AI is used only for spelling/grammar checks, and for compiling and plotting the data in the chart.
When I applied for my PhD last year, I certainly didn’t expect that just before I started it, there had been a millennium problem drama. Amongst my friends, I’m now part of the “Navier–Stokes generation” of PhD students. There are a lot of uncertainties: What will we do as PhDs if an AI can do frontier-level mathematics? Will the journal system remain intact? Will there be a position for me when I graduate?
I’m a numerical analyst-in-training, and some of the problems I work on seem less tangible and less well-defined than those on the pure side. Nevertheless, we felt the shockwaves from the proof of the Crouzeix conjecture and, more recently, the new upper bound on the complexity of matrix multiplication.
There are numerous blogs and essays that have sprouted this year, and many in the community have turned to the thoughts of great mathematicians, notably Thurston’s in On Proof and Progress in Mathematics, which has been widely discussed, for example by Grant Sanderson. Another well-known (more controversial) piece is Hardy’s A Mathematician’s Apology, as referenced (though by no means concurred with) by Kevin Buzzard.
Speaking of Hardy, allow me a small digression. According to “an excellent colleague” of Harald Bohr, “Nowadays, there are only three really great English mathematicians”. The first of them is naturally Hardy, but I personally find Littlewood, the second of them, more agreeable1.
A Mathematician’s Miscellany was written by Littlewood and later edited by Béla Bollobás. I want to share here a few more short quotes from this genius book:
“It is very hard to make a random selection of stars. If, for example, you see a star (with the naked eye) it is probably bright.”
“J. J. Sylvester sent a paper to the London Mathematical Society. His covering letter explained, as usual, that this was the most important result in the subject for 20 years. The Secretary replied that he agreed entirely with Sylvester’s opinion of the paper; but Sylvester had actually published the result in the L.M.S. five years before.”
“When Trinity once had some wine at a lowish price, but not satisfactory and also not selling, they doubled the price, whereupon the idle rich bought it all up.”
The Miscellany has no direct bearing on the current situation, but to me it brings more clarity than some of the serious, timely statements: it keeps me grounded and curbs my tendency to think about AI all the time.
Many in the community have rightly argued for the necessity of the explanatory side of mathematics. However, from the chart, we are seeing only an increase in the AI discussions2. With the current discussion about human understanding of maths, shouldn’t there be a flood of new mathematical expositions as well? The Miscellany, to me, represents the best of them: quirky stories about mathematicians and their lives; small, delicious mathematical nuggets that piqued Littlewood’s interest; or just arbitrary, casual thoughts during research.
There are many important initiatives about the role of AI in maths, and statements are put out every day to respond to the new reality. They are certainly vital voices that need to be heard, but I argue that the less flashy, more casual expositions should also be promoted. They:
- make difficult mathematics digestible for others, particularly for new PhD students and researchers from other areas who may find more specialised material difficult. An example I personally benefited from even as an undergrad is this.
- they (typically) acknowledge their sources well, linking to other useful, digestible materials. This is not only proper practice for academia, but also serve as excellent pointers for their readers. It works both ways: papers/essays that are frequently referenced are probably good explainers themselves.
- encourage public outreach efforts, demonstrating the community’s commitment to public understanding and putting the explanatory side of mathematics into practice.
- give the public and early career researchers (e.g. the N–S generation) more confidence that the community is not single-mindedly focused on AI and that the field is still alive with mathematical activity. This helps balance out the anxiety, which, though justified, affect how we navigate the new landscape.
Back to being the “Navier–Stokes generation”. As junior mathematicians, we face many uncertainties but also many opportunities, so it is natural to think a lot about AI. Reading the Miscellany, however, reminded me of what inspired me to study mathematics. This may seem idealistic and naïve to many, but there are interesting people, good stories, and fun maths in our field, and they are worth recording.
- The final one is, of course, Hardy–Littlewood. ↩︎
- The stats here are very limited by the tools available to me; they only include the partial data that Claude could find, and the format is limited to blogs. This leaves out many other forms of exposition, such as the brilliant videos from SoME. Nevertheless, I hope the point still stands. ↩︎
Received 16 October 2026, revised 25 October 2026.
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