We’re so used to it, we hardly notice that men are bigger than women. But the other night Sam and Emily came over with their baby Willa. Emily was holding Willa for a while, and then passed her over to Sam. Willa shrank 20%!

[20 September 2026]

My recent essay “Reflections on the Millennium Problems” argues that these famous mathematical challenges are not as important as generally imagined both by the public and even by experts. Mathematicians love posing true/false conjectures, the harder the better. My essay suggests that such problems may not capture what’s really important in mathematics.

Now we’ve had the tumultuous past week, in which OpenAI has announced the AI resolution of the Navier-Stokes Millennium Problem and 25 Fields medalists have posted a letter of objection. Finding the yes/no answers to conjectures, they complain, is not what matters in mathematics. Famous mathematics problems are just “landmarks and lighthouses”, they argue, and solving them “is only a tool and proxy for achieving the primary goal of conceptual understanding and insight.”

Of course I agree. Still, one can’t help noting that it was mathematicians who announced the $1m prizes in the first place, and who are now blaming the AI industry for taking them so seriously.

With a sprinkle of cynicism perhaps one can make a prediction. As I describe in my essay, the P-vs-NP problem seemed urgently practical in the 1970s but now looks mostly academic — yet experts nowadays tend to suggest that we knew all along it was academic. Maybe we’ll now see a similar effect with the Millennium Prizes? They were presented in 2000 as urgently important to mathematics, but maybe experts will now begin to say we knew all along they were just games.

[13 September 2026]

We journal editors work valiantly to process the tsunami of manuscripts coming our way, but who knows how long this can last. Yesterday a 47-page manuscript in perfect English was submitted to one of the journals I serve. We told the authors it was too long and would have to be shortened. The revised manuscript arrived today, 24 hours later, 30 pages shorter and also in perfect English.

[6 September 2026]