The Potential for AI in Science and Mathematics - Terence Tao

The speaker begins by expressing their enjoyment of London's hospitality and introduces the topic of AI, noting its potential to revolutionize various fields including science and mathematics. They clarify that AI, while an amazing technology, is sometimes overhyped and is not magic. AI is described as a 'guessing machine' that processes inputs and produces outputs through a series of mathematically mundane steps. The speaker emphasizes that finding the correct weights in AI is more interesting and compares AI to the invention of the jet engine, which drastically changed transportation but required new designs and understanding to be fully utilized.

In this paragraph, the speaker discusses the creative potential of AI, especially large language models, which can understand and generate human-like text. They highlight the trade-off between creativity and reliability, noting that AI can produce varied and sometimes incorrect answers. The speaker uses the example of AI solving a math Olympiad problem correctly but struggling with a simple arithmetic question, demonstrating AI's current limitations. They stress the importance of safety and reliability, especially in high-stakes fields like medicine and finance, where AI's guesses could have serious consequences.

The speaker explores AI's application in scientific discovery, emphasizing its potential to generate numerous candidates for scientific problems, which can then be verified through traditional methods. They liken AI to a fire hose of ideas that need to be filtered for accuracy. The paragraph discusses how AI can accelerate scientific processes, such as drug discovery and material science, by reducing the number of candidates for expensive testing. The speaker also mentions AI's growing role in automating scientific processes and its potential synergy with proof assistants in mathematics.

Here, the speaker delves into AI's ability to expedite climate modeling and weather predictions. They explain how AI can process large amounts of data and simulate complex systems like the Earth's atmosphere much faster than traditional supercomputers. The speaker notes that while AI can provide quick insights, there are still challenges in benchmarking its reliability and integrating it with data collection processes. They also discuss the potential for AI to enable more detailed climate predictions by running numerous scenarios quickly.

The speaker expresses excitement about AI's potential to transform mathematics, particularly in proof verification and formalization. They discuss the benefits of using AI to assist with mathematical reasoning and how it can be combined with proof assistants to ensure correctness. The paragraph includes a personal account of using AI to formalize a mathematical proof in Lean, highlighting the potential for AI to automate parts of the proof process and enable larger collaborative efforts in mathematics.

In this section, the speaker envisions a future where AI enables broader participation in mathematical research, including non-professionals. They discuss the potential for AI to help solve complex mathematical problems by breaking them down into smaller, more manageable tasks. The speaker also considers the implications for academic publishing and funding, suggesting that formalized proofs and AI-assisted mathematics may require new evaluation metrics and incentives.

The speaker reflects on the changing role of mathematics in academia and research, with a focus on how AI and formal proof assistants can lead to more interdisciplinary collaboration and specialization within the field. They anticipate a future where mathematicians can focus on different aspects of problem-solving, from conceptualization to formalization, and where AI plays a significant role in automating and verifying mathematical processes.

The speaker discusses the recent advancements in AI's ability to solve complex mathematical problems, such as those in geometry, which were previously thought to be challenging for AI. They mention the development of Alpha Geometry by Deep Mind and how it leveraged AI to solve International Math Olympiad problems by generating synthetic data and applying strategic shortcuts. The speaker also reflects on the evolving perception of what constitutes a difficult problem for AI and the potential for AI to assist in finding key intermediate steps in mathematical proofs.