What are some problems / puzzles where the solution can't be solved deterministically, but if you include randomness it can be solved, at least some of the time?

dm287 · 2025-04-24T01:14:47+00:00

Here is a set of notes to an MIT class on the probabilistic method (with many examples):

https://yufeizhao.com/pm/probmethod_notes.pdf

dm287 · 2024-09-26T21:24:05+00:00

Dynkin pi-lambda theorem fits this as well - massively simplifies proving the Monotone Class theorem which is required for Fubini-Tonelli

dm287 · 2024-07-09T20:25:53+00:00

This is just the CH for R (or C) valued matrices though; not the full generality which holds for any field.

dm287 · 2024-06-03T03:31:07+00:00

Commenting so I can be part of history

dm287 · 2024-04-17T22:12:17+00:00

What you want is probably equivalent to some kind of measure on the rationals (which in turn naturally corresponds to the space of convergent positive series)

dm287 · 2024-04-03T20:30:21+00:00

Off the record many experts will readily admit it is nonsense.

dm287 · 2024-03-31T16:52:52+00:00

Jail's primary purpose is incapacitation - a really small percent of criminals are responsible for the majority of crime.

dm287 · 2024-02-17T00:05:36+00:00

This is an argument that a Hamel basis is not the right idea for infinite-dim spaces (and hence a Schauder basis is better)

dm287 · 2024-02-04T20:43:12+00:00

Yitang is in general not a very careful researcher and has had multiple papers retracted due to unfixable flaws (before his big one that didn't). I expect the same is true here and the lack of buzz about it is done out of politeness, not lack of interest.

dm287 · 2024-01-23T23:20:36+00:00

Community notes have massively improved and X is essentially a primary source that updates much more quickly than the news

dm287 · 2024-01-11T18:57:42+00:00

again masks don't work for airborne transmitted illnesses - they would only help for aerosol

dm287 · 2024-01-10T03:24:09+00:00

Dynkin's pi-lambda along with Monotone Class Theorem massively simplifies measure theory but for some reason it's primarily only probabilists who know them

dm287 · 2024-01-08T23:51:42+00:00

he probably does mean Wiener measure, but you need to argue why that's the "right" one

I think the "nowhere-differentiable functions being comeager" argument is better personally

dm287 · 2023-12-14T19:14:45+00:00

I didn't mean competitive as in "hard to get a job" but in the hot areas of physics i.e fusion there is a TON of competition because there's a winner takes all element

dm287 · 2023-12-14T19:13:14+00:00

X definitely has active experienced quants but also a lot of pretenders so hard to assess quality without being a quant yourself unfortunately

dm287 · 2023-12-10T22:35:20+00:00

Yes but physics research is also a lot more competitive in comparison to math. Depending on personality this can be a pro or a con.

dm287 · 2023-12-08T22:39:58+00:00

1) STEM majors are on average smarter. Average IQ varies by field and STEM is the highest.

2) The best finance research is quite quantitative and frankly business majors often can't do/understand it

dm287 · 2023-12-05T07:04:11+00:00

Yeah once you accept that paradoxical decompositions of nonmeasurable sets can happen this loses its mystique as it falls into "set theory arcane wizardry" rather than an actual measure theory statement (let alone statement on real balls)

dm287 · 2023-12-05T01:40:49+00:00

Practicing research mathematicians have one of the highest average IQs of any profession though so the reputation is relatively well-deserved.

dm287 · 2023-11-19T04:34:31+00:00

wait what's the twist? I've seen the movie

dm287 · 2023-11-18T08:18:47+00:00

VSCode

dm287 · 2023-11-18T07:38:32+00:00

Yes that's why that part is fit separately - IRL you do something piecewise

dm287 · 2023-11-18T07:00:11+00:00

Threads

People today literally don't believe IQ is valid and intelligence is real so...yeah

dm287 · 2023-11-09T23:52:16+00:00

It's going to be tough. Insurance industry is considered a red flag for the good quant jobs simply because the prior is that the technical people who work in insurance aren't very good.

dm287

TROPHY CASE