Artificial intelligence (AI) is making significant strides in pure mathematics, detecting patterns that have previously gone unnoticed. A team of scientists from the University of Cambridge utilised an AI to explore patterns within the abstract world of mathematical symmetry. The AI, named Minerva, was trained to recognise symmetry in a variety of forms, eventually discovering 17 new types of wallpaper groups.
Wallpaper groups represent distinct patterns that can be repeated indefinitely in two dimensions without overlapping or leaving gaps. Traditionally, mathematicians believed there were only 17 types, but Minerva’s findings have challenged this long-held belief.
Minerva’s success is attributed to its ability to learn in a self-supervised manner, without the need for pre-existing labels or categories. This approach allowed Minerva to discover patterns in an unbiased way, leading to the identification of the new wallpaper groups.
The findings open up new possibilities for pure mathematics and AI. They demonstrate the potential of AI to uncover previously unseen patterns, and suggest that AI could be used to explore other areas of mathematics. The results also hint at a future where AI can contribute to the advancement of mathematical knowledge.
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