Research diary — proof intuitions, open questions, work-in-progress notes, and the thinking behind the papers. Written for mathematicians and curious readers who want to understand the mechanisms, not just the results.
Montgomery's 1973 observation — that the pair correlation of Riemann zeros matches the GUE ensemble of random matrix theory — is one of those results that *shouldn't* work, and yet has been confirm...
People hear "machine-verified proof of the Riemann Hypothesis" and imagine the computer checking every $\varepsilon$-$\delta$ argument from Rudin. That's not what happens, and the gap between expec...
When I tell people the same algebraic framework applies to Navier–Stokes, the Fenton distribution, and neural scaling laws, the first reaction is disbelief. Fair enough — cross-domain claims are us...
The Collatz conjecture is usually stated as: take any positive integer, if even halve it, if odd do $3n+1$, repeat — do you always reach 1?
In 1960, Lawrence Fenton published an approximation for the distribution of the sum of lognormal random variables. His moment-matching approach was elegant, and it worked well enough for engineerin...