The blog post discusses the outcomes and implications of the 2025 International Mathematics Olympiad (IMO), focusing on the performance of AI systems like those from Google DeepMind and OpenAI. It highlights the competition's stru...
The post examines the limitations of AI in accelerating mathematical discovery and emphasizes the necessity of expert human involvement in the process.
The post discusses recent advancements in the formalization of Erdős problems using artificial intelligence, particularly through platforms like erdosproblems.com and the Formal Conjectures project by Google DeepMind. It highlight...
The post discusses the current state and future potential of AI in mathematics, particularly in theorem proving. The author expresses skepticism about AI's ability to autonomously prove complex mathematical theorems but is optimis...
The author expresses frustration with private datasets and the difficulty of judging closed source software. They discuss the flaws in language models and the problems with private datasets. The author also reports on their attemp...
0What is a quotient?
2025-02-09 •
The post explains the concept of quotients in mathematics, starting with the definition of natural numbers and real numbers. It then delves into the concept of quotients, explaining the 'well-defined' functions and the universal p...
0Think of a number.
2025-01-20 •
The author discusses the limitations of AI in mathematics, particularly in number theory, and proposes an experiment to test AI's ability to solve hard number theory problems. The author emphasizes the need for problems beyond und...
0Can AI do maths yet? Thoughts from a mathematician.
2024-12-22 •
The text discusses the recent achievement of OpenAI's new language model, o3, which scored 25% on the FrontierMath dataset. The dataset consists of hard math questions and is designed to challenge language models. The author, a ma...
0Fermat’s Last Theorem — how it’s going
2024-12-11 •
The author discusses the progress of teaching a computer a proof of Fermat’s Last Theorem, focusing on the technical and tedious aspects of the process. They highlight the importance of formalizing modern mathematics and the chall...
0Lean in 2024
2024-01-20 •
The blog post looks back at the events in the Lean theorem prover community in 2023 and discusses what to look forward to in 2024. It highlights the formalisation of certain parts of modern mathematics in Lean, including the expon...
The post discusses the formal verification of a recent result in combinatorics, specifically an exponential improvement to the upper bound on Ramsey numbers. The author discusses the gap between informal and formalized mathematics...
0Lean 2022 round-up
2023-01-08 •
The post provides a round-up of the Lean community in 2022, discussing various projects and developments, including the Liquid Tensor Experiment, the Sphere Eversion Project, unit fractions, p-adic Hodge theory, Kaplansky’s unit c...
0Beyond the Liquid Tensor Experiment
2022-09-12 •
The blog post is a report on the formal verification of an important new theorem by Fields Medallist Peter Scholze and Dustin Clausen. The theorem, known as the Liquid Tensor Experiment (LTE), was formally verified using Lean form...
0The Future of Interactive Theorem Proving?
2022-08-16 •
The history of interactive theorem proving has evolved to allow users to interact with the system at higher levels of abstraction, getting closer to informal mathematics. Recent advances in machine learning suggest a future where ...
The text is about the undergraduate course 'Formalising Mathematics' given by the author at Imperial College London. The course was for 3rd and 4th year undergraduates and MSc students, and it was specifically about formalising ma...