A beginning for mathematics • Hacker News Board

Re: A beginning for mathematics

#111

Post by ipdashc » Tue, Sep 15, 2026, 3:55 AM UTC

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 » Tue, Sep 15, 2026, 4:05 AM UTC

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 » Tue, Sep 15, 2026, 4:46 AM UTC

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 » Tue, Sep 15, 2026, 5:25 AM UTC

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 » Tue, Sep 15, 2026, 6:36 AM UTC

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.