A letter to Professor Bernhard Riemann

Another note on the theme of my bewilderment with pure mathematicians.

The eminent Fields Medallist Alain Connes has published a 3-page letter to the great Riemann for which he set himself the task: “What could I tell to Riemann that would surprise him and that would give him confidence that his hypothesis is true?” The famous Riemann Hypothesis, one of the million-dollar Millennium Prize Problems, is that all the complex zeros of the Riemann zeta function lie on what is known as the critical line.

Working by hand around 1859, Riemann managed to compute the first five or six zeros. In the computer era, by a heroic combination of algorithms and analysis and hardware, more than ten trillion of them have been computed! They all lie exactly on the critical line, just as conjectured.

Connes does not mention these computations in his letter.

[12 February 2026]