Emily Riehl, A New Paradigm for Mathematical Proof? | Natural Philosophy Symposium 2025

Comments · 192

• AD

  @adambruce1688 · 6 months ago

  oooh. I love this format where you have a mathematician and a philosopher discussing the same/similar topics sequentially. Also, both speakers were excellent. Riehl's book on category theory is great!

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• RO

  @rogerwitte · 10 months ago (edited)

  I have heard very similar ideas to Emiiy's expressed by Terrence Tao, Tim Gowers and Andrej Bauer. I think Kevin Buzzard's motivation is more pedagogical - he hopes it will speed up learning in areas where it is currently taking longer and longer to learn the pre-requisites to participating in research.

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• ME

  @meesalikeu · 10 months ago

  yay, a new dr. emily lecture for us! 🎉🎉🎉

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• P3

  @p3nGu1nZz · 10 months ago

  Great talk. I have successfully adopted and implemented these new paradigms for great success. <br><br>Ai augments do not replace formalization and standardization but amplifies coherent algorithms proofs. <br><br>What a time we live in!

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• FB

  @fbkintanar · 10 months ago (edited)

  The commentator after Emily Riehl&apos;s talk is Justin Clarke-Doane, a philosopher specializing in philosophy of mathematics, logic, and metaethics. &nbsp;<a href="https://www.youtube.com/watch?v=fzxW2XJS6SE&amp;t=2254">37:34</a> &quot;Formal proofs have the feature that you and I don&apos;t have to agree at all on what the words mean. We don&apos;t have to agree at all on what the world is like. We just have to agree on whether the following sequence of symbols, every line is either an axiom or follows from the previous line by a rule of formal inference&quot;. I think this description, maybe it is a caricature, makes too bold a claim in its defense of (the modern formal incarnation) of the Aristotelian tradition of proof. The chosen vocabulary does matter, including the notations that appear in natural language proofs. And if there is some mapping, presumably well-defined, i.e. independent of choices of presentation, between the formal and the natural language sides, as the central dogma claims, we have to know what it maps to on the natural language side.

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• RY

  @ryft_music · 10 months ago (edited)

  tldw; Lean proof assistant cool. AI not so cool, but maybe sometimes when verified with Lean.<br><br>Some interesting poking questions at the differences/interaction between formal philosophy and formal math proof assistants.

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• FR

  @friesNcoke · 10 months ago

  Very cool and necessary. Thank you for creating this powerful tool

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• SM

  @SmallKiwiTech · 10 months ago

  This reminds me of debugging. Sometimes a bug exists that is so obscure it might take a million users before it’s discovered, and a billion users before it can be understood (reproduced).

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• HA

  @HarrieHausenman · 10 months ago

  Great talk and very interesting suggestion. Seems like this is the way to go.

• SE

  @SeanWakasa · 10 months ago

  I&apos;d like to second Dr. Riehl&apos;s paradigm of a proof.

• GE

  @geertdepuydt2683 · 10 months ago

  I approve of the message in the main talk 😊

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• SA

  @saaah707 · 10 months ago (edited)

  <a href="https://www.youtube.com/watch?v=fzxW2XJS6SE&amp;t=735">12:15</a> Reminds me of a talk by Daniel Stenberg, lead maintainer for the popular computer program &quot;curl&quot;. &nbsp;The devs have been weathering a blizzard of fraudulent AI-generated bug reports from &quot;vibe debuggers,&quot; wasting their time and energy chasing &quot;hallucinated&quot; bugs.

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