The Future Of Mathematics

TL;DR

Prime Big Deal Days · Oct 6–7Offer from Amazon

Get school and study supplies delivered free — and shop member deals

• Fast, free delivery on millions of items
• Access to Prime Big Deal Days deals on October 6–7
• Prime Video, Amazon Music and more included

Start your free Prime trial →Free trial for eligible customers · Cancel anytime

As an affiliate, we earn on qualifying purchases.Hide

Mathematician Jeremy Avigad argues in an October 5, 2026, post that AI can now help produce results that might recently have been publishable, challenging familiar research workflows. He says mathematics can adapt by pursuing harder problems, choosing broader questions and keeping rigorous reasoning and communication central.

Mathematician Jeremy Avigad argues that recent advances in artificial intelligence are changing the kinds of mathematical results researchers can produce, while leaving open what those changes will mean for the profession. In a guest post published October 5 on Terence Tao’s blog, Avigad says mathematicians should respond by pursuing harder problems and broader questions, rather than treating mathematics as a checklist of problems to solve.

Avigad describes conversations at a meeting of science and technology startups supported by Convergent Research, which oversees the nonprofit Lean Focused Research Organization. Participants asked about AI’s impact on mathematics and the response among mathematicians. Avigad said he found the tone of discussions on mathematics blogs, including Tao’s and Proofs and Prompts, generally positive, even as researchers recognize that their professional routines may change.

He says AI has disrupted a familiar research workflow: mathematicians tackle difficult problems, simplify them when necessary, and vary the resulting approaches. In his account, some results that could have been respectable publications a year earlier can now be generated with AI assistance. He argues that this makes the central question not whether mathematics is still needed, but how people can pursue mathematical understanding when AI can do more of the problem-solving work.

Avigad offers three responses in the post: solve harder problems, think bigger thoughts, and maintain a broader view of what mathematics is for. He characterizes current systems as having access to mathematical literature and the ability to test many possible approaches. He says AI-produced solutions to open problems so far appear to rely on combining existing techniques, while leaving room for the possibility that future systems may produce new insights.

Research Beyond Routine Problem-Solving

The essay matters because it addresses a change that could affect how mathematical work is valued, published and taught. If AI can help generate results that previously met publication standards, researchers and institutions may have to reassess which contributions show meaningful mathematical understanding, and how the next generation should be trained.

Avigad’s response is an argument about priorities, not a prediction that AI will replace mathematicians. He emphasizes that people choose which questions are interesting and which solutions they admire. That distinction puts problem selection and evaluation alongside proof production as central parts of mathematical work. It also makes the effect of AI dependent not just on technical capability, but on choices made by researchers and the wider mathematical community.

His case for continuing mathematics rests on its role as a culture of rigorous reasoning and communication. Those practices, he says, provide abstractions and language that help people think and communicate more reliably. Whether AI can support those aims, rather than merely speed up familiar tasks, remains an important test for tools entering research and education.

A Long History of Mathematical Change

Avigad places the current moment against the history of mathematics, which has repeatedly changed in response to new ideas and methods. He quotes historian and philosopher Howard Stein describing the nineteenth-century transformation of the subject as a “second birth.” The reference supports Avigad’s broader point: major changes in mathematical practice need not mean the subject itself has ended.

As an example of mathematics moving in an unexpected direction, Avigad recounts the story of Bernhard Riemann’s 1853 habilitation lecture. Riemann submitted three possible topics to his adviser, Carl Friedrich Gauss, who reportedly selected the one Riemann was least prepared to address. The lecture, published after Riemann’s death in 1868, helped reshape geometry through its treatment of space and the introduction of the general notion of a manifold, although a fully rigorous treatment came later.

The example connects to Avigad’s call to “think bigger thoughts”: mathematical progress can come from choosing new questions and frameworks, not only from solving a sequence of established problems. The post also refers to Lean, a theorem prover developed by a nonprofit organization supported by Convergent Research, as part of the setting for the discussions that prompted his reflections.

“The question, therefore, isn’t whether we still need mathematics, but rather how to pursue mathematical understanding in the age of AI.”

— Jeremy Avigad

AI’s Capacity for New Mathematical Ideas

The post does not establish how often AI-generated mathematical results can meet publication standards, or how widespread the change is across fields. Avigad gives his assessment of recent developments but does not provide a dataset, study or systematic comparison of AI-assisted and human-produced work.

It is also unclear whether current systems can regularly create genuinely new mathematical insights, rather than combine known techniques. Avigad says that possibility may arise in the near future, but argues that it has not yet been reached. The post does not specify a timeline or define how researchers should distinguish a novel insight from an effective recombination of existing methods.

The supplied text ends during Avigad’s discussion of Riemann, so it does not include the complete essay or all the arguments he may have developed. Its proposed responses should be read as the author’s perspective, not as settled agreement across the mathematical community.

How Mathematicians Adapt Their Work

Avigad’s post describes no formal program, policy change or scheduled milestone. The next developments will depend on how researchers use AI in practice, how journals and institutions evaluate AI-assisted work, and whether such systems prove useful on questions that call for more than applying familiar techniques.

For now, the immediate debate is about research priorities and training: what counts as valuable mathematical contribution when some routine problem-solving can be automated, and how students can develop rigorous reasoning and judgment alongside new tools. Avigad’s essay frames those decisions as choices the mathematical community can make, while leaving their outcome unsettled.

Key Questions

What is the news in Avigad’s post?

Jeremy Avigad published an essay arguing that AI is changing mathematical research workflows and that researchers should focus on understanding, ambitious problems and broader questions.

Does Avigad say AI will replace mathematicians?

No. He argues that AI changes the work mathematicians do, but says people still choose which questions matter and which solutions they value. He does not claim that AI will replace the profession.

What kinds of mathematical work does he say AI can do?

Avigad says some results that might have been publishable a year earlier can now be generated with AI assistance. He characterizes solutions to open problems seen so far as combining available techniques; the post does not quantify how common this is.

What does Avigad recommend mathematicians do?

He proposes solving harder problems and thinking bigger thoughts, while keeping mathematical understanding—not simply producing answers—at the center of research.

What remains unknown about AI and mathematics?

The post does not establish how widespread AI-generated publishable results are, whether current systems can reliably produce new mathematical insights, or how the profession will change its research and training practices.

Source: hn