proofs

I am writing tabulated Hilbert-style derivations, using a proof checker which I wrote in Python. See also: https://math.stackexchange.com/a/5135207/1755256 The book I am studying is Introduction to ...

In mathematics, truth is established through the power of proofs. Built upon axioms and guided by rules of inference, mathematicians construct logically irrefutable arguments. Once a theorem is proven, its truth endures eternally, transcending time and retaining its validity through millennia – like Pythagoras’s theorem. However, finding a proof isn’t always easy. Explore our expert content on ma…

Since the release of my preprint with Tim, Ben, and Freddie proving the Polynomial Freiman-Ruzsa (PFR) conjecture over , I (together with Yael Dillies and Bhavik Mehta) have started a collaborative project to formalize this argument in the proof assistant language Lean4. It has been less than a week since the project was launched, but […]

Proofs in mathematics are what mathematics is all about. They are subject to entire books, created entire theories like Fermat’s last theorem, are hard to understand like currently Mochizuki’s proof of the ABC conjecture, or need computer assistance like the 4-color-theorem. They are sometimes even missing, although everybody believes in the statement like the Riemann...

Introduction This FAQ is about proofs. Proofs are central to mathematics, and writing proofs is a skill many people find hard to master. There are two separate skills to develop: finding the proof and communicating the proof. This article focuses on finding proofs, but it also gives guidance on communicating proofs clearly. What is a...

I want to write a short post giving an example of what seems to me to be a rather nice proof without words. Like all the best proofs without words, they require some words to set everything up, and then … Continue reading →