Terry Tao is one of the world's top mathematicians, having received numerous awards including the prestigious Fields Medal. He currently serves as a professor of mathematics at the University of California, Los Angeles (UCLA).
Although AI has brought revolutionary changes to various fields, it is sometimes overhyped. In reality, it is not a magical technology or advanced mathematics. Essentially, AI is a "guessing machine" that processes inputs and generates outputs such as text, images, or numbers through relatively simple mathematical operations. AI is similar to a newly invented jet engine; while it can significantly increase speed, its full potential cannot be realized without designing new safety protocols and understanding physical laws. Similarly, AI is not magic; it still follows basic logic and rules, but it can accelerate many tasks, making things 10X faster.
The difference between AI and traditional software lies in its ability to process user input through natural language processing and exhibit a certain level of creativity when handling imprecise input. Traditional software usually requires precise input and predictable output, whereas AI may produce uncertain and unstable outputs. Even with the same input, it may yield different results at different times, and they are not necessarily correct. It is a "guessing" system that infers the most likely correct answer through large amounts of training data.
Test cases for the GPT-4 model showcased its surprising performance on some complex mathematical problems.
However, this kind of success is random, with a success rate of only about 1%.
Most of the time, the AI's performance remains quite unstable and even "embarrassingly bad".
At this stage, AI does not truly understand the concept of a "correct answer"; it merely guesses by imitating known answers from its training data. Therefore, in certain fields, the application of AI carries potential risks, especially in areas involving life and property safety such as healthcare and finance. If we overly rely on AI and blindly trust the answers it provides, we may find ourselves in trouble. Just like early flight technology, despite its enormous potential, it cannot be recklessly applied to critical areas until safety issues are effectively resolved. However, in low-risk domains, AI can be very useful, for example, generating background images for presentations or performing other visual tasks. Even though AI still has flaws in some aspects, such as needing improvement in text generation, the risks in these applications are relatively low.
The application of AI in scientific fields
The prospects for the application of AI in scientific fields, particularly its potential to reduce errors and biases. The core of science lies in verification, especially independent verification. Therefore, if we can combine AI's powerful output capabilities with rigorous scientific validation processes, we can filter out valuable results and avoid the impact of errors.
The current scientific research is similar to a faucet with a fixed water output, while AI is like a powerful fire hose that can provide ten or even a hundred times the amount of water output. Although the water quality cannot be directly consumed, it can yield a large number of usable research results after filtration. Currently, the application of AI in some fields has already begun to show great potential, such as drug design and materials science.
Drug development
Traditional drug development is a long and expensive process, requiring extensive screening of candidate drugs and years of clinical trials. However, with the help of AI's modeling capabilities, promising candidate drugs can be quickly identified, significantly reducing the time and cost of trials. Although final validation still needs to go through the "gold standard" of scientific verification, AI can significantly reduce the number of candidate drugs that need to be tested, possibly from 100 to 10.
Materials science
Similarly, materials science is facing similar challenges. AI can help scientists screen out materials that may possess ideal properties more quickly, thereby accelerating the development process of key materials such as superconductors.
Simulation of Complex Systems
Another significant advantage of AI is reflected in model acceleration, especially in the simulation of complex systems. Whether it's climate models, traffic models, or cosmology models, traditional simulation processes rely on physical laws and large amounts of data, often requiring the use of supercomputers and taking months of time. However, AI can be trained on existing simulation data and make predictions based on that, significantly reducing the simulation time. For example, in climate simulations, AI's acceleration capability can reduce work that takes months to just a few hours, or even improve weather forecasting speed by 10,000 times.
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Despite the enormous potential these technologies bring, they still face some challenges. For instance, in climate models, data collection and preprocessing remain major bottlenecks, and ensuring the reliability of AI outputs is an urgent issue to address. Nevertheless, AI has already shown remarkable achievements in certain specific fields; for example, in hurricane prediction, AI has already performed better than the National Weather Service in real-time forecasts.
Applications of AI in Mathematics
AI has the potential to bring about transformative changes in the field of mathematics. Although a complete revolutionary change hasn't occurred yet, it is very likely on the horizon. Errors in mathematics tend to have less severe consequences compared to other fields, so the application of AI here carries lower risks. More importantly, the verification standards in mathematics are very clear: a proof is either correct or incorrect. This allows AI to provide more assistance in mathematics without fully relying on the correctness of its output.
Combined use with proof assistants
One of the potentials for AI in mathematics lies in its combination with proof assistants. Proof assistants are computer software designed to verify the correctness of mathematical proofs. These tools have already been applied in mathematics and engineering, such as ensuring the safety of aircraft circuits. However, the current process of formalizing proofs is extremely time-consuming, with many famous mathematical theorems taking years or even decades to be formally verified.
Nevertheless, proof assistants are becoming faster, especially with the emergence of better software libraries and modern collaborative tools, allowing mathematicians to collaborate on large-scale projects.
Even more excitingly, AI is helping to accelerate these formalized proof processes. For example, tools like GitHub Copilot can automatically generate certain steps in proofs, meaning that in the future, AI may not only handle simple one-line proofs but could also gradually automate more complex ones. The combination of AI and proof assistants can significantly speed up this process, enabling mathematicians to focus on higher-level thinking while leaving tedious technical details to automated tools.
In the future, mathematicians will collaborate with AI to complete the proof process. They will be able to interact with AI as if explaining proofs to students. The AI will attempt to verify the correctness of each step and return for further clarification when encountering issues. Ultimately, AI will complete mathematical proofs faster than traditional methods. If a parameter in the proof needs to be modified, AI can automatically adjust the relevant steps to ensure no errors occur. AI and mathematics will form a significant synergy effect, ushering in a "Great Era of Mathematics." This will not only enable mathematicians to work more efficiently but also promote large-scale collaborative mathematical projects.
The trend of "citizen mathematics"
Future mathematical research will not be limited to professional mathematicians but will increasingly involve interdisciplinary collaborations and the participation of amateurs. With the assistance of AI, cooperation between scientists from other disciplines and mathematicians will become tighter. There may even emerge a trend of "citizen mathematics," where ordinary members of the public can contribute to mathematical research.
Future scientific research may break down the boundaries of traditional disciplines, with scientists increasingly relying on AI for collaboration and exploration. He envisions that future mathematicians will no longer need to personally solve all technical problems but will instead be able to use AI and team collaboration to assign different tasks to suitable individuals, much like how modern software development is divided into specialized roles.
AI has already solved some problems that were once thought to be uniquely human challenges, such as geometry problems in the International Mathematical Olympiad. By generating inspirational constructions, AI significantly reduced the complexity of these problems. Although this method utilized only a small amount of AI, it demonstrated that AI can solve seemingly complex problems in specific fields.
AI Challenges the Pinnacle of Human Intelligence
Many tasks that humans find difficult can be easily handled by AI. In the past, we considered tasks like chess, Go, image recognition, and language translation to be at the pinnacle of human intelligence, but AI has already successfully tackled these areas. Therefore, we need to reassess our definition of difficulty and not underestimate AI's potential in solving mathematical problems in the future.
In the future research environment, he envisions AI not only helping to solve technical challenges but also promoting broader collaboration and exchange through AI-driven tools. As disciplines become increasingly quantitative, the influence of mathematics will further extend to other scientific fields, including social sciences and humanities. With the advancement of AI technology, not only will scientific research become more mathematized, but interdisciplinary collaborations will also become more frequent and in-depth. AI may serve as a "translator" between scientists, helping them understand specialized terminology from each other’s fields, thereby facilitating collaboration.
With the progress of AI, we need to recalibrate our perception of which tasks are truly difficult and look forward to how AI will disrupt our understanding of intelligence and complexity in the future.