With ChatGPT and similar systems developing to the extent of solving problems in numbers, I have always wondered how AI would solve geometry related problems. My question primarily came from heuristics. Usually if we have a problem with numbers, the AI can arrive at the solution possibly with a previous knowledge, trying to form equations, use brute force, etc. because of various reasons like numbers are sequential and it can check on the next number and see if it leads to the answer. But that’s not the case with Geometry. In proofs in Geometry, one can hardly use any of these (except from prior knowledge). That’s because in hard Geometry problems require a creative and intelligent construction where we find a plausible bridge that can help make it possible to find missing gaps to solve the problem. Finding this missing connection is often something like drawing an altitude in the figure and then trying to see if one can make progress with the problem. But how do you come up with that intelligent piece of connection is unknown. It just comes to a math enthusiast. But then, I would wonder, how can it come to AI.
Google has done it again. Here’s an article that explains about their paper on AlphaGeometry on how it solved some of the hardest Geometry problems at high school level in very efficient ways.
This is a huge jump in the development of AI. It means that it could also lead to solving some of the unsolved problems in Mathematics that is still open even after decades or even centuries. I am sure there are many who may be sharing my anxiety and I am curious to know what you think.
When I was discussing about this with a senior faculty and a retired Computer Scientist, he exclaimed with a funny yet profound remark, “Riemann is waiting!”
https://deepmind.google/discover/blog/alphageometry-an-olympiad-level-ai-system-for-geometry/ (must read for any math student, teacher and anyone in general)
Author: A three-time TEDx speaker, Vinay Nair is one of the co-founders of Raising A Mathematician Foundation. He is a mathematics educator passionate about gifted education, history of Indian mathematics and loves to explore mathematics with young students. He can be reached at vinay@vicharvatika.org.
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