I'm gonna talk about math for a sec, cuz I'm working late and being nerdy.
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Replying to @EmilyGorcenski
Most of the underlying methods used in modern computational math (incl. machine learning) were invented well-before the digital computer.
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Replying to @EmilyGorcenski
Runge-Kutta methods--RK4 being the bread-and-butter ODE solver--were invented in the late 1800s/early 1900s.
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Replying to @EmilyGorcenski
This is just one example. My favorite, however, is super relevant to modern computing.
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Replying to @EmilyGorcenski
No general, non-iterated algorithm exists to compute eigenvalues for a matrix over the reals or complex numbers larger than 4x4.
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Replying to @EmilyGorcenski
Is there some more fundamental reason why it stops at 4, or is that just the way it is?
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Replying to @porglezomp
Yes, there is! but it is very complicated to explain.
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Replying to @EmilyGorcenski @porglezomp
The short version is that eigenvalues are the roots k of the determinant of the matrix pencil A-kI, which is a polynomial.
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Replying to @EmilyGorcenski @porglezomp
Abel-Ruffini explains that there is no general solution solvable by radicals for a polynomial of degree 5 or higher.
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Replying to @EmilyGorcenski
Okay, so looks like I guessed right! I can imagine that might need Analysis to prove.
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The elegant proof resides in Galois theory, which is generally considered part of abstract algebra
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Replying to @EmilyGorcenski
Well I'm already looking forward to algebra next semester! Thanks for the explanation.
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