous enough to do the extra work of helping the beauty of what they perceive and play within to be transferred maximally to the rest of our human tribes. The exception to this previous statement is the guy behind 3Blue1Brown, he does a LOT of the extra work to de-abstract and refactor the concepts without losing any of the deeper modalities. 3Blue1Brown is the Carl Sagan and Richard Feynman of our time, at least in terms of being an interface between most of the human population and the abstract beauty of the deep realities of the universe.

I dont think that mathematicians are elitists, it's just that they are aware of the huge effort one has to put in in order to understand the subject. Someone outside that circle might think of the mathematics community as a closed one, but it's not due to some sense of superiority, it's just that it's actually very hard to become a mathematician. Once you get your degree no one will exclude you, instead almost everyone will be happy to have a new colleague working in the field.

As I've come to see it now, Math itself doesn't have to be hard. It's just hard in general to do any great thing like Math because it requires a lot of work, and it's simply hard to do a lot of work. And then it's also hard to communicate the product of all of that work, especially if you're trying to distill it for an audience that doesn't have enough experience or familiarity with all of that work. But all that being said, it's toxic if successful people don't acknowledge how hard they had to work, how often they've had to learn from failure, how often they still make mistakes, how fallible they still are, and how many other people deserve credit for their development and progress. A lot of elitism boils down to that. Some people are only able to devote so much time and effort to math because, for various reasons, they're social outcasts who don't get as distracted by people. Elitism can occur if they interpret their success as a way of paying back any real or perceived unfairness they experienced from others. Mathematical maturity is also very powerful, and I'm sure there are ruling class interests that don't want to make it easy for the masses to match or surpass them in this regard. So that's likely a component to elitism, too.

I am a physicist so mathematics is my language. Like learning any language, it can be difficult at first and you have to stick with it. This I can confidently state: Mathematical intuition can only be developed through practice.

I think it's the obscure and verbose sometimes antiquated type of language math books use. I remember reading somewhere that it's on purpose and a very old habit of competition. The others could not figure things out so easily. I know for a fact that it happens a lot in music theory. What mathematicians could do is work together with language specialists and put those concepts in simple plain english terms. Many complex books could be completely rewritten that way it won't scare many people away the way it does now.

Yes, math is probably the most elitest subject. I barely understood math in high-school, c's in almost all of the classes D in trig and D in algebra 2. I have a degree in anthropology partly to avoid math, but started in on statistics and probability. I randomly started watching math youtube and really fell down a number theory rabbit hole. I taught myself calculus and i am currently working through linear algebra now. It isn't easy exactly, but it isn't difficult either It's very fun and relaxing. the issue to the reputation is the emphasis everyone places on the "work" "difficulty" "this isn't for the feint of heart". Math is just another domain of knowledge it isn't difficult, but like every domain it takes time to learn. It's not magic it's just a precise language to compare, one thing to another thing. If it was not eliteist the emphasis would be on the time investment required to obtain the tools not on any value judgement inherent to the subject itself. No one considers trade school "difficult" but it usually takes a tradesman 1-4 years to reach journeyman and 12-16 years to master the craft. math isn't any different.

Having failed the mathematics entrance exam at a community college, I was required to pass a basic math class. After failing the self-directed option - twice - I enrolled in formal class to get through it. Took me three semester to pass the math competency requirement. My major was Liberal Arts, which required three more math classes - advanced algebra, trig, yadda-yadda. While I was scared I would not be able to pass thoses next classes, the foundational skills I learned made the math classes easy. I ended up with B.S. in Mathematics/Computer Science. But, it was a lot of work for me. Many Saturday nights I stayed home while my friends went to parties. I still have my five three ring binders of handwritten problems. Good times.

Four months studying “Baby” Rudin cured me of any ambition to major in math, but taught me that I was cut out to be a math user instead. Rigorists are obsessed with airtight proofs, whereas users gain intuition by studying definitions, examples, and counterexamples. Ironically, the rigorous style inflicted upon math majors is opposed to the exploratory style by which discoveries are made. Euler was no rigorist. Some say that Bourbaki killed creativity, but there is still hope. Nonlinear dynamics (chaos) is messy enough to defy rigor.

I did engineering undergrad then did comp sci for my masters. While I cant speak too much for math majors specifically, I think stem has a problem where the way it is traditionally taught is not conducive for understanding. In undergrad I would constantly leave lectures lost and while I was able to outperform the other students just enough to get a decent grade, I rarely felt like I was able to intuitively grasp the subjects. I had just assumed that these subjects were too difficult to understand intuitively. However, with computer science, you have a wide collection of online resources available that just aren't present for high level engineering classes. So in these debatably more difficult masters level CS courses, I actually was able to develop an intuition for the subject from these online videos. At this point I don't believe any subject is prohibitively difficult, just poorly explained. And I think traditionally most textbooks and courses aren't designed to optimize understandability, adding to the perception of the subject's elitism

Henri Cartan made it to age 104. Some mathematicians live a long time: Dirk Struik made it to 106; Walter Rudin lived to "only" 89. They all had good lives and while I encountered only Struik, I tend to think they were all good people. Struik was hardly an elitist: his Yankee Science in the Making is perhaps the best book in that field.

As someone who is more into the feild of art, I find myself realizing how similar older math people and old artists are. The way both side talk, the way both side approach new information and learning and skill, are very very similar. In the end, when both sides reach almost their absolute peak, ive found how humbleing they both talk and speak about their craft. Both feel like two sides of the same coin. Some of the smartest people i know talk like artists, and the most skilled artist i know talk aproach their crafts like mathematician.

I had a math teacher in high school who was a super elitist. I mostly remember him getting frustrated that a bunch of high school kids just didn't "get" algebra without him having to you know, actually teach it to them. It was a very surreal experience because he'd go on about stuff none of us understood, then we'd spend our time basically having to self-teach.

To do well in pure math one should be blissful and should be free from all kinds of pressures. Most of the students when they learn math from books like loney, Bernard and child are under the illusion that pure math is is similar to the math found in books like loney trigonometry or hall and knight. When they read books like rudin they feel it is totally different from what they thought. things we learn from books like loney, Bernard and child, hall and knight etc are very important if we want to excell in pure math. The skills we acquire from these books help us in doing pure math. We need those skills if we want to be comfortable with inequalities in pdes, multivariable calculus. These books are very important even though they don't follow a rigorous approach. We will not find any epsions and deltas in books like loney. But the skills we learn from these books are needed to grow as a pure mathematician.

One way you become an elitist is thinking you're in some way "superior" because you're good at something. Writing a book and starting it by assuming the reader knows abstract algebra isn't that, it's just a practical decision about what audience you're focusing on in that particular work. Being aware you have skills X and Y and putting that to a useful purpose is perfectly OK, but you have to be constantly vigilant to not let get to your ego. Every human being who's a part of society is every bit as important as you. No more, no less. Never forget that.

I won't say that Complex Analysis is complicated to read because it's rigorous. I would say that it's complicated to read because the author doesn't present all the details in the text. There are a lot of missing steps and you have to fill them out by yourself. Sometimes, the steps to fill out are not obvious! My comment also applies to Rudin's text.

Whenever I tell people that I'm a math major, they say, " Oh, you must be good at math." I tell them, "No, I'm not good. That's why I'm in this program; to get good." I, for one, am quite a humble learner and hope to stay that way 🙂

This question and its responses are focusing a little too much on the individual and missing out on the institutional and societal level of what makes mathematics and a lot of the people in it elitist. Also for what is explained, I don't think elitism is the best term either. Oftentimes, you may have the potential to be great at mathematics (or anything really) but the demands of our lives often take a greater precedent over studying mathematics. Being able to sit and study for 1-4 hours on a given day isn't something any regular person in the U.S. can do. Most people can't afford to sit for an hour to just study mathematics let alone 2 or more. The language of the books is mentioned aside. What feeds into the elitism in mathematics is the social standing of the people 'doing' the mathematics. You're more likely to encounter someone that managed to complete a university degree (B.S) who comes from a middle/upper-middle-class family or higher than someone who is low income. And a lot of the values from people in the middle/upper-middle is the perceived idea of, 'if you work hard enough you'll make it. This is, on one hand, sorta true(barely), but misleading. You can work hard while staying at your parent's place and not worrying over finances while they do that work, meanwhile, someone who isn't middle-class can't afford to do that, and coming home from work to study mathematics is rather exhausting. Often people search for an example of someone who was in that circumstance and made it work ignoring the dozens, if not hundreds of people that it didn't work out. To diminish elitism in this or any field would require more than modifying textbooks.

Mathematics is not hard (especially if you love the subject), rather there is no respect for it outside of Elitists who believe knowledge should only be permitted to the 1% rich.

Many math people get angry when somebody doesn't understand something that is obvious to them (because they are several levels above in terms of knowledge, not because it was always obvious to them). Then they act superior and often indirectly call you stupid, instead of explaining. I haven't met a mathematician that could explain math well, in terms of geometry or common life situations, which can definietly be done. My major is pure math btw, and I experienced this frequently at the beginning few years of my studies.

Controversial take, but I think the concepts aren’t nearly as difficult as they are made out to be, and it’s more about memorizing vocab and conventions than anything. Once you’re introduced to the infinite series for the exponential and how it relates to Euler’s formula etc, it’s hard not to understand it… the problem is just that those explanations were for some reason not widely available outside of elite universities until a recent explosion of math RU-vid videos. Modular arithmetic? Kids can learn a lot of it as easily as non-Modular. But we just don’t introduce it to them. In fact it might help with other arithmetic to teach it first

It surprises me how many people use Rudins books for beginning graduate level classes given how abstract they are. Almost every book on analysis that I've read (beyond the basic measure theory and functional analysis) has been much more down-to-earth, and quite frankly more user friendly than the Rudin books. Also, in almost every hard problem in analysis one always starts off with the basic, familiar spaces. For Banach spaces it's L^1(R) and L^○○(R), and for hilbert spaces it's L^2(R) and l^2(R). An intimate familiarity with these spaces is, in my opinion, more valuable than spending weeks discussing F-spaces, Frechet-spaces, and locally convex spaces.

This is an incredibly powerful channel. I felt like I could just about keep up with trig and then had no clue with calc.I assumed I’m just one of those “not smart enough/doesn’t get it” people. Each of your videos has me intrigued and inspired to open up my old math books and have a crack at it again.

All 4 are analysis - blah. Not my cup of tea. I think "rigorous" is not necessarily the same thing as "difficult." If a textbook is difficult, it might be because it has a lot of prerequisites (which the reader might be missing), or because the author is excessively concise. As an author, maybe you want the reader to fill in some details: maybe it will be good mental exercise. But on the other hand, excessive concision might make the book unnecessarily difficult to read. So a balance is required. My favorite books are books that are both rigorous and easy to read, even if you occasionally have to fill in a few details here and there.

this is NOT why Math is an Elitist field. Mathematics is for Elites only because it doesn't matter how good you are at math, your research papers won't matter if you don't have a PhD. If I solved the Navier Stokes problem, I would not get full credit if I did not have a PhD because no one would read my paper unless if I had a PhD reference who wants to steal credit from my paper.

Well, depends on the definition, but math is elitist in a way. However, not as commonly understood. Arguments from authority will not work. I am Prof. Dr. Fubar and your counter example is therefore wrong ... will classify as a good joke. Further, your math is wrong therefore your drone can not fly will also not work if the drone flies. There are local errors in math that do not matter, like an even number of sign errors in a linear enough setting. As someone who studied physics and mathematics the former makes you somewhat relaxed with respect to certain kind of errors ... they do not really matter for applications.

This might be an unpopular comment, but I tend to think some people shout 'elitist' or 'pretentious' about anything they're intimidated by, regardless if there's much substance to the accusation. This happens to be true for math, classical music, drinking black coffee... list goes on.

Gatekeeping? Yes, maybe. But you can always find more pedagogical approach to those books. These elitists' books have very specific audiences in mind and if you are not one of them, it is not anyone's fault. Also, there is more to maths other than the most obsessive-compulsive part of maths (analysis).

I can think of many times over the years, where someone's day was made by simplifying the cryptic mess they were taught (typically by people who didn't really love math, or had the "I am smarter/better than you" attitude/illness). I love seeing the "lighbulb" go off, when they understand something new - and their confidence is bolstered. I remember being at a wedding, and a lady bought me a nice lunch after explaining how a LASER functions - making people happy with knowledge can get you fed! Sure, a lot of math is complex ... it is an equal oppotunity heartache ... but much of it is simpler than many teach it to be ... and there's nothing like when it clicks ... why we like your channel. Cheers

I think math can definitely be elitist. People good at math can invest their time into it. That's elitist for a lot of people who have to deal with bad mindsets around them, things to do, and quick dopamine giving them real results. Math is a slow and humble thing that people considered "elite" can do more easily (ie. actually do it.)

"Mathematicians are elitist because they're better than you." Fixed it for you.

Not a math major but currently work often, in an academic setting, WITH math majors. I've interacted in broad spectrum with many across all disciplines and worked in teams where Kineseology students were working every day with ChemE and Stats students. In my experience there certainly are math elitists, but the correlation is not necessarily in how much rigor they have in their studies or how much they know about a certain subject, but rather how often they have worked with other disciplines and other people in general. I've met math undergrads who frankly seemed to be elitist out of clear lack of self-confidence and drive to be great, and math post-docs who intently listened to me talk about boring engineering project-related subject matter to the point of taking notes(which really blew my mind). Those who tend to be more personable, empathetic, and easy to work with always have a sense of wanting to know more. Those who tend to not listen, criticize, and are hard to work with always seem to think there is nothing more they can learn. The Dunning-Kruger effect might be totally pseudo-scientific but it is certainly useful to have something that describes this phenomenon :)

They are elitist because they make mathematics difficult - I would be better for authors to increase the size of their books to include more history and context showing how dead ends were worked around and why certina approaches matter. It has been said quite rightly that most books in mathermatic are "cathedrals" jammed with "rigor" - we see the amazing cathedral but NOT the scaffolding used to build the "rigor" into the cathedrals - a most self-seeking attitude - hence elitism. They say struggle more when infact they had a helping hand from professors at the graduate level "passing on" the true feel of mathematics - only after many others have been filtered out (left the field for other paths).

The Baby Rudin book looks really fun, I will definitely check it out.

'Baby Rudin' is to learning analysis as artificial insemination is to sexual reproduction. It's not good, it's not bad, and there are more fun ways of going about it, but at least it gets the job done.

You are quite correct, the 3rd edition of Baby Rudin now has Dedekind cuts in the Appendix. I have all these books btw! My treasures!

I want to buy such these books i love maths so much and i am from egypt

Math people are not elitists, but they ARE absolutists

Yo, I will solve the whole baby rudin by the end of this week.

The thing is, there is nothing preventing you from joining the club.

I think elitism is present in any discipline, and it's most noticible in especially difficult or challenging disciplines. Math is no exception. I also think any type of elitism is always unjustified, and any discipline would benefit from less elitism about it, because it's so often used to gatekeep and prevent others from practicing the discipline. I think math is a great example of something beautiful that gets disregarded by newbies because the people entrenched in mathematics don't take enough time to introduce newbies to the coolest parts.

Thank you for emphasising the hard work that goes in, there's such a societal discourse around "maths geniuses" that really affects the perception. Such an interesting video and comments. I worked so hard at GCSE maths (exams age 16 in England) and wanted to get the top grade but couldn't (and I get quite bad 'maths anxiety'), my husband on the other hand barely had to put any work in to get the top grade and he took Maths A Level (17-18yo) early. I find it so interesting how these books look like they're written in a different language but if you can't read a book in a foreign language you'd never say "oh you're clearly not smart enough" we'd say "oh you just can't do that yet but you could if you wanted to". Similarly people who aren't good at English Literature (like if they find it hard to write essays on books for example) don't get told they're not smart enough (not commonly anyway, I'm sure someone somewhere has been!), It's just "oh they're not very interested in that". But if you keep getting questions wrong in maths it's like that says something about you and your value intrinsically as a person. Anyway I'm still not good at Maths (I find fairly basic algebra hard tbh) but I'm still trying, just to try and learn something new.

I don't know if they are elitist but it does seem that there is a subset of mathematicians that have set out to write the most unreadable math book of all time.

I was taking a conference course with "Papa" Rudin (aka Real and Complex Analysis), and I couldn't believe how hard the book was for me. I would sleep through class to an A in my calculus courses, but this book made me want to cry at first. I have to check myself because it's very easy to feel elite because it's so far removed from almost everyone else's mathematical understanding and that sense of superiority tends to creep up on me. That's usually when I get brought down to earth. I was working on some problems at the pharmacy as I waited for them to fill an order and the pharmacy tech asked me what I was working on. I showed him the book, and he was like "Papa Rudin... nice"... Looking back it makes me laugh, because I was such an ass. I was thinking, this pharmacy tech isn't gonna have any idea how hard the thing I was doing was... lol, thankfully I've had plenty more experience like that to finally get it through my head I'm not as smart as I thought I was.

Well of course math people are elitist, but certainly not in a bad way. They're the only group that deals in absolute certainty, which takes tremendous care of a kind not really seen in other fields. But many of these folks, like von Neumann, Lanczos, Lebedev, Bellman - and many others - are also happy to get their hands dirty with practical applied work, and provide tremendous service for physics and engineering as well.

Apostol's book Mathematic Analysis is also an excellent book and as rigorous as a math book could possibly get.

0:39 As much as I'm not denying your lived experience, I think it's worth pointing out that math being "hard" is subjectivity being slipped in. Excelling at any given thing is "hard" but what often strikes me about "math people", or other interests which are often given as schenectady for 'intelligence'; chess players and economics majors also tend to be solid examples of this, is a tendency to overestimate their general intelligence based on their internalized cultural perception of that interest and make axiomatic assumptions about the world around them and treat these as a null hypothesis and themselves as the standard bearers of all reason. Let's take 'elitism' as an example; a particularly difficult or rigorous book on a subject doesn't strike me as meeting the definition of 'elitist', but to go into a video without really knowing what 'elitist' means and, perhaps for a malformed conception, defending the relevance of particularly difficult material is.. kind of illustrative of the sort of blind spots that might crop up if you're self-conception is 'doing a hard thing for smart people'. I have notebooks full of astrology, much of which is mathematical in nature and is not far removed from something Galileo might have possessed, I make no conceit of this being the study of science (though it is as complex); what would be elitist is the belief that your practice is intrinsically superior or separate from your field. Of course, I do not think this all adds up to you being some sort of 'elitist', but rather that I simply relate to dealing in objectivity and struggling with subjectivity and thought you might benefit from a different perspective.

I suggest everyone listen to the former bourbaki members conversations on YT, i.e. Jean-Pierre Serre, Jacques Dixmier, Pierre Cartier and Alain Connes, even if you don't understand anything about the content it rings like poetry to any math loving ear :)

Should also added TOPICS IN ALGEBRA BY I.N Herstein Btw, great video.

They kind of are, just today I asked a math question on the internet and they told me that I shouldn't care about it because I'm a physicist.

I feel like the problem with mathematics in an educational setting is how often we're taught material in a class, and then subsequently the next class barely mentions much of the previous material. Sure, Calculus is just an evolution of basic Algebra, but it's not the most important part of that class. Not much of what you learn in Algebra, and even Pre-Calculus ever really builds into it unless you're taking several Calculus classes in a row. It's a very harsh and sharp learning curve for many as a result. What also can make it more complicated is how teachers/professors with these more complicated math subjects may be brilliant at them, but can't find the words to explain all of the mechanics that go into them. While it is no doubt the student's job to seek out information and study it in order to get better, having a teacher/professor who can comfortably explain their material in easier-to-digest wordings and lectures helps tenfold, and having a bad teacher/professor can really demotivate you from wanting to get better at it. Another fundamental issue of mathematics classes as a whole is the odd lack of freedom. This may just be a problem in classes before later Calculus, but a lot of teachers expect you to solve a problem in their way. The problem, of course, is that math has multiple different avenues that allow you to get the same answer in a logical way, effectively allowing different people to use a favored or multiple kinds of methods. Teachers that expect students to show their work on assignments, in my experience, would dock you for not writing absolutely every part of your problem solving correctly, or by using the "wrong" method. I understand the intention is to challenge students to solve problems in new ways that change how they think about the way they solve math problems, but it ends up alienating and confusing even more people since now they have to throw all their understanding out in favor of forcing themselves to think in a new way the professor expects them to, even if it doesn't help them fundamentally. I just think the field of mathematics needs to humble itself and re-think how they deliver their material in textbooks and lectures.

Math can be used for anything. 🤗

I do think that it induces "elitism", my friend stopped coding because he feels he is too good at math (he is in 10th std). And, he says coding is for suckers and practicality sucks then ponders over theories and proof. For example, when I told him about TensorFlow, he asked what is tensor and told me that we should first know math to know tensor, but there's no need for those to understand TensorFlow. Probably this is a mental disease. I don't know really.

Math people are driven by challenge. By definition, the Common is boring and well, common. By definition, Math people are elitist. Like mountain climbers.

I like how this video literally doesn't even address Elites at all.... just some guy showing off cool math symbols in UNDERGRADUATE math. PhD mathematics involves Algebraic Geometry/ Category theory/ Proof Theory/ Modular Forms/ Diophantine Equations and a million other related topics and unsolved problems that research papers are tackling today.

I was decent at math back at grade 9, but due to mental health issues that only seem to get worse and worse, i essentially skipped 1-2 years of school. I don’t have a GCSE math grade, i barely got through AS level with a C (even with the advanced info bc covid) and now I have to force myself to understand this foreign language so I can get into uni for computer science. I have no other choice bc most unis require a maths at B grade or higher. It really doesn’t help that all my friends are straight A students and the type to still ace an exam even if they barely revise. Its just so hard to understand maths without knowing why it works the way it does, or why is something done in a certain way.

I think what people fail to understand is that just because a person is not knowledgeable about a topic that you are knowledgeable about, doesn't mean you get to speak to them in a condescending manner just because they've asked a rudimentary question or having difficulty understanding a concept you might've learned long ago. It's about respect, and if you don't want me running circles around you in a demeaning manner, with topics that I am familiar with & you are not, then you (elitist) need to chill. Just because you worked really hard on topic (A) doesn't mean someone else didn't work equally hard on topic (B). The elitism comes in especially when people try to prove that topic A is superior to topic B, so if you understood that then why would you ever work towards topic B? Kind of infuriating when people take this stance. This is why I prefer "functional over abstract", because you can go sit in a corner & ponder concepts you may never grasp in your lifetime, while I'll be the one applying the things I learn & actually putting to use what I've learned for the betterment of myself, those around me, & the society I'm a part of. I can agree that both functional & abstract are necessary, as abstract helps push what we think is possible. BUT, the majority of abstract thinkers I have met believe themselves to be superior over the more functional/applicable thinkers. From my perspective, intelligence is often rated/defined by "how quickly can you grasp a concept", which may lean on the side of the abstract person having the advantage. However, it's like the "with great power comes great responsibility". If you're going to be a douche, nobody wants to talk/work with you. This whole argument about who is what type & why, could just be the result of the following question: "where did you spend your free time growing up & was it your choice".

Mathematics is hard, rigorous and exact. It demands a lot from you. But some of the kindest most humble and selfless people I have met were mathematicians. From high school to college. My maths professors always tried the most to teach me something, or to put it better, did the most to help me learn maths. I am studying chemistry. Professors I respect the most are my maths professors, and not for the subject they teach.

Difficulty of content =/= Elitism. Monetary and pedigree gatekeeping are examples already mentioned here in the comments that make this point already. Seems weird and bad to look at a couple old texts and say "can't find elitism here, it's just hard" without addressing who were the mathematicians, what roles did they play in the history of the subject, and doing an honest analysis on whether they helped proliferate or withheld knowledge from people because of pedigree or profit. I can't imagine a 10th century merchant giving up his accounting methodology, but I'm speculating here to be clear. Didn't Ramanujan originally get rejected by some Cambridge professor despite having already published papers in India? Do these not count as Elitism?

These are going on my reading list. A few months ago, I was watching a physics video that referenced the book "Lorentzian Wormholes" by Matt Visser, and I was immediately intrigued by the title and incredible cover art; I had to get a copy. Well, when it arrived, and I opened it up for the first time, it was like hitting a brick wall! Far beyond the purview of my computer science/mathematics undergrad degree, to be sure. But it is still a beautiful book, and it has sparked a personal quest for me to learn enough to actually be able to read it. A little intro to analysis could help!

Metaphor: In the series Squid Game, a man is entered into a twisted murder-competition where he's forced to kill many people.. And once he wins he decides the game is a good thing(!) Maybe he's lying to himself, to give meaning to the pain. Or maybe he already believed that, and the game just selects for his personality. Either way, he becomes the managing "front-man" of the competition, and even killed his brother who was trying to stop the competition. That's an extreme metaphor, but I think other fields have a problem where they restrict entry to only those who pass an unnecessarily-difficult "gauntlet" test. The people who pass the test, who now have the power to change the system, are the ones most likely to uphold it or make it more difficult. Ask yourself, why is it that the tersest books are also the most famous? Why does math education skip so many intermediate steps, that it can't be understood without trying to guess every possible step in stacks of paper? Why not just spell it out to save time? You might argue that students must derive those steps, when that can now be automated with Mathematica or MATLAB, so why force _everyone_ to do it by hand? Should architecture students be forced to build pyramids because that was? Math education is elitist because it's not designed to be understood by newcomers; It's designed to exclude them to protect other people's status.

I think elitism can be generalized to be a form of gate keeping, based around a criterion involving a skill or trait. In this video you discuss an elitism centered around the trait of intelligence. Though I do think this is prevalent, I have also found another form of elitism to be prevalent too. The idea that in order to study math, it should be that you work and study hard, if you are not intellectually gifted. The idea that someone who works harder at math, deserves to study the craft more than someone who does not work as hard. I think the interpretation should instead be that everyone deserves to be good at math, and it is unfortunate that there are barriers to that end. I am currently in university for Undergrad Physics. I am finding it to be challenging. I find when classmates hear of my challenges, they tend to think I am lazy because I am not working hard enough. The truth is, I have a severe cognitive disability. I can’t work in the same ways that they do. This often conveys an impression of lack of work ethic. At my university, I have extended time on tests and exams as an accommodation for my disability. This is often seen as an unfair advantage. The perception is that if I had only studied as much as my other classmates, I would not need the time. The truth is, that if I didn’t have that accommodation, I would be completely unable to participate in the study of Physics, and by extension, Mathematics. You pose the question of whether elitism is a problem. I think it is. Elitists restrict what information they share. An intellectual elitist may only be interested in sharing knowledge with someone who they perceive to be as smart as them. A hard-work elitist may only be interested in sharing information with someone they perceive to be a hard worker. The free sharing of information is essential for any healthy academic environment, and so I believe elitism is a net negative. I know for sure that if either category got their way, I would be considerably more ignorant than I am today about Mathematics, and STEM in general.

Language is certainly a massive part of why maths is considered elitist. Bad maths people treat explanations in English like bad programmers treat code; as if a massively complex and hyperspecialized language that is used to textualize it's own formulae, is somehow supposed to be self-explanatory. And as if brute-forcing a student's understanding of it was supposed be meritorious, instead of an absolute intellectual bankruptcy declaration on behalf of the teacher.

When people talk about math people being elitists, they are - at least in my experience - responding to the attitude some mathematicians have towards other fields of study. STEM students/faculty are notorious for looking down on those in non-STEM fields, even going as far to claim that they are not as "real". Because mathematics seems to appear everywhere in our universe, it's easy to see why one might think that math is "more important" than other fields. Nobody ever questioned the rigour that goes into studying math. It's the opposite. Math people doubt the rigour of every other field of study (In my experience).

I was failing math in 7th grade but then i found math channels on youtube in 8th grade and then I was doing linear algebra and multivariable calculus in 11th grade lol yea your perspective of the subject can make a huge difference

Before I watch the video or dare read any other comment, I will share my own annecdotal experience untained and see how it lines up with yours/others. Personally, it less math people at large, but usually a vocal minority, usually specialists in a subfield with extremely narrow tunnel vision. Ever seen people who go bananas over "0^0 = 1, people saying it is undefined are mentally re tarded and I am okay being being ableist and using old terminology as a general insult actually" because it is a common and convenient definition in their specific sub field of maths, and they can't understand math as a whole can't be dependant on "obvious" assumptions limited to some subfields they personally lke, value more and frequently pretend math is fundamentally those fields [because of course they do these sorts of bs too]? Yeah, those Emuanuels and it is both not a surprise at all they act like this, and pretty obvious why when put like that. The other people are sort of similar, they're applied maths people. Or, as I prefer to call them, voluntary iditos who just happen to do complex calculations much better than they can understand wtf they're doing or saying, let alone wish to understand (because that would force them to shatter their superiority complex horseshit, and that is not on the table for them). Basically, one loud subgroup is bullshit, the other is horseshit, they come together often are are otherwise indicits, because the part that counts is that they're just piles of shit. /rant (Yes, I don't like those two types at all).

Anyone doing "real analysis" or "complex analysis" is not rigorous in the slightest. Endless handwaving and malleable definitions at the fundamental level. Rudin and the rest apparently think building a rigid structure on a foundation of squishy terms is "rigor." No, that is fake rigor. See John Gabriel or even Norm Wilderger to start to understand what rigor is.

Well society certainly doesn't see Mathematicians as elitist. The best Mathematician at UCLA makes about a half million dollars per year, where as Duke University basketball coach makes around 8 million per year. Also, high school Math teachers don't get paid any more than their coworkers that teach easier subjects.

How ironic to go about the question of whether maths people are elitist by showing off how incredibly smart maths people must be to get through this material, all the while completely misunderstanding what it means to be elitist. Yes, maths people are often elitist. Maths people are often incredibly good *in their very narrow studied field(s)*, but they're also incredibly elitist. Maths people are generally nowhere near as smart outside of what they've specifically studied. That goes for literally everyone who has only studied a very narrow set of things.

Elitist is not a good word - as an aerospace engineering student, you can certainly get the feeling in some of the upper level math classes that you feel left out of a certain "club", but the reality is that the math students have so much more math to learn that they simply don't have time to slow down and review the quadratic formula in the middle of class. It's the same reason we have aerospace-exclusive classes; we can't afford to stop the entire class to teach a math student the lift equation because we have so much more advanced topics to learn. On a side note, authors have no right to start skipping steps that involve topics covered in just the previous chapter in elementary math textbooks. Professors race through those textbooks at the race of a section per class, and oftentimes two days isn't enough for a student to understand a topic that was just covered two days ago, on top of other homeworks. Oftentimes I would find myself completely lost while trying to follow an example due to a "trivial simplification" only to realize that the only example of that topic being offered was in a chapter 50 pages back.

Good choice of books (mostly). Good mathermaticians are not elitists. They simply have put in the necessary hours with a lot of enthusiasm. If you study math in a diligent and thorough and intelligent manner, reading every word in every line and understanding it, it will get easier with time. Ahlfors book is very pleasant and is written to be understood. Cartan's book is beyond me. Richard Feynmann, both a great mathematician and physicist, is my inspiration.

Nicolas Bourbaki actually left a legacy that makes french math books very hard to get through even to this day

The title sounds silly. Top mathematicians are the elite of mathematics. To say that Euler, for example, was not in the elite would be ridiculous. I don't even know what "elitist" means. Does it mean recognizing that there is an elite group?

I know plenty of elitists who could not understand page 1 of any of those books. Folks need to spend a little more effort on trying to put people down with terms. There is something special about those who understand what these books discuss - accomplished is one term that I’d use, but there are plenty of others that apply equally well and likely better! And where would we be today without people who understand the material inside these books? Answer: In the dark ages!

Actually good math teachers are extremely few and far between. What most teachers fail to understand is that the only absolute in math is the result. The path to the answer is rarely if ever absolute. The way to learn math is NEVER absolute

It's Elitist because mathematical education is so crappy that very few people ever get through it, you would have to be borderline masochistic to see it through. But I believe it doesn't have to be this way, if math education was improved this wouldn't be the case anymore

This guy is a classic example of the bias self centerness of the techie, engineering, math firld. With his first statement of math takes a lot of work and all the pages to do. All fields take a lot of work to master. Try being a gymnast, or a chef, or a writer. Also the amount of pages doesnt mean much. Or else librarians would have the most pages.

I think you can definitely write things harder than they actually are, either due to lack of educational talent or elitism, yes. If someone needs to sit and carefully decipher, not understand, not think about, but decipher each sentence in your book, it's just not a very well written book.

What's the point of this video? It feels a bit like showing off. Also, I think these books are not elitist for todays standards. A math book where I need an hour to digest one page is worth nothing to me. The standard of didactics has shifted in the last decades, and for the better if you ask me. Math is the art of making complicated things easy.... for everyone, not for elites.

It's a legitimate hierarchy. I track down those who are better than me and pester them with questions. They are generally very willing to share their knowledge and advice. If you see someone as elitist, remember that this may be the envy talking and perhaps you should look up to them instead.

I think where math gets really elitist isn't from mathematicians, but from those other academic disciplines for whom math is fundamental to their research. You get a lot of this elitism from the natural sciencies directed at the social sciences, and from within the social sciences from quantitative disciplines (ahem economics) to other disciplines which use other methods of inquiry.

Methematicians can be ellitist, but they don't have to be. Some of the world's greatest are humble people who realise there's always more to learn and improve upon and know that just because they know a bunch of math doesn't mean they are better than anyone else.

Those books are still basic level and mostly still friendly with the reader. Try Federer's Geometric measure theory. That's the real deal.

I think math people often use word definitions that are not normal. This is hardly what I think elitist means. Computer scientists are elitist because they look down on people with less ability.

A lot of math people I see are elitist online, but I also see a lot willing to help others learn. It really just depends on the person.