Not just by supplying accurate jargon, but by actually teaching you at least one clear example of genuine genius thinking.
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Replying to @MathPrinceps @MrGrahamMoore
Which is a very considerable challenge, even for an expert. Because, alas, pedagogy is an art of little interest to experts.
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Replying to @MathPrinceps @MrGrahamMoore
But it's possible. Here's a beautiful and transparent illustration of your doctrine, drawn from the early career of Ramanujan
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Replying to @MathPrinceps @MrGrahamMoore
Ramanujan observed that 9 = 1 + 2x4 16 = 1 + 3x5 25 = 1 + 4x6, and that 3 = sqrt(9) 4 = sqrt(16) 5 = sqrt(25), etc, etc.
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Replying to @MathPrinceps @MrGrahamMoore
These observations were not new to him, of course. His genius was to see what they actually meant. To fashion them into art.
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Replying to @MathPrinceps @MrGrahamMoore
Ramanujan saw that these mundane facts fit together in a dazzling way. He saw that 3 = sqrt(1 + 2x4) is just a first step.
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Replying to @MathPrinceps @MrGrahamMoore
It has infinitely many counterparts, 4 = sqrt(1 + 3x5) 5 = sqrt(1 + 4x6) 6 = sqrt(1 + 5x7) which nest like Russian dolls.
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Replying to @MathPrinceps @MrGrahamMoore
So that 3 = sqrt(1 + 2x4) = sqrt(1 + 2xsqrt(1 + 3x5)) = sqrt(1 + 2xsqrt(1 + 3xsqrt(1 + 4x6))) = ... , etc., ad infinitum.
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Replying to @MathPrinceps @MrGrahamMoore
This is 3 as an infinitely long string of nested square roots -- a novel mathematical beast, when Ramanujan encountered it.
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Replying to @MathPrinceps @MrGrahamMoore
Like one of Holmes' deductions, no one else was able to put these pieces together. Ramanujan alone recognized 3 in this form.
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This is a humble yet authentic picture of how his mind worked - a genuine example of his genius that can fit into a film.
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