Grant Sanderson – AI and the future of math
The discussion centers on the rapid advancements of AI in mathematics, exploring its implications for the future of math and related fields. The conversation highlights how AI's capabilities impact traditional mathematical roles, the process of knowledge creation, and the potential for new insights in various domains.
Summary
In the conversation, the hosts discuss the remarkable progress AI has been making in the field of mathematics, with a particular focus on how these advancements mirror potential developments in other domains. They examine past questions regarding the implications of AI excelling in mathematical competitions, such as the International Math Olympiad (IMO), and consider whether this indicates a broader capability for artificial general intelligence (AGI). They clarify that AI achievements should be seen as benchmarks rather than definitive milestones signifying AGI, given that mathematics consists of varied domains with different levels of complexity.
The conversation delves deeply into the fractal nature of progress in mathematics, illustrating that while AI may excel in specific categories like geometry, it still struggles in areas like combinatorics. They explore the potential of AI generating new mathematical conjectures and definitions, with speculation on how AI could redefine what constitutes significant contributions in the field.
Additionally, they discuss the role of educators in an increasingly AI-driven landscape, arguing that teaching remains a stable career path as relationships and mentorship in education are irreplaceable. As AI proves its ability to assist and enhance mathematical exploration, the discussion considers whether this will lead to a renaissance of knowledge or if mathematical pursuits will become increasingly esoteric and disconnected from practical applications. The hosts hypothesize about the societal impacts of these advancements, including the future roles of mathematicians, the changing nature of mathematical work, and how AI insights might not yield immediate economic benefits but could ultimately enhance various engineering and applied sciences.
About this episode
<p>Always so much fun to chat with <a href="https://www.youtube.com/c/3blue1brown" target="_blank">Grant</a>.</p><p>AI has been making much faster progress in math than in other fields. As a result, mathematics is showing us, very concretely, what AI progress in other fields will look like. Even within mathematics, there’s a jagged landscape. What does it look like?</p><p>What is the nature of the most important conceptual breakthroughs in the history of mathematics, and how different are they from what AIs are currently able to do?</p><p>Does AI (on net) increase or decrease human understanding of the field?</p><p>How big is the overhang from having AIs systematically try to connect ideas already in the literature?</p><p>And what advice does Grant have for aspiring mathematicians, coders, and other students who are passionate about fields that are being most transformed upon by AI?</p><p>Watch on <a href="https://youtu.be/TfyPshgMbug" target="_blank">YouTube</a>; read the <a href="https://www.dwarkesh.com/p/grant-sanderson-2" target="_blank">transcript</a>.</p><p><strong>Sponsors</strong></p><p>* <a href="https://ai.studio/live" target="_blank">Gemini 3.5 Live Translate</a> is what I wished I’d had on my last trip to China. It detects more than 70 languages and translates them in near real-time… and it preserves your original pacing and intonation. If you’re building an app that needs live translation, you should check out Gemini 3.5 Live Translate. Get started at <a href="https://ai.studio/live" target="_blank">ai.studio/live</a></p><p>* <a href="https://cursor.com/dwarkesh" target="_blank">Cursor</a>’s harness lets me use models for a huge range of tasks at the podcast. For example, Cursor cuts out the ads from each episode I produce so I can post them on Bilibili. It also helps me prep for interviews — I have a repo full of books and papers that Cursor sorts through to find the exact right file for any given question. Try Cursor yourself at <a href="https://cursor.com/dwarkesh" target="_blank">cursor.com/dwarkesh</a></p><p>* <a href="https://janestreet.com/dwarkesh" target="_blank">Jane Street</a> sponsors 3Blue1Brown, so Grant has gotten to spend a lot of time with various Jane Streeters. He actually just recorded an interview with a few of them, so when we sat down for this episode, he told me about some of the things he learned, like how Jane Street keeps their role definitions fuzzy to make sure their people keep learning and growing. Go check out Grant’s full interview at <a href="https://3b1b.co/janestreet" target="_blank">3b1b.co/janestreet</a></p><p>Timestamps</p><p>(00:00:00) – AI is discovering new proofs. Is that AGI?</p><p>(00:11:32) – The verification loop on conceptual breakthroughs can be a century long</p><p>(00:26:12) – Will we understand an AI proof of the Riemann hypothesis?</p><p>(00:38:08) – Can AI find the hidden bridges between fields?</p><p>(00:53:48) – Why real-world tasks don’t fit into RL environments</p><p>(01:07:07) – Good writing requires theory of mind that AI still lacks</p><p>(01:16:02) – Why learning will still depend on human curation</p> <br /><br />Get full access to Dwarkesh Podcast at <a href="https://www.dwarkesh.com/subscribe?utm_medium=podcast&utm_campaign=CTA_4">www.dwarkesh.com/subscribe</a>
Key Insights
- AI's progress in mathematics is considered a rapid advancement compared to other fields, reflecting its potential influence on society.
- The achievements of AI in competitions like the IMO provide benchmarks rather than definitive indicators of AGI, as they highlight specific skill sets rather than general intelligence.
- The discussion suggests a fractal nature of mathematical problem-solving, with certain areas being more accessible to AI than others.
- AI's ability to solve problems doesn't necessarily equate to generating new ideas or conjectures, which often require creative connections and intuition.
- Mathematicians stress the importance of understanding the economic value of their work, linking it to teaching and public engagement to secure funding.
- Educators can play a crucial role in a future where AI is involved in mathematical research, as human mentorship and social interaction remain valuable.
- The exploration of new mathematical concepts through AI doesn't guarantee immediate practical applications or economic benefits.
- There is skepticism about whether the increasing focus on pure mathematics will yield significant results in applied fields.
- The conversation highlights various paths available for mathematicians, including teaching roles that might remain stable amidst AI advancements.
- AI's capacity to generate insights could lead to valuable applications in engineering and physical sciences, although this is uncertain.
- The future of mathematical discourse may shift towards societal impact and practical application of AI-generated insights in various fields.
- The hosts recognize the potential for AI to formalize and verify mathematical proofs, creating opportunities for novel forms of research.
Topics
Transcript
Today I'm chatting with Drance Anderson, who runs Stiglue and Brown, and is now working on a new project documenting the progress AI is making in math. I wanted to talk to you about this because AI has been making the fastest progress in mathematics as of any other field. So whatever is happening here and whatever we were seeing AI progress happen or not happen would tell us about what will happen to the rest of the world as AI gets better and better. So I wanted to start with this question I asked you when I first interviewed you three years ago. And I asked you, once we have AIs that can get gold in the International Math…
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