@xenaproject.bsky.social
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xenaproject.bsky.social
My talk at the Simons Foundation last week is now up on YouTube youtube.com/watch?v=K5w7VS2sxD0 . It is a hopefully-comprehensible general audience talk about what I think is a big decision which mathematicians will have to decide whether to back or not.
Kevin Buzzard - Where is Mathematics Going? (September 24, 2025)
YouTube video by Simons Foundation
youtube.com
xenaproject.bsky.social
My colleague Jon Mestel pointed out to me that whether you use the US 09272025 date system or the pretty-much-everywhere-else-in-the-world-and-far-saner 27092025 system, today's date is a perfect square, as is the current month and the year! Will this ever happen again??
xenaproject.bsky.social
Of course Barbara! Thanks for asking!
xenaproject.bsky.social
Amongst the projects funded is my project www.renaissancephilanthropy.org/a-dataset-of... to create what in 2025 is a super-hard dataset of pairs (informal hard proof, formal statement) of recent results from top journals. The challenge for machine is to formalise the rest of the paper.
www.renaissancephilanthropy.org
xenaproject.bsky.social
Renaissance Philanthropy have announced the first 29 grants they've given from their AI For Math fund www.renaissancephilanthropy.org/ai-for-math-... . Interesting to see that around half of the funded proposals mention Lean.
AI for Math Winners Page — Renaissance Philanthropy – A brighter future for all through science, technology, and innovation
www.renaissancephilanthropy.org
xenaproject.bsky.social
Mathematics is also incomplete (assuming it's consistent) and that hasn't stopped lean from engaging with it at research level
xenaproject.bsky.social
Could you ever envisage lean being useful to verify nontrivial code written in common programming languages or is this asking too much?
xenaproject.bsky.social
I absolutely agree; IPAM is the notable absentee from the list. I organised a conference there in 2023 www.ipam.ucla.edu/programs/wor... bringing together people from mathematics and machine learning and formal methods, and it was a fascinating week!
xenaproject.bsky.social
Lol that was me a few years ago
xenaproject.bsky.social
I did read parts of Langlands document about defining local epsilon factors locally and it was just page after page of representation theory (so it looked like groups acting on vector spaces)
xenaproject.bsky.social
I have never read the algebraic proof of the first inequality in global class field theory, I've just heard that it exists. I read the analytic proof last week though :-) The elementary proof of the prime number theorem still has plenty of basic real analysis in it.
xenaproject.bsky.social
Featuring a sorry-free proof that 2+2=6
xenaproject.bsky.social
The construction of local epsilon factors in the Langlands program was done by Langlands in an unpublished document which is hundreds of pages long. Then Deligne discovered a global construction which uses L-functions at some point and which fits into 30 pages
xenaproject.bsky.social
The fact that there exists a class formation for global fields (this is a higher reciprocity statement in number theory) boils down to proving two inequalities and traditionally one of them was done analytically (using L-functions like PNT) but now purely algebraic proofs are known.
xenaproject.bsky.social
Thanks for asking Barbara. The salary range is £48,056 - £56,345 per annum. I made some enquiries and the visa question is infinitely more complicated because there are a gazillion different kinds of visas depending on the applicant. The price could range from hundreds to thousands.
xenaproject.bsky.social
Why is this a worthwhile project?

1) It will create a hard dataset for autoformalization AI's;

2) It will force us to formalize the definitions of mathematical objects which are being used today in the top journals, thus making Lean's mathematics library more relevant to modern math researchers.
xenaproject.bsky.social
I am advertising for 4 post-docs to come to Imperial and formalize, in Lean, *statements* of theorems from recent issues of the top generalist pure mathematics journals.

www.imperial.ac.uk/jobs/search-...

Positions are for 2 years, start date 1st Oct this year. Deadline 15th August.
Description
Please note that job descriptions are not exhaustive, and you may be asked to take on additional duties that align with the key responsibilities ment...
www.imperial.ac.uk
xenaproject.bsky.social
I am advertising for 4 post-docs to come to Imperial and formalize, in Lean, *statements* of theorems from recent issues of the top generalist pure mathematics journals.

www.imperial.ac.uk/jobs/search-...

Positions are for 2 years, start date 1st Oct this year. Deadline 15th August.
Description
Please note that job descriptions are not exhaustive, and you may be asked to take on additional duties that align with the key responsibilities ment...
www.imperial.ac.uk
xenaproject.bsky.social
Note that no official IMO markers were involved in the marking of the solutions. I am also unclear about whether many solutions were generated and then humans chose the ones most likely to be correct, or whether the machine gave one "final answer" to each question with no human intervention.