A human has outwitted Google's DeepMind AI in a battle of intellectual wits, solving the centuries-old 'kissing problem'. This feat is not about romance, but rather about advanced mathematics that could soon have far-reaching implications for telecommunications and satellite arrays.
The "kissing problem" refers to a famous mathematical riddle where researchers aim to determine how many circles or spheres can be arranged in such a way that every individual simultaneously touches or "kisses" a single rounded shape. The answer to this question is relatively straightforward when dealing with one, two, or three dimensions - the numbers are 3, 6, and 12 respectively.
However, things become increasingly complex as we venture into higher dimensions. Mathematician Oleg Musin proved in 2003 that for four dimensions, the number is 24. Nevertheless, solving this problem has proven to be a significant challenge even among top mathematicians, with experts having been stuck for nearly two decades without establishing new lower bounds of objects for any dimension below 16.
But now, thanks to a breakthrough by doctoral candidate Mikhail Ganzhinov at Finland's Aalto University, humans are once again in the running when it comes to solving the kissing problem. In his recent dissertation work, Ganzhinov has managed to find three new lower bounds: at least 510 in the 10th dimension, 592 in dimension 11, and a staggering 1,932 in dimension 14.
It's worth noting that while Ganzhinov has made significant strides, he acknowledges that AI still holds an advantage - particularly when it comes to higher dimensions. DeepMind's AlphaEvolve system, for instance, had previously managed to increase the lower bound of kissing objects in the 11th dimension to 593.
Ganzhinov's achievement serves as a reminder that while artificial intelligence is becoming increasingly powerful, humans still have much to offer when it comes to intellectual pursuits. Moreover, his work has significant practical implications, particularly for fields such as communications and telecommunications.
The "kissing problem" refers to a famous mathematical riddle where researchers aim to determine how many circles or spheres can be arranged in such a way that every individual simultaneously touches or "kisses" a single rounded shape. The answer to this question is relatively straightforward when dealing with one, two, or three dimensions - the numbers are 3, 6, and 12 respectively.
However, things become increasingly complex as we venture into higher dimensions. Mathematician Oleg Musin proved in 2003 that for four dimensions, the number is 24. Nevertheless, solving this problem has proven to be a significant challenge even among top mathematicians, with experts having been stuck for nearly two decades without establishing new lower bounds of objects for any dimension below 16.
But now, thanks to a breakthrough by doctoral candidate Mikhail Ganzhinov at Finland's Aalto University, humans are once again in the running when it comes to solving the kissing problem. In his recent dissertation work, Ganzhinov has managed to find three new lower bounds: at least 510 in the 10th dimension, 592 in dimension 11, and a staggering 1,932 in dimension 14.
It's worth noting that while Ganzhinov has made significant strides, he acknowledges that AI still holds an advantage - particularly when it comes to higher dimensions. DeepMind's AlphaEvolve system, for instance, had previously managed to increase the lower bound of kissing objects in the 11th dimension to 593.
Ganzhinov's achievement serves as a reminder that while artificial intelligence is becoming increasingly powerful, humans still have much to offer when it comes to intellectual pursuits. Moreover, his work has significant practical implications, particularly for fields such as communications and telecommunications.