Artificial intelligence (AI) is not only changing the way we use technology, but also how we understand the world. One of the fields that is being revolutionized by AI is mathematics, where new algorithms and methods are enabling new discoveries and applications.
Mathematics has always been a human endeavor, driven by curiosity, creativity and logic. But for thousands of years, mathematicians have also relied on tools and techniques to help them solve problems and prove theorems. From ancient geometry to modern calculus, from pencil and paper to computers and software, mathematics has adapted to the latest advances in logic and reasoning.
Now, AI is offering a new set of tools and techniques that can augment human intelligence and creativity. AI can help mathematicians find patterns, generate conjectures, verify proofs, explore new domains and communicate their results. AI can also pose new challenges and questions for mathematics, such as how to ensure the correctness, fairness and explainability of AI systems.
Some examples of how AI is transforming mathematics are:
- A team of researchers from Google and Stanford University used a deep neural network to discover new formulas for calculating the volume of complex shapes, such as a donut with a pretzel-shaped hole. The network was trained on millions of examples of shapes and their volumes, and then tested on new shapes that it had never seen before. The network was able to generate formulas that were simpler and more accurate than existing ones.
- A group of mathematicians from France and Switzerland used an automated theorem prover called Coq to verify one of the most famous conjectures in number theory, the odd Goldbach conjecture. The conjecture states that every odd number greater than five can be written as the sum of three prime numbers. The mathematicians used Coq to check every possible case up to 10^20, which took about a year of computing time.
- A computer scientist from Carnegie Mellon University developed a new algorithm called AlphaZero Generalized that can learn to play any two-player game with perfect information, such as chess, checkers or Go. The algorithm does not need any human input or prior knowledge of the game rules or strategies. It learns by playing against itself and improving its skills over time. The algorithm has surpassed the best human and computer players in several games.
These are just some of the examples of how AI is transforming mathematics. As AI becomes more powerful and ubiquitous, it will likely have a profound impact on the future of mathematics and science.
