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…

@KristapsBalodi3 Congrats!

It's Dr. Balodis now

@Duderichy > job consists of interacting with people whose budgets are so bad they need professional help > their budgets are bad Pikachu

what

@mouse_math @khoiiiind I'm guessing here they mean to describe free objects (ℤ is the free ring on 0 generators)

@khoiiiind i know of only one field of math where structures are actually "generated" purely from the axioms, and that is set theory.

The structure generated purely by axioms often has accidental properties not present in other objects of its category. This fact is well known, yet surprising to me.

@simplicialcube @johnald42 Yeah tbh I'm not sure! It's a useful setup in topos theory, though

@DiracDeltaFunk @johnald42 but in algebraic geometry, is there any site we are interested in, which doesn't have pullbacks?

So like what’s the deal with covering sieves

@Rafi3AK @justinskycak (not to mention that using 'equivalent' to mean 'equal' in this context is unpleasant)

@Rafi3AK @justinskycak If I was proofreading someone's work I would point out that "the functions g and h are equivalent to function f" is ungrammatical. Did this appear on a real standardized test in English?

Many SAT questions are intentionally set up to increase cognitive load and confuse/trick students. If a student is encountering these types of questions for the first time while taking the exam, then they're cooked. It doesn't matter if you could have figured it out eventually on your homework, but ran out of time on the test. It doesn't matter if you got the core of the solution right but just fell for a "silly mistake" trap while executing it. It doesn't matter if the question is long-winded and all you missed was some little detail that you would have realized if the question had just been stated more clearly and concisely. That's why it's so important to prepare beforehand. Not just baseline mathematical athleticism, but also practicing against on the specific plays your opponent (the SAT) is going to run. To illustrate, here's an example from an official SAT practice test -- we informally refer to this question type as "riddles" with exponential functions (and this category shows up across quite a few other official tests too, not just one).

@johnald42 The main advantage of defining Grothendieck topologies with covering sieves instead of covering families is that your category doesn't need to admit pullbacks for the definition to make sense

@johnald42 It's just covering families but harder to wrap your head around

@TimHenke9 @ModalMetamodel I wonder if you can use this somehow... arxiv.org/pdf/1202.6371

@ModalMetamodel Really? What's the characterization of Q?

For every algebraic number field K, a sentence φ exists in the language of fields such that K is the only algebraic number field satisfying φ.

@strawndk @TylerAlterman I do think a Moore-method style of science instruction could be great!

@strawndk @TylerAlterman I love the Moore method, but it's not that much like this. In the Moore method, the instructor still delivers the distilled, pre-developed theory from on high. The job of the students is only to digest it and prove the theorems.

Why don’t science curriculums just re-enact the history of science? You confront young students with a confusing phenomenon like magnetism, have them come up with theories about how it works, test them by messing around, and then debate which theory is right on the basis of the evidence.

@TylerAlterman The primary downside of this approach is that it would be almost impossible to cover a nontrivial amount of material.

@goblinodds @tautologer Most mask mandates began in Trump 1 and were not federal. It's weird to look back on the early pandemic -- positions shifted wildly a few times before we settled into our current equilibrium. x.com/i/status/12852…

@goblinodds @tautologer That isn't quite the right picture of the timeline. Trump 2 started in 2025 -- there was no more mask mandate at that point! The fed mask mandates (which started and ended during Biden's term) applied to people on fed property and to public transit. ...

everyone criticizing Anthropic unflinchingly complied with mask and vaccine mandates right?

@weilsd_puberty3 Ridiculous, I can easily construct hundreds of different identity homeomorphisms!

Certains matheux te disent "à homéomorphisme près" mais ne sauraient pas te construire un (1) homéomorphisme concrètement si leur vie en dépendait

@JJ_McCullough Not Coffeezilla's -- Jmail is the creation of @lukeigel and @rtwlz. It is amazing!

Wow, Coffeezilla's recreation of Epstein's Gmail inbox is one of the most amazing internet things I've ever seen. You gotta check it out if you have not already.

@alpha_convert Congrats!

@sgodofsk In a counterfactual world where air travel infrastructure did not exist in the US, would the fact that interstates allow people to travel across the country mean that we shouldn't build any airports?

@sgodofsk Similar example: long ago, demand for *all travel* was satisfied without any cars or planes or trains existing. It is nonetheless good (imo) that we invented cars and planes and trains! Infrastructure examples: the interstate system, supermarkets and food distribution, etc.

and these flights clearly satisfy the demand, so what does the rail add?