# The Potential for AI in Science and Mathematics - Terence Tao

TLDRIn this talk, Terence Tao explores the impact of AI on science and mathematics. He likens AI to a 'guessing machine', capable of accelerating tasks but not without its limitations. Tao emphasizes AI's potential to transform fields like drug discovery and climate modeling by reducing trial and error. He also envisions a future where AI collaborates with mathematicians, possibly leading to an era of 'big mathematics', and discusses the need for a new academic incentive structure to accommodate these technological shifts.

### Takeaways

- π€ AI is seen as a transformative technology in science and mathematics, but it's not magic and often uses relatively simple mathematical concepts.
- π§ AI operates as a 'guessing machine', processing inputs through a series of mathematical transformations to produce outputs.
- π The potential of AI is compared to the invention of the jet engine, which drastically changed transportation but required significant adaptation and new systems to be fully realized.
- π AI's ability to accelerate tasks is highlighted, but its reliability and predictability can be inconsistent, similar to a student's guesswork without a calculator.
- π AI's success in solving complex problems is noted, with examples from math Olympiads, but its performance is variable and not consistently accurate.
- π‘ AI's role in science is discussed, with its potential to generate numerous candidates for scientific validation, much like a fire hose increasing water output.
- π§ͺ The application of AI in drug design and material science is seen as transformative, potentially reducing the number of candidates for expensive testing phases.
- π AI's capacity to accelerate modeling processes, such as climate simulation, is highlighted, offering the potential for quicker and more varied scenario predictions.
- π The synergy between AI and proof assistants in mathematics is emphasized, with AI aiding in the formalization of proofs and verification processes.
- π The future of mathematics with AI is envisioned to involve more collaboration, the potential for 'big mathematics' projects, and a shift in academic practices to embrace formalization and automation.

### Q & A

### What is Terence Tao's perspective on the potential of AI in Science and Mathematics?

-Terence Tao believes AI has the potential to significantly change Science and Mathematics by accelerating various processes. However, he also cautions that AI is not a magic technology and its capabilities should not be overhyped.

### How does Terence Tao describe AI in non-technical terms?

-Terence Tao describes AI as a 'guessing machine' that takes inputs and produces outputs through a series of mathematical operations, which are not necessarily advanced but are performed in a way that can generate creative responses.

### What analogy does Terence Tao use to explain the impact of AI on society?

-Tao uses the analogy of the invention of the jet engine, which initially was just a small toy but eventually led to travel speeds 10 times faster than land-based vehicles. He emphasizes that AI, like the jet engine, requires new ways of thinking and designing to harness its full potential.

### What are the challenges AI faces according to Terence Tao?

-Tao points out that AI faces challenges such as reliability and predictability. It can provide different answers to the same query and does not guarantee correctness, which makes it a 'guessing machine' rather than a tool that thinks on its own.

### How does Terence Tao view the use of AI in mathematics competitions?

-Tao mentions that AI, such as GPT-4, has been tested on math olympiad problems and occasionally solved them correctly. However, the success rate was low, indicating that while AI can provide impressive results, it can also fail spectacularly.

### What is the role of verification in the context of AI's application in science as per Terence Tao?

-Terence Tao emphasizes that science is about verification, especially independent verification, which can help mitigate the risk of errors and biases when using AI. Combining AI's powerful outputs with rigorous verification can filter out incorrect results and retain valuable insights.

### How does Terence Tao see the future of AI in scientific research?

-Tao envisions AI accelerating scientific research by reducing the number of candidates for testing, automating the design and synthesis processes, and enabling faster modeling. He believes AI can help generate a large number of candidates quickly, which can then be filtered through traditional scientific validation.

### What is Terence Tao's opinion on the use of AI in mathematical proof verification?

-Tao sees AI as a potential tool for speeding up the process of mathematical proof verification, which is currently time-consuming. He suggests that AI could assist in automating parts of the proof formalization process, making it faster and more efficient.

### How does Terence Tao view the collaboration between humans and AI in mathematics?

-Tao believes in the synergy between AI and human mathematicians, where AI can handle the technical aspects of proof formalization, allowing humans to focus on the conceptual and creative aspects of mathematics. He foresees a future where mathematicians dictate proofs to AI, which then verifies and formalizes them.

### What are Terence Tao's thoughts on the future of mathematics research with the advent of AI?

-Tao anticipates an era of 'big mathematics' where AI and proof assistants will enable larger collaborations, faster proof formalization, and potentially even the solving of problems that were previously intractable. He sees a future where the role of mathematicians may evolve to include project management and other specialized tasks within mathematical research.

### Outlines

### π€ AI's Impact on Science and Mathematics

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.

### π§ AI as a Creative Tool with Limitations

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.

### π¬ AI's Role in Scientific Discovery and Verification

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.

### π AI's Acceleration of Climate Modeling and Predictions

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.

### π AI's Synergy with Mathematics and Formal Proofs

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.

### π€ The Future of Collaborative Mathematics with AI

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.

### ποΈ The Evolving Role of Mathematics in a Digital Age

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.

### π The Potential of AI in Solving Complex Mathematical Problems

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.

### Mindmap

### Keywords

### π‘AI

### π‘Mathematics

### π‘Science

### π‘Guessing Machine

### π‘Encoding

### π‘Weights

### π‘Language Models

### π‘Reliability

### π‘Formalization

### π‘Proof Assistants

### Highlights

AI is changing and promising to change the world, including Science and Mathematics.

AI is sometimes overhyped and is not a magic technology; it's more of a 'guessing machine'.

AI's process involves mundane mathematics, encoding inputs and combining them through a series of weighted multiplications.

Finding the correct weights in AI is more interesting and complex than the basic process.

AI can accelerate various tasks but is not yet as reliable or predictable as traditional software.

An analogy is made comparing AI to the invention of the jet engine, which drastically changed travel but required new designs and safety protocols.

AI tools, especially large language models, are more creative than traditional software but come at the cost of reliability.

AI's ability to provide different answers to the same query can be both a strength and a weakness.

Examples of AI's success in solving complex math problems, albeit with a low success rate.

AI's struggle with simple arithmetic shows its limitations despite successes in other areas.

The potential of AI in science is vast, especially in areas where the bottleneck is finding good candidates for solutions.

AI can help in drug design by modeling proteins and narrowing down promising drug candidates.

AI-driven labs are being developed to automate the synthesis of chemicals, potentially transforming scientific research.

AI can accelerate climate modeling and other complex simulations, offering faster insights with existing data.

The combination of AI with proof assistants in mathematics could lead to an era of 'big mathematics'.

Formalizing mathematical proofs with AI assistance can lead to more reliable and collaborative mathematics research.

The future of mathematics may involve more collaboration with AI, changing the way mathematicians work and prove theorems.

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