The most beautifully symmetric object in physics is not the intricate snowflake or something like that of Mcsher but rather once again coming back to my cow as a sphere a sphere. There's nothing more beautiful than a sphere because there's nothing more symmetric than a sphere.
I think the problem itself is important right this is new knowledge for humanity that the proof itself is actually very elegant and beautiful and I think that there's a lot to learn from it
Today's models can grind through calculations, combine known techniques, and search enormous spaces, but still struggle with intuition, theory building, identifying the right questions, and developing the kind of big-picture understanding that drives much of mathematical progress.
The fact that symmetry restricts things in physics is central to our modern understanding of nature as we'll get to. But there's another feature of symmetry that's important that symmetry restricts how you can describe the object.
It's funny that AI systems are all still pretty bad at elementary school arithmetic, but getting increasingly good at very high-end abstract math. That raises some big questions for the field of advanced math.
Humans are becoming the bottleneck of verification for AI. And now the question is, where does that leave us? Is this the end of the road for reliable mathematical discovery? Are we resigned to drowning in a sea of unverified claims where we can't really tell truth from fiction?
