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"Pessimism of the Algebra, optimism of the Geometry"
Simon Pepin Lehalleur
16.8K posts
Simon Pepin Lehalleur
@plain_simon
Mathematician (algebraic geometry, motives & friends, singularities in statistics and ML).
'Geometry is successful magic' (R. Thom)
University of Essen.
- It's like this, but sometimes you turn your head for a second and somehow there is a fully functional rocket that you have no idea how to even build yourself.Mathematicians watching physicists do math
- Replying to @NC_Renic and @RafaRuizdeLira"What a nice semicolon; hardly anyone knows how to use them." was right there!
- In a talk I attended recently, the speaker said: "Recall, or learn very quickly, that..."POV: A mathematician just said "recall"
- Does anyone actually use Research Gate, or is it just designed to pollute Google searches and generally annoy academics?
- How Claude Shannon decided on the name "entropy" in information theory (image from the nice survey arxiv.org/abs/1405.1003):
- I am really surprised by how revelatory this seems to many of the people in the thread... Isn't pseudocode notation as complicated conceptually as sum/product? Or is it an audience of programmers who all had terrible math teachers?btw these large scary math symbols are just for-loops
- I want to try to explain in simple terms the context of this paper and what it is roughly about.Peter Scholze: Geometrization of the local Langlands correspondence, motivically arxiv.org/abs/2501.07944 arxiv.org/pdf/2501.07944 arxiv.org/html/2501.07944
- Machine learning is still missing a solid mathematical theory of how the discrete/computational structure latent in natural data generating processes percolates through gradient descent and precipitates the formation of discrete/computational structure in models. Discuss.
- Replying to @chai_ste and @GrieveWatchEveryone who really wants to respect the solemnity of the occasion needs to spend the next 24 hours perfectly still. Shallow breathing is acceptable, provided every tenth exhale is a long mournful sigh.
- I have recently become very interested in "Singular Learning Theory", a fascinating connection between singularity theory and Bayesian statistics developed by Sumio Watanabe, with emerging applications to machine learning interpretability. 🧵 Last week I gave two lectures
- Replying to @spikedoanzThe problem with this (and basically any) approach to visualizing higher dimensions is that it completely destroys the natural symmetries of higher-dimensional spaces 😢
