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> When asked where his formulas came from, he claimed, “They grow in my garden.” This makes me think of Ramanujan's notebooks. And based on my limited interact
by falcor84 2y ago
> When asked where his formulas came from, he claimed, “They grow in my garden.”
This makes me think of Ramanujan's notebooks. And based on my limited interaction with professional mathematicians, I think there is something to this - some hidden brain circuitry whereby mathematicians can access mathematical truths in some way based on their "beauty", without going through anything resembling rigorous intermediate steps. The metaphor that comes to my sci-fi-fed mind is that something in their brains allows them to "travel via hyperspace".
And this then makes me think of GenAI - recent progress has been quite interesting, with models like o1 and o3 at times making silly mistakes, and at other times making incredible leaps - could it be that AI's are able to access this "garden" too? Or does there remain something that we humans have access to, while AIs do not?
- ysofunny 2y agoit's like learning the letters of the alphabet permits one to see meaning behind their glyphs, namely the words; and then through reading text you perceive stories and so on when somebody learns enough letters of "the mathematical alphabet of concepts" one begins to perceive a sort of "meaning", the mathematical realm i.e. the "garden"
- PhilipRoman 2y agoTerrence Tao wrote a nice blog post which captures this idea (post-rigorous phase) https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/ https://terrytao.wordpress.com/career-advice/theres-more-to-...
- sdwr 2y agoI appreciate that he cites corroborating sources for his ideas, it makes the whole thing feel well-rounded
- heisenzombie 2y agoAlso see David Bessis: https://www.quantamagazine.org/mathematical-thinking-isnt-what-you-think-it-is-20241118/ https://www.quantamagazine.org/mathematical-thinking-isnt-wh...
- anthk 2y agoLeaves and branches/roots in nature are fractal.