Sharing a few thoughts on the future of math
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If you want a finger on the pulse of how mathematicians are feeling right now, take a look at this post on Proofs and Prompt:
Timestamps
0:00 – Math student angst
3:10 – How does math work?
11:24 – A proof machine
25:12 – A conjecture machine
26:59 – A theory machine
31:31 – If AI is better at everything
34:58 – The best time to enter math
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Looking back at this, there's one thing I allude to at the end, but wish I had included more in the middle: I don't think you have to use the models to actively contribute to math. As the emphasis shifts more towards theory building, and proof is treated more like raw data, some will lean into using models to see new proofs, but there will undoubtedly be many who prefer not to. You already see this; Max Weinreich uses the term “AI-vegan mathematicians”. There's plenty of work to be done in deepening understanding even if you restrict yourself to reading only what people have written, which is already far beyond what any individual could digest in a lifetime. If math was funded per proof, as if there was some market for theorems out there, then you'd run into trouble abstaining from a proof-generating machine. But luckily that's not at all how this works.
Mathematicians have been writing a lot on this topic. Here are just a few links you may enjoy to see how others are thinking about it:
https://math.mit.edu/~etingof/futuremath8.pdf
https://proofsandprompts.com/2026/10/14/the-dialectical-theorem/
https://proofsandprompts.com/2026/10/08/100-reactions-to-100-solutions/
Math is dead. No new theorems are getting made, just old ones.
Wtf?
There has never really been a good time to get into math. As a profession it has always had very limited opportunity. There are only so many tenure track positions. Outside of tenure track professor jobs, there are very few "mathematician" jobs. There's likely more professional athletes than professional mathematicians Most of the famous mathematicians of the past have had other jobs, like lawyer, or had a pretty tumultuous and unstable academic existence. Yes, there are many "uses math" jobs but that's not really what we're talking about , right? but even those, only the finance jobs actually make any money. Your own career choice is a prime indicator of this situation. You are a YouTuber. If you weren't, what would you be doing for a living? Probably not math…
If AI solves every mathematical problem there is, every open problem, comes up with new theorems, or advances enough in the coming years to reach, to some extent, artificial consciousness and dig even deeper, I will still wake up and grab pen and paper.
Is it scary? Yes. Is it confusing? Totally. Can it even push people toward existential questions? For sure. BUT every craft, every passion and every “job” people have done throughout history has been challenged in this way. On a bright note, I think this is good: it will test the passion mathematicians have for their math. Are you doing it for fame, status or money? Or because you like it and are naturally drawn to it? This is an ingredient that may make society different, but it will never erase our thinking skills, unless we let it. I genuinely think it might encourage a more artistic approach and a utterly math-driven mindset when doing things. Math is almost as old as the universe itself, and these challenges are a natural, organic part of history. In my opinion, seeing the bigger picture and being free of fear of the future is the key. For that, everyone needs to be open. I see musicians and cinematographers having the same fears, and it is getting deeper and deeper with time.
Going to point out here that asking if AI will unilaterally get better than humans at math is asking the wrong question. Like, as it is now there are mathematicians who are just better at math than other mathematicians, but that doesn't mean only the first group of mathematicians have jobs, because there is so much work to be done in math and only so many people who can do it so everyone who can do it gets paid to do the work. AI is inherently limited in how much work it can do it do in that computation is a physical process with physical constraints so a machine can only do so much compute at a time, and it's already been proven that infinite compute would be required to even just prove all that can be proven, so as long as people are interested in doing more math there is going to be more work to be done, and people with the minds to do it can some of whatever work that isn't currently being done by the machines. This relates to the economic concept of comparative advantage, where you don't need to be objectively the best to do a job, you just need to exist, and people will continue to exist because we exist for ourselves while the machines exist to serve us. This is the fundamental crux of all the AI arguments that gets overlooked in most the discussions.
After 45 years as a scientist, R&D leader and now a fixer at the intersection of technology and business, the ability to solve problems with whatever tools available is the most coveted of all skills. Will mathematically perceptive individuals need to evolve? Without question they will. But the transferable skill of identifying the problem to be solved and the tools to do it will remain in demand. Sorry that the purity will be lost, but we in applied sciences have been dealing with that for a long while.
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I think much of the anxiety about AI and the future of mathematics comes from confusing a crisis in the culture of mathematical prestige with a crisis in mathematics itself.
AI doesn't threaten the fundamental purpose of mathematics, which is to develop understanding. A beautiful theorem remains beautiful, a deep insight remains profound, and the satisfaction of finally understanding something doesn't disappear simply because an AI got there first.
What AI does threaten is the status that some mathematicians derive from being exceptionally good at mathematics. If your intellectual identity is built around being among the very best at discovering and proving new results, then the arrival of an intelligence that can outperform you is understandably unsettling. But that's a threat to your position in an intellectual hierarchy, not to mathematics.
Mathematicians can still pursue understanding however they wish. They can ignore AI-generated proofs and discover things independently, or they can study those proofs, extract deeper insights and develop entirely new ideas. None of that becomes less valuable because an AI has already established the result.
Perhaps the real challenge AI presents to elite mathematics is not whether mathematicians can continue to do meaningful work, but whether they can accept doing meaningful work without necessarily being the first or the best.
The value of understanding mathematics has never depended on humans being the most capable mathematical intelligence. I suspect much of what is being presented as an existential crisis for mathematics is actually a crisis of professional identity and, frankly, ego.
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Honestly, a lot of the concern about AI and the future of mathematics seems like hype about nothing. I really don't see why AI should have any negative impact on the human pursuit of mathematics. Surely the ultimate goal of mathematics is understanding, not simply accumulating proofs.
Mathematicians can continue to pursue that understanding however they choose. They can ignore AI-generated proofs and work things out for themselves, or they can study those proofs, extract deeper insights and build new ideas from them.
The only real change is that someone might no longer be able to claim they were the first to prove something. But that has never been the most important part of mathematics. That's more about recognition and ego than understanding.
The real joy of mathematics is that moment when something finally clicks, when you understand something deeply and suddenly see possibilities you couldn't see before. AI cannot take that experience away from anyone.
A PhD student can still spend years exploring a problem that AI has already solved, uncovering the underlying ideas and finding ways to communicate them. Their work is no less valuable for it. If anything, AI simply gives them another tool that may or may not help them along the way.
Mathematics doesn't need to change its purpose just because AI can produce proofs. Perhaps what needs to change is our attachment to being the person who got there first. The pursuit of understanding is as meaningful as it ever was.
It is as simple as that.
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This was super well done. Thank you!
There's a spiritual component as well, which I suppose you're getting at with "aesthetic joy" but I think is worth mentioning specifically. The pursuit of truth, of understanding the universe, is to me no different from pursuing a God who is truth personified and who's creation I am studying. In a way, I feel like math could come full circle – much of it started out as philosophy and worldview, not practical application.
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AI is the latest mathematical tool science can provide, but it is also an amazing resource to help you learn math. In the end humans need to understand the math no matter how it is generated.
sorry but this is just COPE. math is over. its fucking DEAD. just face reality and admit it already!
just like software engineering. we DON'T have humans auditing code written by AI anymore, because the auditors make mistakes which the AI then has to correct
Your focus on theory building leaves open what happens to the market value of traditional proof-writing skills.
3blue1brown.
I've been watching your videos for a good 10 years – nice to see your face for the first time!
I like to think of it the same way as when chess engines beat grandmasters. Millions of people still play chess, and they still compete against each other. I think mathematics will be the same. It might become better than us at everything, but that doesn't mean we'll stop playing with it or appreciating its beauty.
You got this Goose.
Agree with the video, and I think it’s also worth being optimistic about the future of philanthropic support of math. The Simons Foundation, which is essentially just a rich guy who was also a mathematician, funds mathematics on a scale similar to the NSF. Many of the people making a fortune on AI also have mathematics backgrounds.
this is true iff P == NP
AI is basically an empirical unlock for math, letting us ask questions we couldn't even reach before. Sure, the AI might eventually just give us the answers, but exploring these complex systems ourselves is just an incredibly fun way to spend time.
Math has the unique chance to meet itself: the search for beauty instead of the quest for answers. Whilst the first requires reformulating certain questions, the second involves answering given questions,… no matter how.
When AI presents an idea of a new bigger particle accelerator or whatever new giant dark matter physics device and says “i did all the math, if my model is correct it should not explode and should be a new source of innovation”. I’m pretty sure there will be a LOT of funding to have mathematicians and physicists try to understand and explain what it is. And it may be so complex that it will require a lot of research and jobs
We should look at history to understand these changes more scientifically. Machinery and factories replaced skilled craftsmen in the 19th century. AI will replace intellectual work in a similar way. Also, our higher education system has already made the transition to primarily being about vocational training with funding coming from industry (and student loans).
My prediction is that employment of professional mathematicians at universities will fall 80-90%, their funding will come from big tech (which will also dictate the areas of research), and there could be a moderate increase in hiring of PhD mathematicians at big tech firms. I also think the days of relative freedom for tenured faculty will go away, and big tech will start managing mathematicians as staff who will have to become accustomed to taking directions from business managers.
40:01 perpatao type of philosophy
Everything in the world can be defined by math. If AI becomes strong enough at math then everything can be replaced by ai. On the plus side, if it can actually produce new stuff it could lead us to some sort of sci-fi future.
There is now chessplayer with 2800 elo thx to the theory built with ai. & They’re still learning.
For the beauty of the game. Chriosity & Pleasure are powerful driver. I like to think of AI the way Cimak did : nor Slaves nor master but equals.
So… in summary, for the love of the game?
Grant I went back to uni at 34 years old to study civil engineering, you helped me a lot to gain confidence and I am really grateful for that!
yeah i dont agree. The fun parts are gona be AI, you are just gona maybe "lead it" a bit. Cool, if you like to be the product owner, then it s the perfect time to be alive … for a few more years. Or well, if you are good enough to be in RD at the very edge of creativity, but that s such a small percentage of people I sincerely doubt 2.5 mil of viewers fall into that category.
I think we need to love one another. 🙂
IMO, mathematicians are in existential battle (along with many other fields) to make the case that their field/subject requires consciousness, that AIs based in the Turing computational framework cannot be conscious, and cannot achieve mathematical creativity – else they indeed will just be replaced. Penrose actually started this effort – but he was given no support by mathematicians while being heavily attacked by cognitive scientists (a field useless in this effort since it's completely captured by the computer model of mind). But it's doubtful that mathematics has any such perception – even yet, while staring at their own demise.
All of this seems so much whistling past the graveyard. Math as conducted by academics is going to become thin on the ground. There is simply not going to be enough budget to support the same numbers of those who have lived and died (academically) by journal citations. Puffing up some nibbling-at-the-edges just isn't going to survive the continuous stream of math that will now come from AI. Industrial Math (co-called) may thrive longer. That is, that kind of applied mathematics (sniffed at by many academics) will continue to be needed because engineering needs it. But it, too, will feel the presence and eclipsing power of AI.
I think I always enjoyed never getting to see the content creator's face since I think it puts people's attention on the wrong thing since it's the content that matters and not how the content creator looks.
I’m an idiot striving to be less of an idiot so I’ve started reading and doing high school calculus from a old textbook and realize how enriching math is. I suck at it, yes… but heckin heck.
Maybe so many people come here is just because AI still can’t explain things as well as you do, rather than for the social side of math.
What about the day when AI will administer AI generated molecules into our brain so we feel mathematical joy and understanding?
I like the weight lifting analogy, where we go to the gym for our own sakes while there are machines like excavators that do the heavy lifting for us where it's needed.
When was the last time you were paid to go to the gym?