> An LLM can discover a new solution in high dimensional geometry that hasn’t advanced in 20 years!? That goes way beyond glueing little bits of plagiarized tra

> An LLM can discover a new solution in high dimensional geometry that hasn’t advanced in 20 years!? That goes way beyond glueing little bits of plagiarized training data together in a plausible way. The first advance in 20 years was by Fred Tyrrell last year https://arxiv.org/abs/2209.10045 https://arxiv.org/abs/2209.10045, who showed that the combinatorics quantity in question is between 2.218 and 2.756, improving the previous lower bound of 2.2174. DeepMind has now shown that the number is between 2.2202 and 2.756. That's why the DeepMind authors describe it as "the largest increase in the size of cap sets in the past 20 years," not as the only increase. The arithmetic is that 2.2202-2.218 is larger than 2.218-2.2174. (If you consider this a very meaningful comparison to make, you might work for DeepMind.)