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Notes -
Interesting developments in use of AI in mathematics and writing
{Math}International Mathematical Olympiad is an international competion for high schoolers around the world. They compete in solving problems related to inequalities, number theory and geometry. It is the last category in which Google's AlphaGeometry leapfrogged the previous SOTA, reaching almost Chinese-team level of success.
It's method is intuitively attractive: it uses both unbiased but blind pattern finding skills associated with LLM today, and rigourous symbolic math honed by millenia of human efforts to find the greatest amount of pure truth. That the latter was included speaks to the fact that we are still at the centaur stage of AI, in that sometimes augmenting AI with what humans already know, allows it to perform better than not doing so.
In the future all AI will be unconstrained by human traditions and biases, thus it will be able to search a wider space, enabling it to beat humans at games humans invented. Such is already the case with AlphaGo. Euclidean geometry has more difficult rules, so some handholding is still needed.
{Writing}Akutagawa Prize is a literary prize expected to awarded twice each year. It is considered one of most prestigous such prizes in Japan. Previous winners include: 石原 慎太郎, 安部 公房, 遠藤 周作, and 大江 健三郎.
The latest winner, 九段 理江, won it for 東京都同情塔, a novel about a high-rise prison tower in futuristic Tokyo and its architect's intolerance of criminals, AI being a recurring theme. In the acceptance speech 九段さま admitted that 5% of the novel was copied verbatim from ChatGPT. Again centaur approach wins out against pure AI.
Had the author attempted to write the 144 pages by asking AI to do it instead, the result would be incoherent, as currently techology isn't there yet to hold in memory so great amounts of data. 九段さま judicious and moderate use of AI to augment, rather than replace, human writing seems to have served them well, beating out works written by only humans.
I wonder how long before AI makes substantial progress with string theory, which based on my limited understanding is based on geometry.
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