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A Beginning for Mathematics

daniellitt.com

91–100 of 110 posts

Re: A Beginning for Mathematics

#91

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 article is more about the goal than the how. Perhaps it will be better to have ai produce human accessible explanations. No one is saying not to do what you propose. The goal remains the same.

Re: A Beginning for Mathematics

#92
post #2

> I propose the following reconceptualization of the goal of a mathematics PhD: to become a world expert on some interesting, deep topic, and to be able to convey that interest and understanding to others. Part of operationalizing this might be a thesis, but the degree would be awarded primarily on the basis of a rigorous defense, in which the student explains the topic to their examiners until they are satisfied. I…

> Now comes AI and it looks like the only bottleneck is people's motivation.

Who pays the salary of the mathematicians and the cost of accessing the AI?

Re: A Beginning for Mathematics

#94

Earlier quoted context omitted.

Remote talks are also a common alternative in such cases. Zoom etc. I also know that another major difference is that American universities tend to hire without a professors involvement, into a generic "program", then the PhD student seeks an advisor after being accepted, so applicants have to woo some unconnected committee pursuing various goals misaligned from the PIs instead of convincing the PI. In much of Europe…

I agree the combined masters + phd is weird tbh. I think almost everyone treats it like "just focus on research and spend as little time on course work as possible." I would prefer it if courses were more flexible. I'm not a big fan of the US application setup. IDK how it is in Europe, but in the US, it feels like there's a lot of not-very-meritocratic "secret" stuff you need to know to up your chances.

> I'm not a big fan of the US application setup. IDK how it is in Europe, but in the US, it feels like there's a lot of not-very-meritocratic "secret" stuff you need to know to up your chances.

In Germany (countries differ quite a bit on these details) a significant chunk (though not necessarily majority) is directly hiring a master's student who worked at the same chair on a part-time student research assistant job and/or a master's thesis and did a good job and typically turned the thesis into a paper submission. In other cases it's still somewhat inside baseball like getting recommendations from other scientists that the PI knows, or coming from a university that the professor knows well. It can also be from an impressive email, from a chat at a conference poster, etc. There is much less of this global casting that committees do, like "we need this and this type of character now" to have a vibrant student body composition, since each PI makes a decision just about their lab, without having a global view, and their goals are basically to get research out of that person, papers, results useful for funding applications etc. So they want to see aptitude in that. Through talk quality, communication efficiency when talking with existing team member one on one, recommendations, sometimes even phone calls with the PI with whom the student worked (these are small worlds). I think it's more organic and natural, though still prone to exclusionary gatekeeping, than the HR-style narrative essay-and-extracurriculars-based admissions though maybe that's more prominent for undergrad admissions even in the US.

Re: A Beginning for Mathematics

#95

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.

I think you're a little naive if you think this is because of gate-keeping by mathematicians rather than the essential complexity of mathematics. Mathematicians individually and as a group would love nothing more than a world which is capable of understanding their work more deeply. In the exact same way that LLMs allow anyone to vibe code an app but do not replace real understanding of system design due to its essen…

Folks keep using the word "gate keeping" -- I never used that term nor implied intentional gate keeping. It's simply not caring if those outside the club understand -- there is no one guarding the door its just folks don't care if anyone finds it.

Re: A Beginning for Mathematics

#96
I was involved in this research a few years ago: https://metamiditoolkit.com/research-paper/

One of the things that struck me was that most people have an area of their workflow that they would be happy to hand off to an AI, so that they can focus on the thing they love. However, that area is different for each person. One person's grind-work is another person's love-work.

This is why it's so hard to build consensus around where the "red lines" are in this space.

Re: A Beginning for Mathematics

#97

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.

I would say the research university is getting comeuppance.

Pedagogy is the primary purpose of educational institutions. That includes universities. However, when research is placed first, you are often left with mediocre teachers, because "who cares?" They were hired to do research and lend the university that kind of prestige; teaching is an afterthought squeezed into the spaces that remain.

And frankly, we haven't the faintest clue today what education is even for. That doesn't bode well.

Add to this the other troubles facing the university, like declining attendance, skyrocketing costs, and AI cheating and we're in for a very interesting transition indeed.

Re: A Beginning for Mathematics

#98

Earlier quoted context omitted.

Do you have any examples of places you felt like there was a lot of gatekeeping? Perhaps having studied mathematics I am a bit blind to the issue here and would like to learn more. I agree making simple things sound complicated to appear more impressive is bad but there are limits. Even with Feynman he could only go so far, e.g. his interview about why questions and magnetism.

I am not thinking of intentional gatekeeping, but more of the kind where mathematicians build themselves their own island of concepts and notation with no thought of building a passageway for others to engage and make use of the theory. I would find modern algebraic geometry highly useful as someone who works in computer graphics and computer vision, but much of the theory is akin to learning a new language and I don…

Ah that's fair.

I do think in a lot of fields there is a lot of impact/influence to be had by people who are willing to do work to bridge different fields. I wonder to what degree this is because practitioners don't always see how their work could be used elsewhere.

Re: A Beginning for Mathematics

#100
post #22

Earlier quoted context omitted.

Lowering the bar for the masses isn't always a good thing

It is not lowering the bar to find better ways to demystify and explain things. In fact, I would say those who can explain it well understand it the best. Richard Feynman would be my best example.

I would say that it is lowering the bar to "find better ways to demystify and explain things." But there is no harm to this bar falling, because this is a bar for entry. There is a separate bar for making research discoveries (being credited for them, specifically), and that one should not be lowered, because it is a bar of standards.
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