We can add suggestions and proofs of mathematical theorems to the long list of artificial intelligence possibilities: Mathematicians and artificial intelligence experts have come together to show how machine learning can open new avenues for research in this field.
While mathematicians have used computers to discover patterns for decades, the growing power of machine learning means these networks can process large amounts of data and recognize previously unrecognized patterns.
In a recently published study, a research team used artificial intelligence systems developed by DeepMind, the same company that implemented AI to solve complicated biological problems and improve the accuracy of weather forecasts, to solve some long-standing math problems .
Mathematics problems are widely considered to be some of the most intellectually challenging problems, says Geordie Williamson, mathematician of the University of Sydney, Australia.
While mathematicians have used machine learning to aid in the analysis of complex data sets, we are for the first time using computers to make guesses or suggest possible lines of attack for unproven ideas in mathematics.
The team demonstrates how AI provides a proof of the Kazhdan-Lusztig polynomials, a mathematical problem with symmetry in higher dimensional algebra that has remained unsolved for 40 years.
The research also showed how a machine learning technique called the supervised learning model was able to detect a previously undiscovered relationship between two different types of math nodes, resulting in an entirely new theorem.
Knot theory in mathematics also plays a role in several other challenging areas of science, including genetics, fluid dynamics, and even the behavior of the sun’s corona. Hence, the discoveries of AI can lead to breakthroughs in other research areas.
We have shown that machine learning, when guided by mathematical intuition, provides a powerful framework that can uncover interesting and provable guesswork in areas where large amounts of data are available or objects are too large to be investigate with methods, says the mathematician András Juhász from the University of Oxford in the UK.
One of the advantages of machine learning systems is that they can look for patterns and scenarios that the programmers haven’t specifically programmed – they use your training data and apply the same principles to new situations.
Research shows that this type of highly reliable, high-speed, large-scale computing can serve as an additional tool for mathematicians to work with natural intuition. When it comes to long, complex equations, that can make a world of difference.
The researchers hope that their work will lead to many more partnerships between scientists in the fields of mathematics and artificial intelligence, which will open up opportunities for knowledge that would otherwise remain undiscovered.
AI is an extraordinary tool, says Williamson. “This work is one of the first times it has been useful to pure mathematicians like me.”
Intuition can get us far, but AI can help us find connections that the human mind cannot always easily see.
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