https://thalens.org/blog/ Research blog by Dr. Tamás Nagy — machine-verified proofs, open problems, mathematical insights en Thu, 23 Apr 2026 16:32:13 +0000 https://thalens.org/blog/why-random-matrices-riemann/ https://thalens.org/blog/why-random-matrices-riemann/ 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... Wed, 22 Apr 2026 00:00:00 +0000 number-theory riemann-hypothesis random-matrices GUE https://thalens.org/blog/what-lean4-checks/ https://thalens.org/blog/what-lean4-checks/ 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... Mon, 20 Apr 2026 00:00:00 +0000 lean4 formal-verification methodology https://thalens.org/blog/one-algebra-many-problems/ https://thalens.org/blog/one-algebra-many-problems/ 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... Sat, 18 Apr 2026 00:00:00 +0000 latent-framework cross-domain tensor-algebra methodology https://thalens.org/blog/collatz-lyapunov/ https://thalens.org/blog/collatz-lyapunov/ 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? Wed, 15 Apr 2026 00:00:00 +0000 collatz dynamical-systems lyapunov number-theory https://thalens.org/blog/fenton-solved/ https://thalens.org/blog/fenton-solved/ 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... Fri, 10 Apr 2026 00:00:00 +0000 quantitative-finance lognormal closed-form fenton