On the latest episode of the Science podcast, Alex Kontorovich and I discuss the challenges of communicating mathematics among professional mathematicians: www.science.org/content/podc...

In a talk called "A reintroduction to proofs" emilyriehl.github.io/files/reintr... I've speculated about teaching an undergraduate level introduction to proofs course but using dependent type theory as the implicit formal system in place of set theory and first order logic.

very fabulous and provocative talk for a non-specialist audience about developing new mathematics, vibe proving and mathematical rigor between human mathematicians and computational mathematics in the age of AI by @emilyriehl.bsky.social, among other things-- highly recommend

One of my favorites from Bill Thurston ❤️:

I wrote about the challenge of mathematicians explaining mathematics to other mathematicians for Science Magazine's Expert Voices column series: www.science.org/doi/10.1126/...

Kudos to Terry Tao for this: newsletter.ofthebrave.org/p/im-an-awar...

@sciam.bsky.social gave me the opportunity to share some personal thoughts about the recently reported AI results from the #imo2025: www.scientificamerican.com/article/math...

While reporting, I stumbled across a recent talk that Tao gave on the subject of his latest research. youtu.be/cXqz5hgxlLM

Math at UCLA suffered the greatest blow. I spoke with Terry Tao—Fields Medalist and arguably the preeminent mathematician of his generation—who is apparently now doing his summer research in number theory without external funding.

The Trump administration is launching a new wave of attacks on universities, and UCLA is the latest target. My reporting on how the university has been hit and how some of its scientists are responding: www.science.org/content/arti...

One thing I've always appreciated about the NSF is their broad mission to "promote the progress of science" both through new research and its public communication. See the following thread for #DMSFunded work describing recent developments in category theory, homotopy theory, and formalization:

I'm halfway through the @londmathsoc.bsky.social Hardy Lecture Tour. Titles and abstracts can all be found here: emilyriehl.github.io/talks/ and slides (when available) will eventually be added.

Last chance to see @emilyriehl.bsky.social at the LMS next month!

With of course insightful comments from Alison Gopnik @alisongopnik.bsky.social, Thomas Hertog, Margaret Johnson @mejohnson81.bsky.social, Harrison Hartle, David Haig, and Claudia Passos Ferreira. Next, a panel moderated by JHU's Elizabeth Ogburn, and we're done!

Afternoon: * Jenann Ismael talks about agency and the role of interference in prediction. * Simon Levin told us about complexity and self-organization from ecology to society. * Michael Tomasello reflects on the relationship between social cooperation and agency in primates (including humans).

Natural Philosophy Symposium day 3! * Melanie Mitchell @melaniemitchell.bsky.social puts limits on how much LLMs understand the world. * Emily Adlam says there aren't rational credences when you don't know who you are in the world. * Chris Kempes argues that there are easy questions in biology.

Thanks also to commentators for today: Saakshi Dulani, Steven Gross, Naftali Weinberger @dagophile.bsky.social, Jeremy Goodman, Justin Clarke-Doane, and E.J. Green. So many big ideas bouncing around a collection of wonderful people. Looking forward to the big finale tomorrow.

I should also have tagged @sandradmitchell.bsky.social from yesterday, and extended major props to our panel moderators, Chanda Prescod-Weinstein @chanda.bsky.social (yesterday) and Robert Rynasiewicz (today). And Alison Gopnik @alisongopnik.bsky.social's talk last night was a huge success!

* Simon DeDeo explained how some theorems might only have ungraspably long proofs. * Emily Riehl @emilyriehl.bsky.social talked about computers proving theorems. * Anil Seth @anilseth.bsky.social suggested that it could be harder than you think for AI to ever be truly conscious.

Day 2 of the Natural Philosophy Symposium is in the books! * Alan Guth talked about getting an arrow of time in a universe with time-symmetric laws. * Jennifer Nagel explained what it means for two people can have common knowledge. * David Albert related thermodynamics to our causal abilities.

Plus wonderful comments by Ryan Smith, Brandon Ogbunu @cbo.bsky.social, Henry Farrell @himself.bsky.social, Sharlen Moore @sharlenmoore.bsky.social, and Michael Wong @miquai.bsky.social. That's just day one! Looking forward to Alison Gopnik @alisongopnik.bsky.social's public lecture tonight.

* Kevin Zollman @kevinzollman.com explaining game theory as a wide-ranging tool for social and biological science * Malcolm MacIver showing how the capacity to plan arose after organisms climbed out from water and onto land * Nick Lane tracing the origin of life back to alkaline hydrothermal vents

* David Chalmers @davidchalmers.bsky.social suggesting that a mathematical theory of consciousness will inevitably leave something out * Sandra Mitchell emphasizing the pragmatic, complex, and socially-situated features of science * Nima Arkani-Hamed giving two cheers for "shut up and calculate"

The Natural Philosophy Symposium is underway! I had some idea of live-skeeting, but the real-time event is too absorbing. www.naturalphilosophyhopkins.org/natural-phil... Anyway, we've had: (cont)

"Part of the reason that the AI community is so interested in math is that math is hard." @emilyriehl.bsky.social on Testing Artificial Mathematical Intelligence at the Simons Institute's workshop on AI for Mathematics and Theoretical Computer Science. simons.berkeley.edu/workshops/si...

I am proud today to join the editorial board of a new diamond open access journal in logic: Zeitschrift für Mathematische Logik und Grundlagen der Mathematik zml.international The website includes an open letter from the editorial board with the following text:

Upon learning that yesterday would be my last day as a program officer at the National Science Foundation, I shared this parting message with my colleagues. The next few months will be frenetic and stressful for them. Here are some things that you can do to help them with the mission ahead. (1)