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No country for mediocre mathematicians

garvvee.substack.com

11–20 of 159 posts

Re: No country for mediocre mathematicians

#11
I have some bad news for the non-mediocre mathematics. Given it another year or two or so and there won't be much need for non-mediocre mathematics either. Instead everyone will have on call a near magic mathematician who can push the state of the art for their needs.

Math is actually a perfect fit for AI because it is possible to express everything in terms of written language and you can write formal verifications of things. It is just a set of abstract rules, perfect for a computer.

And remember computer science was initially a sub-discipline of mathematics. So after Claude/Codex conquer writing code, it makes sense to move on to mathematics.

Re: No country for mediocre mathematicians

#12
post #2

It's interesting that this piece stands well enough if you replace mathematics with probably any other intellectual profession, including software development or pretty much anything else. And, I lie to anyone who asks me why I’m a mathematician. It is much easier to claim “I love learning the laws of life,” while literally handwaving, than it is for me to flashback to the twenty or so pivotal moments that lead to me…

A PhD in Arithmetic Geometry and a publication in a top tier journal is hardly mediocre in and of itself, as far the author is concerned. The equivalent for a software engineer is probably a leading AI engineer, with a strong publication count. I think a lot of people who are not mediocre are unaware of what mediocrity actually is. Yeah if you're only in the top .1% and comparing yourself to the literal best in the world, you will feel mediocre in that sense . A mid mathematician maybe publication in worse journals, teaching community college.

Re: No country for mediocre mathematicians

#14

I have some bad news for the non-mediocre mathematics. Given it another year or two or so and there won't be much need for non-mediocre mathematics either. Instead everyone will have on call a near magic mathematician who can push the state of the art for their needs. Math is actually a perfect fit for AI because it is possible to express everything in terms of written language and you can write formal verifications…

Whenever there is a breaking AI-generated proof, it's the job of actual leading mathematicians to formalize/check it . Laypeople are not checking or writing these AI-assisted proofs. Even when Lean is used, it's mathematicians writing these proofs and checking if the formalization was done right. Terrance Tao's career trajectory has reached new highs due to AI. He's more relevant than ever. This is the exact opposite of Ai making mathematicians obsolete.

Re: No country for mediocre mathematicians

#15

Earlier quoted context omitted.

They would not even be wrong.

Yeah seems like most programmers just do it for the money. I imagine only like 20% of us do it just because we enjoy it.

I'd just say there are scores of people who like programing. But that's about it.

Re: No country for mediocre mathematicians

#16

Earlier quoted context omitted.

They would not even be wrong.

Yeah seems like most programmers just do it for the money. I imagine only like 20% of us do it just because we enjoy it.

I feel like the number is higher for software work where I'm at, and lower for every other profession. Scary when you think that your doctor is in it for the money

Re: No country for mediocre mathematicians

#17

Hobbies aren’t as fun when you have an overbearing friend who constantly shows off how much more they know and how quickly they can switch to talking about anything you want but in greater depth than you.

I do not have a single hobby where I'm very far beyond the median hobby-haver in skill (that is to say: if you took all other humans who share my hobby, I'm likely somewhere near median for all of them). This may put me in top whatever percentile among all humans, since most humans don't share my hobbies and so are terrible at those things, but there are enough humans out there, and enough humans who share my hobbies, that I have always known that there are people who are vastly better at them than I am. Now yes, if I was constantly being followed around by one of the top 10 hobby-havers, pointing out to me all the mistakes or sub-optimal decisions I was making, that would indeed be annoying and reduce my enjoyment in the hobby. But why do you expect AI to be like this? I would love if I had one of those top 10 hobby-havers on call to answer every one of my (often inane) questions with infinite patience (and who would only talk about the hobby when I specifically initiated the topic). I'm already under no illusions that I'm the best, but it's now easier than it has ever been (for some hobbies, I expect others to join them over time) to get better at them....if one so desires.

Re: No country for mediocre mathematicians

#18

Hobbies aren’t as fun when you have an overbearing friend who constantly shows off how much more they know and how quickly they can switch to talking about anything you want but in greater depth than you.

mathematicians or physicists fall into this category of knowing a lot about many thing . Sabine videos for example . she knows everything it seems

Re: No country for mediocre mathematicians

#19

I have some bad news for the non-mediocre mathematics. Given it another year or two or so and there won't be much need for non-mediocre mathematics either. Instead everyone will have on call a near magic mathematician who can push the state of the art for their needs. Math is actually a perfect fit for AI because it is possible to express everything in terms of written language and you can write formal verifications…

Whenever there is a breaking AI-generated proof, it's the job of actual leading mathematicians to formalize/check it . Laypeople are not checking or writing these AI-assisted proofs. Even when Lean is used, it's mathematicians writing these proofs and checking if the formalization was done right. Terrance Tao's career trajectory has reached new highs due to AI. He's more relevant than ever. This is the exact opposite…

To the credit of the original commenter, that is why they said "give it one or two years". _Right now_ we need the experts to formalize/check. They're saying they think LLMs will reach a point in the near future where that won't be necessary.

Re: No country for mediocre mathematicians

#20
post #16

Earlier quoted context omitted.

Yeah seems like most programmers just do it for the money. I imagine only like 20% of us do it just because we enjoy it.

I feel like the number is higher for software work where I'm at, and lower for every other profession. Scary when you think that your doctor is in it for the money

You can be a software developer without any formal training and without any licensure. Not so for an MD.

It's going to attract more people who have the mentality of artists or musicians, i.e. people who do it for the love of the craft and as a creative outlet.

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