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What's a mathematician to do? (2010)

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Re: What's a mathematician to do? (2010)

#21

Post by nimonian »

bloaf wrote: post #16

So I've got a gut feeling that math (like human languages (like programming languages)) is best learned in service of some greater end. I look at some truly impressive projects like CLASP which sprang into existence not because of someone noodling around, but because they had a bigger goal which required the team build it. So my advice to any mathematician who feels lost, like they don't know what to work on, would b…

It's a delightful counterintuition that your gut feeling is mostly wrong: https://webhomes.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf

Far from being motivated by some applications, the most useful discoveries in mathematics are usually discovered "for their own sake" and their application is only discovered later. Sometimes centuries later!

Re: What's a mathematician to do? (2010)

#22

Post by morkalork »

generic92034 wrote: post #4
Schlagbohrer wrote: post #2

After reading another post about the most recent advances LLMs have made in finding and writing up novel, correct proofs, it sounds like the frontier models are now at the point of PhD student level. I wonder how a math student could contribute today, if they're just starting on the PhD track? Maybe by using LLMs as a mighty tool and providing skilled usage and oversight? It must feel similar to those who wanted to b…

I wonder if AI is one means to overcome the natural limits of human knowledge aggregation [0]. On the other hand, in the very long run, what does it mean if a talented human being does not have enough years of life to fully analyze and understand an extremely advanced proof created by AI? [0]: https://slatestarcodex.com/2017/11/09/ars-longa-vita-brevis/

Perhaps it will become like those cathedrals that took centuries and many generations of humans to build.

Re: What's a mathematician to do? (2010)

#23

Post by jebarker »

r_lee wrote: post #19
jebarker wrote: post #14

“Comparison is the thief of joy.” Do the math because you enjoy doing the math and if you do it long enough you may well do something of value to someone else. Same goes for most intellectual and artistic pursuits I think. I’ve learned for myself that as soon as enjoyment is based on some future achievement or ranking my work against others the day to day satisfaction dries up.

and so how exactly are you supposed to provide for your family in this scenario?

By having a job. If that job is the same as your intellectual/artistic pursuit then you have to balance the needs of satisfying your employer and what keeps your motivation going over the long term. All I’m saying is that worrying too much about future achievement or “great contributions” are a recipe for burnout and disappointment.

Re: What's a mathematician to do? (2010)

#25

Post by r_lee »

DoctorOetker wrote: post #17
dataviz1000 wrote: post #12

Earlier quoted context omitted.

LLM models can only predict the next token. The can't predict the consequences of an action predicting one token after another. They can't solve a Rubik's Cube unlike a 7 year old human who can learn to do it in a weekend. They can't imagine the perspective of being a human being unlike a 7 year old human if asked to imagine they where in the position of another human.

Those are very strong claims, do you really believe an LLM can't be trained to solve Rubik's Cubes? Can you imagine what if feels like to be a LLM? Can one LLM have a better sensation of what it feels like to be a different LLM (say one that score a little better?)? You design circularly defined criteria...

honestly I'm pretty sure opus could solve a rubiks cube if you just gave it the layout if the sides and looped until it would solve it

or even just take a picture of the thing, since they can digest visual input now

Re: What's a mathematician to do? (2010)

#26

Post by jvans »

bloaf wrote: post #16

So I've got a gut feeling that math (like human languages (like programming languages)) is best learned in service of some greater end. I look at some truly impressive projects like CLASP which sprang into existence not because of someone noodling around, but because they had a bigger goal which required the team build it. So my advice to any mathematician who feels lost, like they don't know what to work on, would b…

Lots of fun counter examples to this. Complex numbers were introduced in the 1600s with no practical application for almost 300 years until they were used in electromagnetism and quantum mechanics.

Re: What's a mathematician to do? (2010)

#27

Post by 4qshT »

Schlagbohrer wrote: post #2

After reading another post about the most recent advances LLMs have made in finding and writing up novel, correct proofs, it sounds like the frontier models are now at the point of PhD student level. I wonder how a math student could contribute today, if they're just starting on the PhD track? Maybe by using LLMs as a mighty tool and providing skilled usage and oversight? It must feel similar to those who wanted to b…

The Mathoverflow question was asked 15 years ago. The top answer says that the human community part is very important and spreading knowledge an critical thinking is valuable.

The most recent advances are stunts by a handful of famous prompters who are funded in various ways by the LLM industrial complex.

How many theorems are proven by mathematicians each year? Let's guess 10000. Then the Erdos toy proofs with unknown token and resource usage are less than 1%.

Re: What's a mathematician to do? (2010)

#28

Post by TimorousBestie »

morkalork wrote: post #22
generic92034 wrote: post #4

Earlier quoted context omitted.

I wonder if AI is one means to overcome the natural limits of human knowledge aggregation [0]. On the other hand, in the very long run, what does it mean if a talented human being does not have enough years of life to fully analyze and understand an extremely advanced proof created by AI? [0]: https://slatestarcodex.com/2017/11/09/ars-longa-vita-brevis/

Perhaps it will become like those cathedrals that took centuries and many generations of humans to build.

Mathematics as an aggregate already is that cathedral. It is grander and more beautiful than any earthly cathedral.

Re: What's a mathematician to do? (2010)

#29

Post by GuB-42 »

I think it is like for a programmer to ask "How can one contribute to computer science?", while thinking about people like, Dijkstra, Knuth, or maybe even Carmack.

There are some geniuses who do groundbreaking work, but this wouldn't be of much use it it wasn't for the millions of people who do actual work with these theories (applied math), and teachers who train the next generation. In the academia, small discoveries exist too, these can be the stepping stones for the big things to come, even if they don't have a direct application now.

Re: What's a mathematician to do? (2010)

#30

Post by s5300 »

GuB-42 wrote: post #29

I think it is like for a programmer to ask "How can one contribute to computer science?", while thinking about people like, Dijkstra, Knuth, or maybe even Carmack. There are some geniuses who do groundbreaking work, but this wouldn't be of much use it it wasn't for the millions of people who do actual work with these theories (applied math), and teachers who train the next generation. In the academia, small discoveri…

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