A human has outkissed one of Google’s superpowered artificial intelligence systems. The achievement isn’t in the realm of romance, however. Instead, this win is in the intellectual realm of advanced mathematics. While largely conceptual in nature, the ramifications could soon help boost advancements in telecommunications and satellite arrays.
What is the kissing problem?
The “kissing problem” isn’t the term for a junior high dance conundrum—it’s actually a reference to a famous mathematical riddle. The setup is simple: How many circles or spheres can be arranged so that every individual simultaneously touches or “kisses” a single rounded shape in the center?
The answer is relatively simple when dealing with up to three dimensions. The answer for one dimension is 3, two dimensions gets you 6, and a three dimensional situation can support 12 kissing spheres. In 2003, mathematician Oleg Musin proved that the kissing number for four dimensions is 24. If that concept is hard to wrap your head around, it only gets weirder as the dimensions increase.
Stuck in the 16th dimension
Kissing problem experts have been stuck for about two decades. Despite their efforts, no one had established a new lower bound of objects for any dimension below dimension 16.
However, in May 2025, Google’s DeepMind laboratory announced its artificial intelligence system AlphaEvolve had managed to increase the 11th dimension’s lower bound of kissing objects to 593. Like in many other fields, the news seemed to indicate the future of kissing problem investigations belonged to AI.
But thanks to the work of doctoral candidate Mikhail Ganzhinov at Finland’s Aalto University, humans are still holding their own when it comes to kissing. Ganzhinov’s recent dissertation work showed three new lower bounds: at least 510 in the 10th dimension, 592 in dimension 11, and at least 1,932 in dimension 14. Basically, Ganzhinov outperformed AlphaEvolve in two out of three cases.
‘Far from omnipotent’
Understanding how Ganzhinov calculated these solutions is beyond most people’s mathematical prowess, but he still attempted to distill his approach for his university’s announcement on October 23.
“I reduced the problem size by looking only for arrangements with a high degree of symmetry,” he said, for what it’s worth. Regardless, the implications are much easier to digest.
“Artificial intelligence can do amazing things, but it’s far from omnipotent,” added Ganzhinov’s thesis advisor, Patric Östergård.
His former student likely isn’t done, either. According to Ganzhinov, the 11th dimension’s current lower bound is “still quite weak” and can probably extend “well beyond 600.”
“The game may still turn to Mikhail’s favour in dimension 11, too,” said Östergård.
Ganzhinov isn’t alone in challenging AI’s abilities. Mathematicians at MIT are readying a paper that pushes kissing number bounds in dimensions 17 through 21. Their work marks the first progress in those dimensions in over half a century.
“This riddle has challenged mathematicians since the famous conversation between Newton and [17th century mathematician David] Gregory,’ explained Ganzhinov. “Yet solving them also has a practical purpose–understanding connections to spherical codes has real life implications in the field of communications.”
