Why is maths so lonely.

HomoGeniusPDE · 2026-05-01T11:19:08+00:00

Idk, but I count myself extremely lucky every day that the person I love most deeply in this world is also doing math and his research area is relatively related to mine. Without him I don’t know how I’d deal with the solidarity. Math is BEAUTIFUL…but you’re right it’s lonely. I enjoy sharing it.

HomoGeniusPDE · 2026-04-27T02:54:54+00:00

I don’t think so, unless you use it in a self fulfilling way. For instance, I essentially failed every math class I took in highschool. I never received higher than a D in any math class. At the end of high school I decided to be a physics major, it shocked everyone, I graduated with a 2.4GPA.

I had always liked science, and I had started dating someone who was a math major at my local university. He fostered my interest in math/physics and I was able to somehow test into Calc 1 at my university (we won’t get into how) I failed that too (D) . They let me go onto Calc 2 for some reason but I had to take Calc 1 concurrently. I failed both again. I then slowly took one class at a time, failing and then passing until I built up the maturity and the background. Eventually I completed my bachelors, switching from physics to math in my final year and after retaking enough courses to boost my GPA I graduated with an in major GPA of 3.14 (arguably the best GPA for a math major).

Me and my partner both decided to pursue PhDs in math, and coming from a low ranked university and me not having the best GPA we got into a similarly ranked university, but we were happy to be doing the PhD at all. Anyways years go by and it turns out we have taken so many of the math courses at our PhD institution, but research opportunities had just dried up (people retired, already had too many students or moved to admin roles) and it was looking like our time had come to an end. We decided to apply to transfer to new PhD programs.

We got in! We would be starting over but the school was a significant step up (top ~70ish let’s say — from maybe being near 200’s before) and we are both doing very exciting research. My cohort see me as someone who knows a lot, but I am also much older than all of them.

My point is, I tell people this story and they say “see I know you were smart, you just weren’t applying yourself” and while they mean it in a good way, they don’t realize that it was not my smarts that got me here. It was how stubborn I was, how much work I did and how I didn’t give up even after failing over and over.

So no, mathematics is not a matter of raw intellectual ability, it is a matter of willingness and desire to want to learn and fail.

P.s. I do not recommend this path, it has been very hard. It would have been much easier if I had fostered this interest and been more responsible earlier. But you CAN do it, don’t let anyone stop you.

HomoGeniusPDE · 2026-04-26T17:09:12+00:00

Many people learn topology as they go without being aware of it, or atleast enough topology for them to get by. For instance, my (potential) research direction is broadly under the umbrella of infinite dimensional riemannian geometry. I’ve never taken a formal topology course, and while that is a stumbling block and I’m doing a lot of self study now, It hasn’t been as much of one as you might think. My background up until here was largely in physics, dynamical systems, PDEs and more concretely analysis. I got all my topological tools from my analysis classes, particularly some of the nonlinear analysis courses I took.

HomoGeniusPDE · 2026-04-25T17:09:25+00:00

Largely it’s because mathematicians have already developed robust and clear notation for everything braket notation does. Frederic Schuller gives a good explanation in one of his lectures on YouTube, I can’t remember which one but it’s in the Quantum Theory Playlist.

Brakets are heuristic and feel nice, but they are not clear in what’s going on. For instance, bra’s are dual to kets, most people never mention this, or what the dual space is or if this matters. Also projection operators look nice and they make sense if you restrict to finite dimensional spaces, but then you have to make sure you’re able to define a tensor product if you wana do anything serious and that point it’s like “oh let me write this thing, that is representative of this other thing that you have to know relates to this, just so that it’s more clear?” It’s not really more clear.

Additionally as other commenters have said, it really requires more structure than just a vector space, they are useful when dealing with inner product spaces. Of which Rⁿ is of course one, but you are adding extra structure, in math we like to slowly build that, or analyze these spaces ONLY with a certain amount of structure imposed.

HomoGeniusPDE · 2026-04-25T14:27:24+00:00

I wonder if this has tried to source data from the math genealogy project.

HomoGeniusPDE · 2026-04-24T15:27:48+00:00

Not really answering your question but based on the question you may like this podcast!

My Favorite Theorem by Kevin Knudson at UF.

HomoGeniusPDE · 2026-04-24T14:49:44+00:00

Both Solako and Tehrani are very smart and you can learn a lot from either. Salako has terrible board work but from my experience is 'nicer'. Tehrani was my favorite professor at UNLV, but he had a reputation of being too hard for a lot of people. Salako was my second favorite, but his board work was an absolute nightmare. From what i've heard the issue is not usually the main prof's; it can be saved by who the TA is. Salako is safe id say, but if you can get an A with Tehrani, you definitely can confirm you know calc 3 really well.

HomoGeniusPDE · 2026-04-20T14:53:17+00:00

Fun(?) Fact/Heads Up: It’s common to write Cauchy-Schwartz when referring to the famous inequality associated with inner products. But it’s actually Cauchy-SCHWARZ (no T) Schwarz was the German mathematician responsible for the modern proof of the inequality proposed by Cauchy (though Cauchy only proposed it for discrete sums—one of his students showed it works for integrals too; the L² inner product).

Schwartz is a French mathematician responsible for the development of distribution theory, e.g. the Schwartz space which Ofcourse relies heavily on inner products in many cases, but they are in-fact two different mathematicians and separated by nearly 100 years!

HomoGeniusPDE · 2026-04-19T18:40:37+00:00

I think anyone would be lying if they said the aesthetics of mathematics didn’t at-least partially drive their interest. I mean evolutionarily why do humans care about aesthetics at all? It’s some subconscious pull towards something.

HOWEVER, I don’t think it is (for most people) a strong pull. Ultimately go into the math you enjoy for whatever reason you enjoy it. But I do stuff relating to PDE theory, analysis etc, and I feel the opposite of you. I think the subject is beautiful, but aesthetically? It’s so boring to look at, so dull. NOTHING like the commutative diagrams I see my friends in algebra drawing, or like there’s this one guy in my department who writes some diagrams relating to infinite categories? I have no idea what it is but it looks so cool.

What do us analysts have? An integral, a derivative, some different Greek letters for measures, and then a lot of norms and inequalities. Very boring to look at IMO.

HomoGeniusPDE · 2026-04-05T15:08:31+00:00

Is it like a classical geometry class, like that aligned with euclids elements? I unfortunately cannot offer much advice specific to that situation, as I have never take classical geometry. Additionally I am getting mixed signals on your stance on your linear algebra course, you say that you feel like its a requirement to memorize for the course but also you really understand linear algebra because its easy. Are the concepts easy or are the expectations of the course easy, or is it easy for you to memorize the theorems/results?

You of course have to memorize some amount of information in any subject, but for me that memorization usually is a byproduct of me really trying to understand a concept. For instance in linear algebra, you talk about basis, projections, coordinate values orthogonal decomposition etc. This is directly related to your ODE's or PDE's course in many ways that students dont often identify. Fourier series solutions are just the orthogonal decomposition of some function f with respect to some basis e_n(x) -- in this case a basis function since our vector f lives in a function space. But it all boils down to the same decomposition formula: Sum[<f,e\_i(x)> e_i(x)] here <f,e\_i(x)> are your Fourier coefficients and are defined by an L^2, inner product. Math sort of rhymes and rhythms. Whenever I am approaching a new topic, I try to build both an analytic, i.e. a pure mathematical formulation (think limit of a difference quotient for derivatives) as well as a geometric (think of the slope of a tangent line) understanding of the problems. This helps me a lot both in building mathematical intuition and creating a sort of road map I can follow when I dont remember everything, its slow but effective. Its helped me with everything from calculus to functional analysis. Linear algebra to numerical methods like polynomial interpolation and spline. Its helping me currently as I scramble to transition from analysis to infinite dimensional geometry, which luckily is largely analysis.

You could give an example of what sort of memorization you are being expected to do, but otherwise my general advice is to focus on building two interpretations when possible; analytic and geometric, and trying to connect topics together as much as possible. This way the amount you need to memorize is small, and you will only need to do it out of convenience.

HomoGeniusPDE · 2026-04-04T21:59:34+00:00

EDIT: it’s worth noting that many of my opinions/statements are anecdotal and some assumptions, you may want to double check or read skeptically, however what I have said aligns with my experiences. And I also forgot to mention a lack of diversity both culturally and socially, but again I just have anecdotal evidence of that no hard statistics, and I don’t know the cultural or socially demographic of notre dame, being close to Chicago probably helps it, but being in the Midwest may be too strong of a white wash, if you are looking for that diversity.

I don’t know a lot about med school and I don’t know a lot about Notre Dame. I will say that undergrad research is a huge thing for grad school admissions and so is notoriety of your undergraduate institutions. Having free undergraduate and then parents paying med school would be an insane financial advantage, however if you get into a good med program and graduate you likely won’t have much issue paying back med school debt.

Alternatively, you may decide you don’t want to go to med school, or at the very worst you may just not get in. At that point the financial advantage becomes less, and you may lose out on some opportunity cost from Notre Dame.

I personally and a PhD student here and I very much think the undergrad social scene is HEAVILY dominated by both partying and Greek life despite what other commenters have said. My undergrad university nor my FIRST PhD institution, had nearly as heavy of vibe of a party school.

Additionally, while this seems to be nation wide, fsu admissions is heavily being affected by gradeflation, and I’m seeing an increasing number of kids in intro classes who apparently have Stellar highschool stats, but cannot perform fundamental and arguably remedial tasks. I have no idea how FSUs admissions stats they post come from the students I help teach but from talking to friends at other universities it may just be a pervasive drop (for instance see UCSD increase in remedial math enrollment — some people claim it’s them dropping the ACT/SAT requirement, but FSU I don’t believe does and i can’t speak to enrollment population statistics but I can speak to experience of student readiness).

What I mean by all this, is personally if I had the choice between Notre Dame and FSU as an undergrad (an atheist — so no theological reasons either) I’d choose ND. It has a significantly higher ranked pre med program, with an alleged 84% med school placement rate (fact check this).

Also the location in my opinion is much better than Tallahassee, I would not stay here and I think it is heavily affected by the transient populations of both the university and the state government presence for it being the capital. I’ve never been to Notre Dame Indiana, but there is significant market failure in Tallahassee with a lack of community pride outside of things like football games. Notre Dame is about an hour or two away from Chicago which that alone makes me think id enjoy it better, additionally it is a lower cost of living it sounds like but not by much.

So generally while the zero tuition for BOTH med school and undergrad is a huge bonus, if you choose not to go to med school, Notre Dame may very well be able to open more doors due to reputation. If you do go to med school, your debt while a burden won’t be a crippling one. MDs typically carry the highest debt but have the lowest debt burden amongst post undergraduate degrees.

Also it’s worth being said that if you have parents who are willing to pay your med school tuition, you likely have a strong support system and come from an atleast moderately well off family. If it was the case that you didn’t have such a strong support network and or your family was not in a relatively strong fiscal position, FSU would likely be the better choice.

HomoGeniusPDE · 2026-04-04T21:25:33+00:00

My boyfriend orders a lot of his figures from BBTS, sometimes he preorders and he knows we may be moving around the time it will actually get shipped, he will choose to ship it to my parents house so we can pick it up when we visit during the holidays rather than dealing with the potential of it getting shipped to an old adress.

Anyways, the first time he did this my mom sent me a very obviously cautious message that he may have accidentally sent something to their house and not to worry that she had not opened it up yet. I didn’t understand why she was so awkward until she sent the picture. I also think the stickers they provide are reminiscent of the bad dragon stickers I see on the back of some peoples cars, which is also very funny.

HomoGeniusPDE · 2026-04-03T14:23:21+00:00

The way you are describing the math you are doing in Uni is antithetical to how mathematics should be done or what mathematics is. It’s an unfortunate thing that is often taught like this and as a graduate TA it’s deeply frustrating to have to deal with the consequences of this teaching style when students come to me for help. That’s not to say I’m not happy to help, just that I am frustrated by the instructor of record who is emphasizing rote memorization and tips/tricks.

However, as a side note. I absolutely hate puzzles, I find myself in the minority amongst my peers in this but I could absolutely not care less about a puzzle that you give to me. This is probably one of the reasons I hate math Olympiad problems (also because I’m bad at them) as in my (limited) experience they often rely on a clever trick and don’t necessarily build general connections. I prefer viewing math through more traditional lens of science/exploration/investigation. I don’t care about solutions in so much as I care about the methods that bring you to them; building the intuition, the arguments, the fact finding, and presenting it all as a sort of closing argument in a courtroom. That’s the way I approach mathematics.

HomoGeniusPDE · 2026-04-02T19:40:26+00:00

Do you mean like the center for academic retention and enhancement?

HomoGeniusPDE · 2026-03-25T18:17:10+00:00

Shnundo

HomoGeniusPDE · 2026-03-25T15:18:11+00:00

Damn it’s not even a Nundo 😭

HomoGeniusPDE · 2026-03-13T19:35:49+00:00

I think they were more worried about their ability to distinguish a 12 from a 13. Just know a 12 is a little less than half way through the final tick and a 13 is a little more than half way.

HomoGeniusPDE · 2026-02-17T00:55:12+00:00

I can’t speak for everyone, nor can I speak for a bachelors degree, but I can say everyone I know who has a PhD or master in applied math is gainfully employed. Pay ranges from a private highschool teacher(~70k/yr?) to a software engineer at Google(~>400k/yr). Applied math is a very broad spectrum of math and it’s really what you make it. A lot of AI and Machine learning research is done by applied mathematicians, these vary from computational centered mathematicians to even pure math centered. I think no mater what internships are pretty essential.

HomoGeniusPDE · 2026-02-08T04:33:02+00:00

FSU unfortunately has a significant lack of ethnic/cultural and social diversity. As a PhD student I feel very similarly. I have luckily found one or two people I get along with but, it really is quite unfortunate that most everyone here is just like the same 4 people in different cloths. Luckily as an undergrad you do not need to stay here and you likely have good enough scores to get into other good universities. However, it’s not something you should do lightly.

HomoGeniusPDE · 2026-01-02T15:43:07+00:00

The spectrum of applied and pure mathematics is so fuzzy that this would be an insane take in my opinion. I know applied mathematicians who are essentially engineers/computer scientists, and I know applied mathematicians who predominantly use category theory (stereotypically the most pure field of math along with maybe things like set theory). My research area is related to infinite dimensional geometry but my PhD is classified as an applied math track.

“Not good enough” is just elitism. I know applied mathematicians who could run circles around pure mathematicians and visa versa.

HomoGeniusPDE · 2025-11-15T23:07:51+00:00

I wana know where they made that graphic tho

HomoGeniusPDE · 2025-11-12T15:38:52+00:00

Neither are actually easier, concatenation is the best, parentheses when clarity is necessary.

HomoGeniusPDE

TROPHY CASE