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A beginning for mathematics

daniellitt.com

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Re: A beginning for mathematics

#111

Post by ipdashc »

ComplexSystems wrote: post #58

I admit I just don't understand this attitude. People had the same complaints that the code produced by early coding models was messy, lazy, poorly commented, had terrible architecture and so forth. The central complaint was that it was just too difficult for humans to review. The answer is just to improve the models and move on. Similarly now we're getting AI doing math. The proofs compile but are a mess. So just ma…

I think it's pretty analogous to coding, honestly. When it comes to gaining true understanding of a piece of software, I still find today's models almost as useless as they were a year ago.

They can write great code, they can gain understanding of something for themselves, but they still kinda suck at explaining it to people. As the article says, if you want understanding, it seems like there is no replacement for getting in the weeds yourself. A model can help, but it's not going to magically download knowledge into your brain.

Re: A beginning for mathematics

#112

Post by skew-aberration »

waynecochran wrote: post #18

As someone who has a degree in math, I still can't help but think mathematicians are getting a little bit of a comeuppance. In a lot of areas of mathematics there had been little effort to make the work understandable and leaves numerous folks who could benefit from the knowledge on the outside looking in. Now AI comes along and do the same to mathematicians. Makes me chuckle a little bit.

Never been my experience of maths, which is one of the most accessible disciplines to have ever existed.

I also have a degree, but mostly taught myself the important undergrad-level concepts as a kid. I just went to the library and borrowed any of the hundreds of books written to clearly communicate maths to beginners or downloaded any of the free ebooks / lecture notes.

Name a single field of endeavor that is more open in 2026. Software certainly isn't one of them - the best stuff has always been gatekept.

Re: A beginning for mathematics

#113

Post by godelski »

GregBuchholz wrote: post #107
godelski wrote: post #102

Earlier quoted context omitted.

> Mathematics is a part of physics This feels backwards. I frequently joke "physics is the subset of mathematics that reflects the observable world". Math can be as abstract as it wants, but physics has a constraint. It must model an observable world (related, this us part of why people say String Theory is math and not physics)

What about the next 3,900 words after the first sentence? (yes, it is that V.I. Arnold https://en.wikipedia.org/wiki/Vladimir_Arnold )

  > What about the next 3,900 words after the first sentence?
But had I read those I wouldn't have been able to feel smart with egg all over my face.

Re: A beginning for mathematics

#114

Post by gmadsen »

AdieuToLogic wrote: post #106
Frost1x wrote: post #46

Earlier quoted context omitted.

I can see how this trend is going to go. Manager: “Why isn’t feature X available?” Person B: “key pieces are delayed due to the developer not understanding all of the LLM doesn’t and implementation.” Manager: “does it work? What are the risks?” Person B: “well yes it works for now but we’re accumulating tech debt due to a lack of understanding and potential flaws that haven’t been thought out yet” Manager: “they want…

The simulated dialog you have provided is very much representative of what many of us have heard first-hand. However, I disagree with: Most businesses don’t care about later risk or any future planning beyond the quarter horizon, they’re not concerned about how it will effect their performance in 3 quarters or lead to instability or issues, those are future problems for a future person and we’re here for money now. B…

It is also true developers can have a myopic view of what should be valued and that can be incongruent with the business.

You can make a perfectly rational business choice to take on tech debt to get a feature sooner.

Re: A beginning for mathematics

#115

Post by physicsguy »

bonoboTP wrote: post #60

> We already interview faculty hires; we must now do the same for graduate admissions They hire PhD students without hearing them give a talk and then doing interviews? In Germany, the applicant gives a talk (30-40 min) to the research group they want to join, usually presenting their master's thesis, engage in discussion, often share lunch with the group, then do 1 on 1s with individual members of the group and a lo…

In the UK I had a panel interview with 4 people, in person. But for international students who often brought their own funding sponsored by their government that didn’t happen.

Re: A beginning for mathematics

#116

Post by MarceliusK »

The key shift seems to be from "can you produce mathematics?" to "do you understand mathematics?"... Those used to be correlated strongly enough that a thesis or paper could serve as evidence of both. If AI breaks that correlation, evaluating people through defenses, discussion and live problem solving suddenly makes a lot more sense.

Re: A beginning for mathematics

#117

Post by MarceliusK »

wrs wrote: post #32

The author argues for evaluating Ph.D. candidates based more on the oral thesis defense than on the actual thesis. By essentially the same reasoning, I’ve been arguing for prioritizing in-person design/code reviews over code-only async PR comments. The important thing is to verify that the human has a coherent design in mind and can demonstrate that it got implemented, regardless of who or what was at the keyboard. “…

The tricky part is that live review is much more expensive than async review. But maybe that just means we were getting away with a cheap proxy because it happened to work reasonably well.

Re: A beginning for mathematics

#118

Post by MarceliusK »

jltsiren wrote: post #51
wrs wrote: post #32

The author argues for evaluating Ph.D. candidates based more on the oral thesis defense than on the actual thesis. By essentially the same reasoning, I’ve been arguing for prioritizing in-person design/code reviews over code-only async PR comments. The important thing is to verify that the human has a coherent design in mind and can demonstrate that it got implemented, regardless of who or what was at the keyboard. “…

An oral defense is ultimately a meeting, with the same weaknesses as other types of meetings. In particular, if new information comes up in a meeting, you cannot reasonably expect to get useful responses from the other participants. First impressions maybe, and plausible-sounding bullshit from those prone to generating that. If you want anything more, you need to provide the information in advance or schedule another…

I think this is true of defenses as they exist today, but that may be partly because the thesis currently does most of the signaling.

Re: A beginning for mathematics

#119

Post by MarceliusK »

bonoboTP wrote: post #60

> We already interview faculty hires; we must now do the same for graduate admissions They hire PhD students without hearing them give a talk and then doing interviews? In Germany, the applicant gives a talk (30-40 min) to the research group they want to join, usually presenting their master's thesis, engage in discussion, often share lunch with the group, then do 1 on 1s with individual members of the group and a lo…

[dead]

Re: A beginning for mathematics

#120

Post by MarceliusK »

physicsguy wrote: post #115
bonoboTP wrote: post #60

> We already interview faculty hires; we must now do the same for graduate admissions They hire PhD students without hearing them give a talk and then doing interviews? In Germany, the applicant gives a talk (30-40 min) to the research group they want to join, usually presenting their master's thesis, engage in discussion, often share lunch with the group, then do 1 on 1s with individual members of the group and a lo…

In the UK I had a panel interview with 4 people, in person. But for international students who often brought their own funding sponsored by their government that didn’t happen.

That's an interesting wrinkle. If anything, externally funded international students seem like exactly the case where you'd still want the interview, since the funding answers "who pays for this?" but not "does this person have the background and understanding to do the work?"
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