Researcher cracks new ‘kissing number’ bounds — besting AI in the process

How many coins can touch one coin, or how many basketballs can 'kiss' one basketball at the same time? This seemingly playful question lies at the heart of the famous kissing number problem, a mathematical riddle that becomes almost supernaturally difficult to work out in dimensions beyond 4D. Despite its whimsical name, similar problems have practical applications in areas such as mobile communications and satellite navigation.

Aalto University doctoral candidate Mikhail Ganzhinov established three new lower bounds for the kissing number: at least 510 in dimension 10, at least 592 in dimension 11, and at least 1,932 in dimension 14. There had been no movement on the riddle for dimensions below 16 for two decades until earlier this year, when AlphaEvolve, developed by Google's artificial intelligence laboratory DeepMind, made headlines in May. It was able to increase the lower bound of dimension 11 to a score of 593. So, only in the 11th dimension did Ganzhinov fall one step short of AlphaEvolve's AI-powered result.