Field notes · 01
Mathematics
Proofs, structures & the maths behind the code
Proofs, algorithms and the maths behind the code: number theory, linear algebra, probability.
// 2026
Proofs nobody understands: Terence Tao, AI and the purpose of mathematics
What Terence Tao has actually said and done about AI in mathematics, and why I think the real test for AI companies is whether humans can still understand the mathematics their models produce.
Principia Mathematica: hundreds of pages to reach 1 + 1 = 2
How Russell and Whitehead tried to build all of mathematics from pure logic, and what their attempt taught us about sets, numbers, types and the limits of proof.
Fibonacci in O(log n): from matrices to fast doubling in Java
Why the naive Fibonacci is exponential, how a 2×2 matrix turns it logarithmic, and a fast-doubling BigInteger implementation that computes F(1 000 000) in a fraction of a second.