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bubble12345

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AI will not do math for us, but maybe eventually it will lead to another mainstream tool for mathematicians. Along with R, Matlab, Sage, GAP, Magma, ...

It would be interesting if in the future mathematicians are just as fluent in some (possibly AI-powered) proof verifying tool, as they are with LaTeX today.

Galois Theory 2 years ago

You are right in the sense that solvability by radicals has no practical importance, especially when it comes to calculations.

It is just a very classical pure math question, dating back hundreds of years ago. Its solution led to the development of group theory and Galois theory.

Group theory and Galois theory then are foundational in all kinds of areas.

Anyway, so why care about solvability by radicals? To me the only real reason is that it's an interesting and a natural question in mathematics. Is there a general formula to solve polynomials, like the quadratic formula? The answer is no - why? When can we solve a polynomial in radicals and how?

And so on. If you like pure math, you might find solvability by radicals interesting. It's also a good starting point and motivation for learning Galois theory.

Galois Theory 2 years ago

That's a common myth. See this paper referenced in the wikipedia article:

Rothman, Tony (1982). "Genius and Biographers: The Fictionalization of Evariste Galois". The American Mathematical Monthly. 89 (2): 84–106. doi:10.2307/2320923. JSTOR 2320923

I just remember making websites using <TABLE WIDTH=100%>, and at some point reading that CSS and using <div>'s was the new, more correct way to do it. I only need a simple personal website for academics, so I still use tables for the layout.