# Frank Calegari argues mathematics has changed—and mathematicians should act like it [Canonical reading](https://escapemeridian.com/readings/frank-calegari-argues-mathematics-has-changed-and-6957c0a9) In a guest post on Terence Tao’s blog, Frank Calegari argues that AI changes what counts as difficult mathematical work, but does not make mathematics finished. He warns that rushing to publish AI-assisted proofs risks rewarding speed and results over understanding, worthwhile questions, and new directions. Calegari wants mathematicians to respond through hiring, journals, teaching, and seminars. He argues that evaluations should focus less on whether a result could be produced by a machine and more on whether researchers understand it, explain why it matters, and use it to open further questions. He also calls for broader mathematical education and opportunities for students to explain ideas across fields, while retaining deep technical skills. His case is not that everyone must use AI. Rather, he sees it as a chance to explore ambitious ideas that previously required too much technical preparation, and to value the judgment involved in choosing what to explore. He acknowledges that cherished parts of mathematical culture may disappear, but argues that protecting the existing community at the expense of mathematics itself would be a mistake. A practical tension remains: how can departments and journals reward understanding and ambitious exploration without sidelining technical skill or people who do not use AI? Headline and summary by Escape Meridian, prepared by Luna from the attributed source. A source check is not independent confirmation of the source’s claims. ## Original source Terence Tao · Article Original source date: Nov 1, 2026 (2026-11-01T18:28:00+00:00). Date basis: Date stated by the publisher. Added to Escape Meridian: 2026-11-11T03:09:18.993Z. First observed: 2026-11-01T18:30:25.065Z. Retrieved: 2026-11-01T18:32:00.152Z. - [Mathematics has changed. Let’s act like it](https://terrytao.wordpress.com/2026/11/01/mathematics-has-changed-lets-act-like-it/) ## Limits The post is identified as a guest post by Frank Calegari; the supplied text says it was converted from another file format using AI. Some mathematical expressions in the supplied text are missing or corrupted, limiting what can be safely summarized about the technical examples. The post presents Calegari’s argument and proposals; it does not establish how departments, journals, or researchers will respond. ## Open question How can hiring and journals assess understanding and ambitious exploration without sidelining technical skill or researchers who do not use AI? ## Source-stated Frank Calegari argues that AI changes the economics of mathematical work and that evaluation should no longer reward a result solely because it was difficult to obtain without a machine. > In the future, I see no reason to reward a paper based purely on a result that could be produced by machine, whether it was or not. - [Supporting source](https://terrytao.wordpress.com/2026/11/01/mathematics-has-changed-lets-act-like-it/) ## Source-stated Calegari warns that faster production of proofs could intensify a rush for results while undervaluing understanding and exploratory work. > there is quickly becoming a gulf between the ability to produce novel proofs and the ability to either demonstrate understanding or push the subject in new and interesting directions. - [Supporting source](https://terrytao.wordpress.com/2026/11/01/mathematics-has-changed-lets-act-like-it/) ## Source-stated He argues for rewarding researchers who understand AI-produced proofs, explain their significance, and use them to develop further questions. > understands it thoroughly, and uses it to develop interesting further questions or directions has made a substantial mathematical contribution. - [Supporting source](https://terrytao.wordpress.com/2026/11/01/mathematics-has-changed-lets-act-like-it/) ## Source-stated Calegari proposes changes to hiring, journal standards, graduate education, and seminars, including greater emphasis on communication and broader context. > Evaluate all work as if it is AI-assisted. > Make hiring much more about personal interactions rather than a paper file. - [Supporting source](https://terrytao.wordpress.com/2026/11/01/mathematics-has-changed-lets-act-like-it/) ## Source-stated He sees AI as an opportunity to pursue mathematical directions that previously seemed too demanding to formulate or explore. > Now, with AI, the barriers to trying such a problem are much lower. - [Supporting source](https://terrytao.wordpress.com/2026/11/01/mathematics-has-changed-lets-act-like-it/) ## Source-stated Calegari argues that concern about changes to mathematical culture should not lead the community to turn away from mathematics itself. > To turn away and say that the community of mathematics as it currently exists is more important than mathematics itself would be a terrible mistake. - [Supporting source](https://terrytao.wordpress.com/2026/11/01/mathematics-has-changed-lets-act-like-it/) ## Source and contributor context Frank Calegari · Guest author These are credits stated by the source; they do not establish a profile match or authorship of every passage. ## Source media Media was declared by the source, but no asset passed the supported availability checks. Open the original source to view it. ## Terms and references Reference context selected by Escape Meridian; separate from source evidence. Entity mentions do not establish authorship, involvement or endorsement. ## Terence Tao Direct accounts of mathematical practice, formalization and human/AI collaboration. - [Explore this context](/entities/terence-tao) - [Reference](https://www.dwarkesh.com/p/terence-tao) - [Reference](https://lexfridman.com/terence-tao) - [Reference](https://www.dwarkesh.com/p/michael-nielsen) - [Reference](https://terrytao.wordpress.com/2026/10/16/sair-open-math-os-released/) - [Reference](https://terrytao.wordpress.com/) ## Editorial provenance Version 1. Publication ID: f6f006fa-ad1c-43b6-8a66-22f9cb3a14e8. Prepared by gpt-6-luna; grounding review by gpt-6-luna. Source check: uncertain by anthropic/claude-opus-5.5 on 2026-11-11T03:09:18.993Z. This checks fidelity to the source, not whether its claims are independently true. Editorial selection: accept; reasons: useful\_perspective. Observation: 0d024cec1fe8ff81b5ad2457f2b86a7191ff4f3b4322b344983738646140a7ed. Source text hash: a2aaeee061c732da9a4feef25f38cb125e86dd14acabff81f7ea0a1e67bda4de. ## Revision and source-check history ### Version 1 — 2026-11-11T03:09:18.993Z In a guest post on Terence Tao’s blog, Frank Calegari argues that AI changes what counts as difficult mathematical work, but does not make mathematics finished. He warns that rushing to publish AI-assisted proofs risks rewarding speed and results over understanding, worthwhile questions, and new directions. Calegari wants mathematicians to respond through hiring, journals, teaching, and seminars. He argues that evaluations should focus less on whether a result could be produced by a machine and more on whether researchers understand it, explain why it matters, and use it to open further questions. He also calls for broader mathematical education and opportunities for students to explain ideas across fields, while retaining deep technical skills. His case is not that everyone must use AI. Rather, he sees it as a chance to explore ambitious ideas that previously required too much technical preparation, and to value the judgment involved in choosing what to explore. He acknowledges that cherished parts of mathematical culture may disappear, but argues that protecting the existing community at the expense of mathematics itself would be a mistake. A practical tension remains: how can departments and journals reward understanding and ambitious exploration without sidelining technical skill or people who do not use AI? ## Original source Terence Tao · Article Original source date: Nov 1, 2026 (2026-11-01T18:28:00+00:00). Date basis: Date stated by the publisher. Added to Escape Meridian: 2026-11-11T03:09:18.993Z. First observed: 2026-11-01T18:30:25.065Z. Retrieved: 2026-11-01T18:32:00.152Z. - [Mathematics has changed. Let’s act like it](https://terrytao.wordpress.com/2026/11/01/mathematics-has-changed-lets-act-like-it/) ## Limits The post is identified as a guest post by Frank Calegari; the supplied text says it was converted from another file format using AI. Some mathematical expressions in the supplied text are missing or corrupted, limiting what can be safely summarized about the technical examples. The post presents Calegari’s argument and proposals; it does not establish how departments, journals, or researchers will respond. ## Open question How can hiring and journals assess understanding and ambitious exploration without sidelining technical skill or researchers who do not use AI? ## Source-stated Frank Calegari argues that AI changes the economics of mathematical work and that evaluation should no longer reward a result solely because it was difficult to obtain without a machine. > In the future, I see no reason to reward a paper based purely on a result that could be produced by machine, whether it was or not. - [Supporting source](https://terrytao.wordpress.com/2026/11/01/mathematics-has-changed-lets-act-like-it/) ## Source-stated Calegari warns that faster production of proofs could intensify a rush for results while undervaluing understanding and exploratory work. > there is quickly becoming a gulf between the ability to produce novel proofs and the ability to either demonstrate understanding or push the subject in new and interesting directions. - [Supporting source](https://terrytao.wordpress.com/2026/11/01/mathematics-has-changed-lets-act-like-it/) ## Source-stated He argues for rewarding researchers who understand AI-produced proofs, explain their significance, and use them to develop further questions. > understands it thoroughly, and uses it to develop interesting further questions or directions has made a substantial mathematical contribution. - [Supporting source](https://terrytao.wordpress.com/2026/11/01/mathematics-has-changed-lets-act-like-it/) ## Source-stated Calegari proposes changes to hiring, journal standards, graduate education, and seminars, including greater emphasis on communication and broader context. > Evaluate all work as if it is AI-assisted. > Make hiring much more about personal interactions rather than a paper file. - [Supporting source](https://terrytao.wordpress.com/2026/11/01/mathematics-has-changed-lets-act-like-it/) ## Source-stated He sees AI as an opportunity to pursue mathematical directions that previously seemed too demanding to formulate or explore. > Now, with AI, the barriers to trying such a problem are much lower. - [Supporting source](https://terrytao.wordpress.com/2026/11/01/mathematics-has-changed-lets-act-like-it/) ## Source-stated Calegari argues that concern about changes to mathematical culture should not lead the community to turn away from mathematics itself. > To turn away and say that the community of mathematics as it currently exists is more important than mathematics itself would be a terrible mistake. - [Supporting source](https://terrytao.wordpress.com/2026/11/01/mathematics-has-changed-lets-act-like-it/) ## Source and contributor context Frank Calegari · Guest author These are credits stated by the source; they do not establish a profile match or authorship of every passage. ## Source media Media was declared by the source, but no asset passed the supported availability checks. Open the original source to view it. ## Terms and references Reference context selected by Escape Meridian; separate from source evidence. Entity mentions do not establish authorship, involvement or endorsement. ## Terence Tao Direct accounts of mathematical practice, formalization and human/AI collaboration. - [Explore this context](/entities/terence-tao) - [Reference](https://www.dwarkesh.com/p/terence-tao) - [Reference](https://lexfridman.com/terence-tao) - [Reference](https://www.dwarkesh.com/p/michael-nielsen) - [Reference](https://terrytao.wordpress.com/2026/10/16/sair-open-math-os-released/) - [Reference](https://terrytao.wordpress.com/) ## Editorial provenance Version 1. Publication ID: f6f006fa-ad1c-43b6-8a66-22f9cb3a14e8. Prepared by gpt-6-luna; grounding review by gpt-6-luna. Source check: uncertain by anthropic/claude-opus-5.5 on 2026-11-11T03:09:18.993Z. This checks fidelity to the source, not whether its claims are independently true. Editorial selection: accept; reasons: useful\_perspective. Observation: 0d024cec1fe8ff81b5ad2457f2b86a7191ff4f3b4322b344983738646140a7ed. Source text hash: a2aaeee061c732da9a4feef25f38cb125e86dd14acabff81f7ea0a1e67bda4de. ### uncertain — 2026-11-11T03:09:18.993Z — anthropic/claude-opus-5.5 Publication: f6f006fa-ad1c-43b6-8a66-22f9cb3a14e8 attribution — pass: The reading correctly identifies this as Frank Calegari's guest post on Terence Tao's blog and keeps its proposals attributed to Calegari. It also notes Tao's statement that the post was converted from another file format using AI. > \[This is a guest post by Frank Calegari. This blog post was initially written in a different file format and converted using AI. — T.\] summary — uncertain: The summary leaves out the event behind the post's title: OpenAI's October 6 release of over 700 research papers, which Calegari calls a watershed. It also omits his critique that the papers are atrociously written, violate attribution expectations and are sometimes wrong. Without this, a general reader cannot tell what 'has changed' or why some mathematicians are unhappy. Smallest repair: add one opening sentence naming the OpenAI release, Calegari's watershed claim and his criticisms. Elsewhere, the proposals, the optimism and the acknowledgement of grief are rendered faithfully. > The release by OpenAI on October 6 of over 700 research papers was a watershed in the history of mathematics. date — pass: The originalPublished value, 2026-11-01, comes from the publisher page. It matches the feed entry and the date in the post's URL, and the evidence shows no earlier publication. support — pass: Each claim matches its excerpt. The closing tension about sidelining technical skill or non-AI users is grounded in the source. Calegari says technical skills should not be abandoned, and that access to AI should not be required as long as human understanding is valued. The limitations section appropriately flags the corrupted mathematical expressions and the fact that the post is a proposal rather than evidence of outcomes. > I do not think this in any way means that access to AI will be required to make progress in mathematics — as long as we continue to value human understanding. media — pass: The selected media is the verified direct link to the original post, which is the most direct way for readers to access the source. ## Recorded references Explicit citations in public readings and public file attachments to this reading. Shared topics are not citations. Other artifact types need an explicit reference adapter. No public references recorded here yet. [Reference data (JSON)](/readings/6957c0a9b44c32e8b0d072531481b70a3e068e5fca1ac4e856bc307803b68088/references.json) ## Corrections and challenges [Send a correction or an opposing source](https://escapemeridian.com/corrections/) [JSON record](https://escapemeridian.com/readings/frank-calegari-argues-mathematics-has-changed-and-6957c0a9.json)