The other day, a undergraduate math student emailed me to ask me whether it still makes sense to get a PhD in math. This isn’t the first time I’ve heard this question, because a lot of young people are asking it, given the recent storm of results released by OpenAI. Basically, AI is getting pretty darn good at mathematics.
Dr. Scott Aaronson is the Schlumberger Centennial Chair of Computer Science at The University of Texas at Austin, and he’s said the following of AI:
Right now, I’d say it’s closer to a normal first year math graduate student who happens to know every existing published technique and can apply them to arbitrary new domains, and can do for thousands of problems in a few weeks, with unlimited motivation and persistence[.]
Naturally, this sort of thing is making a lot of people nervous to the point that hundreds of mathematicians have already joined the AHM or The Association for Human Mathematics, many of whom have committed to not using AI (LLMs) in their research. So, of course students are asking: does it even make sense to study math any more? Should I get a PhD in math.
I got my PhD in math about ten years ago at McGill University in Montreal. It was in number theory, and I still love math. And here’s my answer...
HECK NO! Are you crazy?
If I were going back in time to give myself advice, I’d tell myself to get the heck out of math and do something else, simply for practical reasons. It takes 5-7 years to get both masters and PhD degree and if you can already get a job right after your undergraduate degree, it makes more sense than ever to do so.
And that’s for two reasons, the first being the most practical. The fact is, getting a job after you’ve got your PhD in anything that really demands a PhD was already very difficult before AI. Now, it’s just going to get worse because any of the skills you’re likely to develop are going to be made partially obsolete with AI. Now, I won’t say completely obsolete. I still think there will be some places for human beings in the math realm, but do you really want to take that chance?
After all, mathematics is one of those domains right after programming that’s most amenable to the AI takeover. Indeed, mathematicians already take great care to formalize their results in exceptionally precise language, something that’s been made even stronger with lots of math being put into LEAN (a formal proof verification system). If any discipline will suffer from LLMs taking it over, it’s math.
Of course, I need to make something very clear: even with AI results, it will still be important, at least in the short-term, for there to be people around to understand math. So, graduate programs won’t vanish and there will still be funding for them.
But then, I want to ask you two questions.
- What is the purpose of doing the degree in terms of benefits to your own life? It’s already very hard to become a professor in mathematics. For each academic position, there are hundreds to even thousands of PhDs applying to them. (I know because several universities tell you the numbers after you apply.)
- How will a PhD help you if you’re not going into academia? In the past, some places hired PhDs as programmers but that’s going to be ten times more difficult now that any undergrad who studies programming will be leaps and bounds ahead of you with AI.
Financial jobs too will likely be quite hard to get as trading and other things are taken over by LLMs directed by a few fortunate individuals. The competition will be like trying to become an A-list movie star. In other words, you’re likely to be much better off trying to get a job with just a four-year degree instead of wasting your time with a PhD.
True, in the past, a PhD really meant something to employers, because it meant a lot of dedication to abstract thinking. Now, employers will see your PhD and laugh because PhDs will become a dime a dozen and just indicate that you were good with LLM-prompting, even if you never used AI in your life!
Finally, even if a PhD does land you one of the rare academic positions, which might not even exist because LLMs will become really good at teaching, then you’re going to have to contend with dealing with LLM results. Even if you don’t want to use them, your colleagues will be using them and your students will be using them, both to study and to cheat at homework. Is that the kind of environment you want to end up in? I sure as heck wouldn’t want to be in an environment where everyone is prompting an LLM to mine for new results and help. Revolting.
Yes, yes, there’s the Association for Human Mathematics, with a few hundred professors saying they won’t use AI. Hey, I’m happy some people are standing up to AI. That’s great!
But keep in mind that unless their numbers grow quite a bit, and they create a separate association where they only consider human mathematics, they’re just going to become an anomaly that eventually dies out. And I’ve already looked at their page: they’re not unilateral enough to be strong. Only if they truly separate from the math community will they have any chance of surviving, and they won’t do that. Mathematicians aren’t going to rock the boat, and they’re under the thumb of university administration and policy, who are generally pro-AI as being pro-AI is good business.
No one can know the future, but even with the present state of things today, a PhD is terribly unappealing.
Don’t listen to the professors!
Have you ever heard of Terry Tao? He’s a Fields Medalist and obviously a very bright guy. And recently, he’s been publishing a lot of guest posts on his blog. These guest posts were written by professors urging students to consider a career in mathematics. Here’s what Álvaro Lozano-Robledo, one of the professors said about getting a PhD:
[I]n my opinion, the answer should not have changed from a year ago to today. The most important reason (and perhaps the only reason) to do a PhD in math should be that the candidate is passionate about mathematics and wants to become an expert in a particular topic within our field. If that is the goal, then the presence of LLMs in mathematics is irrelevant, because the goal is achieved when the candidate has gained sufficient knowledge to be an expert on a particular problem.
Is this some kind of joke? I mean, yeah, it’s great to be passionate about math. I love mathematics (at least the human kind, not the AI kind). But this has got to be the most irresponsible advice I’ve ever heard. Because the fact is, no one is going to care about you except you. And after all that exploration of math, you’ve got to eat. You’ve got to buy food and pay rent. And you should figure out a pathway in life that won’t leave you destitute.
Let’s keep something in mind. Professor Álvaro Lozano-Robledo, like so many of the professors today urging people to be idealistic and get a PhD, is an established professor. In fact, Professor Lozano-Robledo is a full professor of Mathematics at the University of Connecticut, and he’s been a professor for over twenty years.
Even if he loses his job today, he’s set. Professors are paid supremely well, especially in the United States, and while professors are not on the level of tech CEOs or oil sheiks, they’ve got enough money to have a place to live and a decent retirement. And if you’ve been a professor for twenty years, yeah, you’re set.
Moreover, professors love to be recognized for their work. They love displaying their stuff at conferences and being admired. And part of that means doing well in academia, which in turn means getting graduate students! Graduate students also in part justifies funding and recognition in the department. Do you really think they’re going to tell you the truth about the situation when their entire career is based on a system dependent on graduate students (among other things)? That would be like asking a used car salesman if you’re getting a good deal on a twenty-year old Fiat with 300K on the odometer.
Now I’m not knocking on Professor Lozano-Robledo. He’s likely to be a pretty nice guy. But his motivations are very different from yours, if you’re thinking about graduate school. The world is a harsh place right now, and it’s hard to get a decent job. And there are plenty of better things you can do to earn a decent living than get a PhD in mathematics now that AI has become so powerful.
Terry Tao is also pretty positive about the future of math. But again, he’s accumulated a lot of unsolved problems that he’s worked for decades at, and it’s fun for him to talk to an LLM to collaborate. And let’s not forget he’s one of the brightest. He won the Fields Medal and is a Fellow of the Royal Society of London. If something goes haywire in math, he’s the last man standing.
In general, professors might be nice people. And they might seem to care about you as long as your success means academic success. But once you’ve fallen through the cracks of academia, they’re not your friends and they won’t do one single thing to help you. In the end it will just be you applying for jobs and not hearing anything back. That’s just the nature of the academic beast.
Conclusion
A PhD in math is not the worst you can do in life. And there was a time where it could open doors. But if I were born eighteen years later, I’d be deciding whether to do my PhD right now. And with the way things are going right now, I wouldn’t even consider it for one microsecond.
Yes, it’s seems like a safe option for now because you can chill out and just float in academia for a while without having to think about life. That does sound very appealing, especially because the world is so messed up. But these days, I wouldn’t even find it enjoyable because it just would be an AI-fest of graduate students prompting ChatGPT all day.
Regardless, once you’ve graduated, you’ll really need some practical way to make a living and have a good life for yourself. And with what AI is doing in math right now, getting a PhD is one of the dumbest things you can do.