r/math

I am a mathematician who lives in Silicon Valley and I keep meeting programmers with extremely strong opinions on foundations. This is mystifying. Why does this keep happening to me? There is no situation that justifies a programmer telling an algebraic geometer that Zorn's lemma is evil, yet I encounter this regularly. They phrase it in terms of the axiom of choice though. It is bizarre and extremely common. One time I told a software engineer I work in algebraic geometry and they told me that sounds like "normie math." When I asked what wasn't "normie math" they said "category theory."

I did not have the wherewithal to tell them who actually uses category theory most in mathematics other than homotopy theorists. I was too confused.

Haskell devs are the largest consistent offender here. Many of them have bizarrely intense investment in type theory as a foundation for mathematics. And a particular passion for univalent foundations. I don't want to say all Haskell devs are like this, but I think about half of the ones I have met are. Do these people think analysts do fake math or something? Why is there such a strong desire to dilute equality to equivalence among people who push around and package lists all day.

What has currying done to these people and how do I fix it?

Everytime hear the phrase "graphs are categories" from a person who does not know what a spectral sequence is it feels like being hit in the face with a sack of wet mice. It is also just not true. A category is a directed multigraph with extra structure. This statement is exactly backwards and is also probably one of the worst things you could tell a person who is only now encountering graphs in a mathematical context.

I can't believe I need to start a conversation on this but what is the correct way to interact with people being rude about my field of study? This is not a problem I should have. I work in mirror symmetry, not environmental contaminants or pediatric medicine.

Do I just start talking about amenable groups and Banach-Tarski to scare them away?

My life has become an infinite clown show, please advise.

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So I know about this subreddit, MSE and MO.
I don't know about other platforms where math ppl gather.

Hi there, second post of my personal writings to consolidade my understanding of things. As the first post, I tried to write it intuitively.

https://stillthinking.net/posts/connections-in-math-two-kinds-of-random/

Hi!

I'm a first year math undergrad. I've had at university this semester a class that I think can be best described as proof-based calc 2 and calc 3, but the professor needed to rush through the material so we didn't get to do that many proofs, and after the R^n topology section most of the exercises at seminars were computational in nature.

The problem I've had is that I'm significantly more excited(and frankly do better with) proofs compared to the more computational nature of a lot of the exercises in this class. But even so, the theory, especially for the multivariate differential calculus side seemed rather... weak for lack of a better word? A lot of the work seemed like not perticularly strong results, excluding the Implicit function theorem and local diffeomorphism theorem, and maybe Lagrange multipliers. It seemed like we really don't understand that much about multivariable functions into multidimensional space, which may be true. I am not expecting results as strong as for single-variable analysis, but a lot of results still didn't seem like they told me much about the functions. Is there a more structural lens to view this through?

This is the only exam I did not ace this uni year(but I am studying for the retake we have soon so I can hopefully raise my grade) since I did 2 really stupid calculation mistakes that cost me a lot. It also makes me question my abilities/potential since even though my interest skews quite a bit more towards algebra and geometry, I do know how important this class is(or is supposed to be) and not having done as well as I would've liked is throwing me off. That's why I am seeking a way to understand that maps better to my brain.

Thank you for your time!

I recently graduated uni with a bachelor's in math and during my studies I've noticed how AI in math has gone from a curiosity to a looming paradigm shift that might destabilize everything. I myself have tried to steer clear of using AI while studying in fear of getting too sloppy but I feel that sooner or later it'll be standard to leave all the theorem proving to the machines and just prompt together an article (if humans are still involved). That the point of creating such AI is to cut out a majority of mathematicians except a few established ones who will be in charge of guiding the development of new math. This is at least the impression I get from the media of AI gurus talking about solving Erdös problems ect. I understand that this is to just hype up AI for investors but currently there is no active alternative for up-and-coming mathematicians other than to hop on the bandwagon or remain ignorant. This just leaves me the question of what is the end goal of this automation of math and what does that mean for the rest of us. I'd love to hear your thoughts on this.

The general form of these series is that each term is a power of 10 (since moving the decimal takes no effort) multiplied or divided by a single-digit number (since single-digit multiplication/division takes far less effort than multi-digit multiplication/division).

It follows the basic principle of simple repeated fractions, but with only adding and subtracting error terms (no taking reciprocals and then cross-multiplying) and with having multiple options at each step from which to choose the best (rather than being given one automatically).

Taking π = 3.14159265, for example, we would start with either

• 3 (underestimating with 10^n times x)

• 4 (overestimating with 10^n times x)

• 10/4 (underestimating with 10^n divided by x)

• or 10/3 (overestimating with 10^n divided by x).

3 is the closest starting point (error of 0.14159265) and 3.33333333 is almost as close (error of 0.19170408), so we would throw 4 and 2.5 away and test 3 first, then 3.33333333.

The error “π – 3 = 0.14159265…” can be estimated as

• 1/10

• 2/10 (which could be re-written as 1/5, but that doesn’t matter here because we’re about to ignore it anyway)

• 1/8

• or 1/7.

1/7 and 1/8 are the closest second-steps for π ≈ 3, so we throw away the 1/10 and the 2/10, and now we see what the closest second-steps would be for π ≈ 10/3.

The error “π – 3.33333333 = -0.1917408” would best be approximated as -0.2 (which could be written as -1/5 or -2/10 depending on the reader’s personal preference), but the two-step calculations 10/3 – 1/5 = 3.1333333333 and 3 + 1/8 = 3.125 are both less accurate than the two-step calculation 3 + 1/7 = 3.14285714, so we can commit to 3 + 1/7 now.

Calculating the new error “π – (3 + 1/7) = -0.00126449” creates a best new error term of -1/800, and so our new value is 3 + 1/7 – 1/800 = 3.14160714.

This approximation “πx ≈ 3x + x/7 – x/800” is accurate to within 1 part in 220,000, but it only takes about as much time and effort as “πx ≈ 3x + x/10 + 4x/100” (which is only accurate to within 1 part in 2,000).

Using continued fractions would take very little time to calculate “π ≈ 355/113” ahead of time (which is accurate to within 1 part in 12,000,000), but this takes more time and effort to use in the moment. If someone was multiplying πx ≈ 3x + x/7 – x/800 and if someone else was multiplying πx ≈ (300x + 50x + 5x)/113, then in the time it took the first person to get a final answer, the second person would only have finished calculating the numerator, and they would still need time to calculate the denominator.

During which time, the first person could be adding more error terms: 3 + 1/7 – 1/800 – 1/70,000 is accurate to within 1 part in 15,000,000 (already more accurate than 355/113 for less time and effort), and 3 + 1/7 – 1/800 – 1/70,000 – 1/5,000,000 is accurate to within 1 part in 880,000,000.

Hello, everyone. I am an undergraduate in my first semester, and I've been self-studying Halmos' "Naive Set Theory." Yesterday, I discovered an alternate approach to a proof that works with fewer assumptions. I discussed this with my professor, who told me to share it here. He confirmed that my result was correct, but suggested I post it to see if there are any gaps.

I'm working through Halmos's Naive Set Theory. In Chapter 12 he proves the successor function is injective on ω using two lemmas:

• (i) No natural number contains itself
• (ii) Every natural number is transitive

His proof uses both. But I think the following works using only (ii) and Extensionality (which was established in the first chapter as an axiom).

Since n ⊆ m and m ⊆ n, Extensionality gives n = m directly, contradicting n ≠ m. Lemma (i) is never used.

Extensionality is an axiom; no proof burden, so this eliminates one lemma from the proof infrastructure entirely.

My question: is there a reason Halmos preferred his route? Is this observation already well known?

Am I the only one who finds the standard notation for polynomials annoying? Like, you have to have a dummy variable, and different people use different ones, like k[x], k[X], k[T], etc.

It's annoying that we still treat polynomials notationally like functions that you sub into to get a number and you have to specify the variable. I guess for individual polynomials, you can treat it as a sequence of ring elements with all but finitely many elements zero, following certain rules for how they add and multiply, but that still doesn't solve the problem if you want to talk about a polynomial ring. I guess you could write k[] or k[·] or k[-] for k[x]?

But then what do you do for the ring in two indeterminates?

arXiv’s next chapter: Updates on our spin out from Cornell University: https://blog.arxiv.org/2026/06/30/arxivs-next-chapter/

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I am researching the topic of snark conjecture, that every snark has the Petersen graph as a minor. (Infamously?) The proof has been claimed like 30 years ago, but one of the papers is still missing (or is in preparation, although Robin Thomas, one of the authors has passed away recently, unfortunately).

A bit more info is here:

https://thomas.math.gatech.edu/FC/generalize.html

https://mathoverflow.net/questions/272067/tuttes-conjecture-on-petersen-graphs

By any chance, does anyone have and is willing to share the draft of manuscript (and the code if applicable) of "Edge 3-coloring cubic apex graphs" paper, please?

Hi everyone

So I’ve been recently self studying geometry and in Tu’s “intro to manifolds”, he has a small section on category theory.

I really enjoyed that section and I liked how he used the idea of functors to prove that two tangent spaces at p and F(p) on N and M are isometric if there exists a. diffeomorphism F between the two manifolds.

I’m starting a masters degree in mathematics in the UK and one of the options in my first semester is to pick catagory theory. I would like to get a strong grounding in it.

For context I’m picking:

Category Theory
Differentiable Manifolds
General Relativity I
General Relativity II
Riemannian Geometry
Lie groups

I would like to do pursue geometry further at PhD, I’m also interested in topology.

Does anyone have any recommendations for good books on this category theory? I tried reading MacLanes book, and whilst not that I lack the maturity, it’s just I can’t deal with these massive pages of text. I’m dyslexic and I have ADHD so I struggle to read basically pages with just text and I get really bored. I like abit of smash n grab, definition, proof, example, definition, proof. That kinda stuff. I don’t really need much context to understand thing.

For more context I really enjoyed Sutherlands metric spaces and topology. If anyone has a recommendation of that kind of style I’d really appreciate it.

Also one more question, sorry. Do my choices have synergy? Is category beneficial for geometry? Thanks :)

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Please. Help.