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.
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:
the mathematical landscape. We will raise questions related to building communities in which all mathematicians can flourish, rewarding collective work, organizing labor, confronting climate change, and anticipating AI.''
Norms are local — they are how individuals interact with each other and how individuals act in an institution — and global — our work at the local level building community glues to the work of our colleagues at other institutions, creating a systemic awareness and change across
Abstract: ``This talk will report on a multi-year conversation that aims to critically examine the cultural practices that affect the mathematics profession with a particular focus on our often unstated professional norms.
Today is the final stop on the @londmathsoc.bsky.social Hardy Lecture Tour. I'm in Bristol to give a talk entitled “A conversation on professional norms in mathematics”
We argue that deploying a bespoke synthetic formal system for a particular kind of mathematical object — ∞-categories in this instance — is a promising tactic to simplifying definitions and proofs, without sacrificing rigor."
After considering the role that category theory and ∞-category theory play in 20th and 21st century mathematics, we describe a radical potential solution to these problems: to change the foundation system.
Put more pithily, will we ever be able to distill ∞-category down to the point that it could be taught to undergraduates, much like ordinary 1-category theory is sometimes taught today?
Abstract:"While the last decades have seen considerable advances in our understanding of ∞-category theory, experts in the field have not yet solved the problem that confronts users of the theory: namely how to develop proficiency with this technology on a compressed time scale.
Frankly the highlight of this talk is the list of references at the end, starting with Clive Newstead's wonderful textbook "An infinite descent into pure mathematics."
Equally, intuitions built from an early informal introduction to dependent type theory will make it easier for those who aspire to write computer formalized proofs later on."
Furthermore, dependent type theory is the formal system used by many computer proof assistants both “under the hood” to verify the correctness of proofs and in the vernacular language with which they interact with the user.
