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Max-Planck-GesellschaftAbsolutely thrilled that Dennis Gaitsgory from the Max Planck Institute for Mathematics has won the 2025 Breakthrough Prize in <a href="https://wisskomm.social/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematics</a> for his central role in the proof of the geometric <a href="https://wisskomm.social/tags/Langlands" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Langlands</a> conjecture - often referred to as the Rosetta Stone of math! 🥳 Congratulations - this is such a well-deserved recognition for decades of deep work!🎉

Chuck Darwin<a href="https://c.im/tags/Dennis" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Dennis</a> <a href="https://c.im/tags/Gaitsgory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Gaitsgory</a> has dedicated the past 30 years to proving the <a href="https://c.im/tags/geometric" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#geometric</a> <a href="https://c.im/tags/Langlands" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Langlands</a> <a href="https://c.im/tags/conjecture" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#conjecture</a>. Over the decades, he and his collaborators have built an extensive body of work, forming the foundation of the new proof. Although the geometric Langlands program is highly abstract, it forges deep connections between different mathematical structures and has the potential to drive breakthroughs in theoretical physics, number theory, and even quantum computing. The <a href="https://c.im/tags/Breakthrough" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Breakthrough</a> <a href="https://c.im/tags/Prize" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Prize</a> was established in 2012 by Sergey Brin (Google), Mark Zuckerberg (Facebook), and others to recognize outstanding researchers for their groundbreaking discoveries. It is awarded in the fields of life sciences, physics, and mathematics. In 2016, the Breakthrough Prize in Life Sciences was awarded to <a href="https://c.im/tags/Svante" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Svante</a> <a href="https://c.im/tags/P%C3%A4%C3%A4bo" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Pääbo</a> from the Max Planck Institute for Evolutionary Anthropology in Leipzig, and in 2022, to <a href="https://c.im/tags/Anthony" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Anthony</a> <a href="https://c.im/tags/Hyman" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Hyman</a> from the Max Planck Institute for Molecular Cell Biology and Genetics in Dresden. <a href="https://www.mpg.de/24476145/breakthrough-prize-mathematics-2025?c=2249" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.mpg.de/24476145/breakthrough-prize-mathematics-2025?c=2249</a>

The Krononaut Moon Project 🌑A <a href="https://me.dm/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#geometry</a> masterpiece: <a href="https://me.dm/tags/Yale" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Yale</a> prof solves part of math’s <a href="https://me.dm/tags/RosettaStone" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#RosettaStone</a>. Yale’s <a href="https://me.dm/tags/SamRaskin" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#SamRaskin</a> has solved a major portion of a math question that could lead to a translation <a href="https://me.dm/tags/theory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#theory</a> for some areas of <a href="https://me.dm/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a>.❛❛ The [Robert] <a href="https://me.dm/tags/Langlands" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Langlands</a> Conjectures … suggested in the 1960s that deep, unproven connections exist between <a href="https://me.dm/tags/numbertheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#numbertheory</a>, harmonic analysis & <a href="https://me.dm/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#geometry</a> — 3 areas of math long considered distinctly separate. ❜❜🔗 <a href="https://news.yale.edu/2024/11/01/geometry-masterpiece-yale-prof-solves-part-maths-rosetta-stone" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://news.yale.edu/2024/11/01/geometry-masterpiece-yale-prof-solves-part-maths-rosetta-stone</a> 01 Nov 2024 🔗 <a href="https://Wikipedia.org/wiki/Langlands_program" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://Wikipedia.org/wiki/Langlands_program</a><a href="https://me.dm/tags/KrononautMoon" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#KrononautMoon</a>

kamstrupCannot contain my excitement over the possibility of a breakthrough on the Geometric Langland's <a href="https://www.quantamagazine.org/monumental-proof-settles-geometric-langlands-conjecture-20240719" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.quantamagazine.org/monumental-proof-settles-geometric-langlands-conjecture-20240719</a><a href="https://fosstodon.org/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://fosstodon.org/tags/Langlands" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Langlands</a>

ƧƿѦςɛ♏ѦਹѤʞ<a href="https://www.youtube.com/watch?v=_bJeKUosqoY" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.youtube.com/watch?v=_bJeKUosqoY</a> Geometric Langlands Conjecture Proven: <a href="https://www.quantamagazine.org/monumental-proof-settles-geometric-langlands-conjecture-20240719/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.quantamagazine.org/monumental-proof-settles-geometric-langlands-conjecture-20240719/</a> <a href="https://mastodon.social/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#maths</a> <a href="https://mastodon.social/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a> <a href="https://mastodon.social/tags/Langlands" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Langlands</a>

Marcel FröhlichCC <a href="https://mathstodon.xyz/@m_artigiani" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@m_artigiani</a> this helped me to skim some context. Nothing compared to an expert’s thread, still exciting. <a href="https://mathstodon.xyz/tags/langlands" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#langlands</a> <a href="https://mathstodon.xyz/tags/rag" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#rag</a> <a href="https://mathstodon.xyz/tags/llm" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#llm</a>

Mauro Artigiani🍉What is a good reference to understand what the geometric <a href="https://mathstodon.xyz/tags/Langlands" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Langlands</a> proof that came out, for somebody in <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#maths</a> but not in algebraic geometry?Boost appreciated

Marcel FröhlichDid some stress testing of Gemini 1.5 Pro (using the Gemini Advanced subscription) this evening. Google’s latest LLM version with a context window that can handle the equivalent of about 1500 pages of text. So RAG is no longer about picking some chunks from documents but digesting large amounts of content entirely. I uploaded the five papers that together prove the geometric Langlands conjecture (about 1000 pages in total) and asked very general questions about the proof structure and more detailed questions and some background stuff. Processing is slow (no surprise) but the output is quite convincing. It is a reasonable way to get very complex facts and connections explained.<a href="https://mathstodon.xyz/tags/langlands" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#langlands</a> <a href="https://mathstodon.xyz/tags/rag" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#rag</a> <a href="https://mathstodon.xyz/tags/llm" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#llm</a>

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