What should we tell our students?

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> With the latest ChatGPT models, these problems are more equivalent to homework questions: the answer is `in the back of the book.’ I am not discovering new solutions. Instead, I am working on problems whose answer exists and is simply waiting to be retrieved by a user of the model. In fact, I mentioned a problem that I was interested in working on to my advisor and he informed me that he and a collaborator had completely resolved it using ChatGPT – they have no plans to write up the result, so it will sit there until another `researcher’ pulls the proof slot machine.

There is another good point that the most tenured researchers have a sense of what problems are most worth exploring and therefore are more likely to feel excitement than younger researchers:

> I have also heard the contention that math research has `gotten more exciting,’ mainly from established researchers. They have decades of open problems that they care deeply about and want to see resolved. I have no such problems.

I have the same optimism as Prof Tao. That said, I can understand why so many mathematicians have been so upset or stressed out. It turned out much of the mathematical work is about clever combination of existing methods - this already requires enormous amount human ingenuity and years of dedicated learning. Unfortunately, or maybe fortunately, AI can be very good at knowledge transfer and finding combination of existing ideas to solve seemingly impossible problems. Even though mathematicians are extremely smart and capable, only a small number of them are capable of truly inventing "alien ideas", discovering new ground-breaking mathematical structures, or coming up with new problem-solving techniques. That is, AI can eat many mathematicians' cake. That said, I'm still hopeful. Mathematicians still understand mathematics deeply. If someone can prompt AI to solve an important problem, that person is more likely a good mathematician than an average joe like me. So, I think mathematicians do have a bright future: leverage AI, and make more and bigger math discoveries. It's still the same north star: we must know, and we shall know. It's just that with AI, we will know sooner and more.

As a student, I am actively making decisions which will shape my career for the next forty or so years. At a minimum a discussion like this should acknowledge the possibility that the current rate of AI progress continues apace. I understand the desire to be encouraging, but the best preparation for students involves the consideration of possibilities that current mathematicians negligently paper over.

Of course it will get better at exposition than humans. And it will prompt itself in due time.

I expect it will remain true into the future (10+ years). I have moderately high confidence (75% or higher) in this prediction.

I use frontier AI models in my work all the time. I think they accelerate my work by helping me understand faster and prompt better.

The models are most useful and most productivity-enhancing in the hands of experts and in the area of their expertise.

I don’t expect a jobs apocalypse, not even in math.

It's not like "should I get a PhD" is a new question. It's not unheard of for unpredictable events to drastically affect the career prospects of PhDs in my field. During my lifetime:

1. Mandatory retirement of professors was ruled illegal. While good for civil rights, it created a 10+ year gap in faculty retirements.

2. End of the cold war.

3. Transition of college teaching from tenured professors to gig workers, aka "adjuncts."

The one constant during this time was the perpetual optimism of the faculty for the employment prospects of PhDs. "There will always be a need for physicists." My dad, also a PhD, confirmed that this goes back as early as the 1950s.

I would add one question to the student's letter: What are the ethics of AI and its owners?

My own suspicion/guess is that AI can break out of the bounds of the convex hull in math, and that’s going to become apparent soon.

At least for now someone still has to decide what to prove and why. Like why are you trying to prove that thing to begin with? Presumably it's a step along some journey, right? Maybe the journey is where you need to start deriving your satisfaction from, then.

AI is never to take the place of understanding, knowledge, and education.

It's best that AI sycophants smarten up.

> will math academia be big enough and accessible enough for anyone with sheer passion (despite not being the brightest mind in the field) to pursue a career in, or will it inevitably shrink such that it will only really be accessible to the brightest minds?

Could someone with a recent math PhD experience tell me if it this hasn't been so for years? Competition is incredibly high because people have to compete with every "brightest mind" from all around the world. PhDs are overproduced relative to the number of permanent positions. It's not a question that you only start to think about after you've seen LLMs do mathematics, and if that's the case the student should be made fully aware of what he's getting into. I don't want to call the original post "dishonest" but I wish this was addressed here without the LLM angle. However, it was written by a tenured professor, so he did say the only thing he realistically could.

God, the absolute decimation that is going to come for middle income countries.

Hell, right now the people quitting frontier labs are rediscovering trust and safety isues, like language parity problems, except all the work being done is in the first world and exported back to the rest.

[...]

> After I finished writing this blog post, and had already sent it to Terry, OpenAI released a huge treasure trove of results in mathematics [including] the resolution of the so-called quasi Riemann Hypothesis

We ought to all be careful about underestimating the speed and magnitude of the change that is coming.

> if you are a student who is passionate to learn what is new and what is left to do, then a PhD is definitely the right path for you

This is an awful lot of confidence to put behind career advice in a wildly changing world. Markets are real and tradeoffs bite. We're not in gay communist space utopia yet.

So this Calculus class was 100% online. I discovered only at finals week that the instructor was firmly based at a distant satellite campus.

The class was brutal to me, and I needed a lot of time in the tutoring hall just to barely grasp concepts as they paraded past us. I used my calculator in good faith.

I discovered that there were websites that would solve integrals and complex equations, but I recognized that as outright cheating, so I resisted those tools.

However, the online LMS was set up with frequent quizzes with unlimited attempts. Not being penalized for attempts meant that I could brute-force every answer for every quiz throughout the course and get perfect scores. Though I felt kinda evil, I did just that.

When the final exam came around, our phantom remote instructor suddenly expected everyone to show up on her campus in-person. This was absurd to someone who was (1) on FAFSA funds and (2) riding the bus, and when I protested, the solution was a proctored session in the Disability office, all alone.

I solved every last question on that thing with paper and pencil and I required every single minute of the extended 3-hour limit they granted to me. I got an A- or whatever final grade.

Perhaps I didn’t deserve it, because all those learings drained out of my skull within 3 months, but it was a textbook example of gaming the system without strictly cheating, and since I was not aspiring to a math career, who cares?

The department deleted the Calculus requirement shortly after I finished that semester.

What actual industries where you could get a phd in, died?

If I was to ever suggest one, it would be Philosphers.

Yet they have found ways to get tenure and/or other jobs for as long as the field exists.

SWE is a capitalistic game and Academia seems to be a game of status ?

Regardless, they are not going to make it if they remove LLMs.

Someone, somewhere will use SOL/Opus and mog the big boys.

“42.”

But no one could understand what the answer even meant. So they designed a computer to build the question itself again, and that was Earth. Then the story begins with Earth being destroyed because of a cosmic highway problem (I won’t write more since that would be a spoiler). In the opening background of this work, I found it interesting that after calculating for 7.5 million years, they didn’t even know what they had originally been asking. The story now feels similar to that story from back then.

This is a great moment to be a hassadeur, a madmen, somebody who wants to jump of the cliff with just a rope on his feet.

If you are that- great times- otherwise- good luck.

If you are one of those who try to drag down people oustanding, congrats on the team effort. Now try that with a machine..

You should also tell them “better luck next time” as they have to create and find their own luck unfortunately.

This game was meant to be unfair because the ones who have “won” want to keep it unfair for others, and cannot stand losing due to complete greed.

The truth is they (students) have to find a way to outsmart the incumbents. The best advice is to find your own strategy and listen to no-one.