Ben Spitz (63/100 improv meals)

I worked with UVA undergraduate Seth Bernstein on this fun project in homotopical combinatorics: arxiv.org/abs/2511.02982 He'll be presenting a poster on it at the JMM this year! meetings.ams.org/math/jmm2026/m…

@HunterEKozak @LinkofSunshine The choice here is between guaranteed 0.1*X vs. 1% chance of 10 billion dollars, in a hypothetical world where your yearly income is 0.9*X, where X denotes your current yearly income. It is *not* a choice between guaranteed 100 million vs. 1% chance of 10 billion.

@LinkofSunshine People keep calculating with EV but forget marginal utility. 1% of 10 bil is not 100 mil, bc to the average person, these are functionally identical.

Would you, right now, pay 10% of your yearly income for a 1% chance to win 10 billion? (no hedging or calling for help)

@anderssandberg The basic idea to use rings of integers of number fields is actually pretty obvious -- the problem is reminiscent of the classic "which quadratic rings of integers are euclidean domains?" Disclaimer: I am not a number theorist

This is interesting (assuming the proof actually works out) since Mythos solves the Erdös problem in a different (simpler?) way, yet also makes use of algebraic field methods. I wonder if this is convergence due to LLM similarity, or because the problem has a deep algebra link.

@BibimbapNom @MTabarrok Because it's a logic puzzle, not a sphinx riddle

@MTabarrok I don't get it, how do the islanders know the other islanders heard this, they are only perfect logicians not perfect listeners, and how do they know no one was deaf?

follow up question to test your true understanding: how can the guru's statement change anyone's actions when she's saying something that everyone already knows?

@SpiritDirtbag @MTabarrok But there are not just 2 people on this island! If everyone already knows the information in the guru's announcement, being perfect logicians, couldn't they just run the inductive argument before the guru says anything? Would the outcome be exactly the same if there was no guru?

@MTabarrok It only matters for the base if induction if n=2, more than that and the guru makes no difference.

@MTabarrok rot13: Rirelbar xabjf gung gur theh frrf fbzrbar jvgu oyhr rlrf. Naq, rirelbar xabjf gung rirelbar xabjf gung gur theh frrf fbzrbar jvgu oyhr rlrf. Ohg, vg vf *abg* gehr gung rirelbar xabjf ... (99 gvzrf) ... gung rirelbar xabjf gung gur theh frrf fbzrbar jvgu oyhr rlrf!

@chmonke My martingale gambling strategy is to just wander randomly around the casino floor

I remember when I was early in undergrad I was talking to a guy and told him I study math and then he proceeded to tell me his gambling strategy which was literally just a martingale. I was like uhhhhhhhh okay good luck with that dude

@chmonke Think step-by-step, make no mistakes

I’ve been wanting to get into thinking. Any recommendations on where to start? Any thoughts that are good for a beginner?

@gro_tsen I'm pretty sure he had early access to the result.

Wait, Will Sawin has already improved on the result published ONLY YESTERDAY by OpenAI? 🤯 arxiv.org/abs/2605.20579

@KnightShore Thanks, I should have been more specific -- I mean pure math

@DiracDeltaFunk You are blissfully mistaken about mathematics. The "authorship inclusiveness" in applied and computational mathematical disciplines is similar to applied and computational sciences. There are co-authors you haven't read their own papers.

The new arXiv policy is obviously v good for papers in math, where a paper has your name on it if and only if it is your work. The new policy enforces the very low bar that you read your own paper before you submit it! Of course, this is not how authorship works in other fields.

If you're going to have a culture where you get academia points for having your name on good papers you didn't contribute to, you need to also receive negative points when the papers are bad / have serious problems. Not reading your own paper is a serious problem.

For comparison, imagine someone in your lab writes a paper which is completely fraudulent -- they just totally fabricated the data or whatever. All of the authors should suffer some consequence, even if they did not actually write the paper or contribute to it in any way!

@qualiascript People say this but I contend that his solution to the bridges of konigsberg problem is unrelated to (the development of) topology. You could maybe argue that the Euler characteristic is the first appearance of algebraic topology, but that's separate work.

the usual claim is that Euler invented graph theory and more broadly topology with his solution to the seven bridges problem, but id be curious about potential predecessors in the same direction

@martinmrmar @lolleka What is your exact definition of V₄?

@DiracDeltaFunk @lolleka Correct. I wouldn't use = sign though... My keyboard lacks the isomorphic symbol... Sad

Tonight's question: Zmod2 X Zmod2 is isomorphic to which group? Hint: it's not Zmod4...

@martinmrmar @lolleka If you really wanted to define V₄ to be a specific group, the most common definition is ... V₄ = ℤ/2 × ℤ/2.

@martinmrmar @lolleka In this sort of context, names like V₄ and Dₙ refer to *isomorphism classes* of groups. On the other hand, ℤ/2 refers to a *specific* group. So it's fine to say something like "ℤ/2 × ℤ/2 is V₄", but it feels weird to say that V₄ is a "different group".

@martinmrmar @mathandcobb Are you going for D₂ (the dihedral group with 4 elements)? This question is a bit silly.

@mathandcobb You are looking for a different group that is structurally the same as Z2 xZ2.

@RadishHarmers Cursed but understandable, have a nice day

@DiracDeltaFunk Yes, unless one alternatively decides to define (n choose k) as the coefficient of x^(n - k) in (1 + x)^n.

More generally: when 0≤k≤n, the binomial coefficient (n choose k) is equal to the coefficient of x^k in the polynomial (1+x)^n. For k,n arbitrary integers with k≥0, one should extend this by defining (n choose k) to be the coefficient of x^k in the formal power series (1+x)^n

@DoozerDiffuser In math there is a distinction between a "maximal element" and a "maximum element" of a poset! x is maximal if ∀y (x ≤ y ⇒ x = y) x is (the) maximum if ∀y (y ≤ x) I agree this is a bit weird linguistically.

@DiracDeltaFunk The Maximum: Noun A Maximal thing: Adjective The Maximality: Noun Categorical mismatch.

Missing from mathematical english: "Maximal" is to "Maximality" as "Maximum" is to ????