Timeline for What, if anything, do we hope and expect to understand about (classical) Galois groups?
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| Feb 28 at 17:11 | comment | added | plm | @PVanchinathan, thank you. I've read the short paper. The author defines what he calls "root quantum number" of $f\in K[X]$ and a root $\alpha$ of $f$, the number of roots appearing in the extension $K(\alpha)$. It turns out to be independent of $\alpha$ and divides the degree of $f$. He makes a number of observations and proposes 4 exercises which he has solved, but i do not see any open question. In any case that does not say anything a priori new about Galois groups though of course it is a concept of field theory and Galois theory so it may lead to new insights about Galois groups. | |
| Feb 28 at 8:16 | comment | added | P Vanchinathan | @plm This an important question. Directions for research are set by some people who can see far. That sets a trend and many people work on that. Not knowing the deeper reason for that when I set out to read and understand their work I feel lost. In Galois theory Alexander Perlis in his 2004 paper) published in American Mathematical Monthly had asked a very basic classical question. He wonders why people seem to be unaware of that question ( was he too polite to say why people are indifferent to a fundamental question?). Please read that paper titled "Roots appear in Quanta". | |
| Aug 1, 2023 at 10:35 | comment | added | plm | Thank you @TimothyChow. I will ponder this. Perhaps the lack of answer or comments already gives me information about my question. So thank you for tolerating it. | |
| Jul 30, 2023 at 13:59 | comment | added | Timothy Chow | I did not vote to close, but the question strikes me as too broad and unfocused for MO. Maybe consider asking a more targeted question? | |
| Jul 30, 2023 at 13:57 | review | Close votes | |||
| Aug 5, 2023 at 3:06 | |||||
| Jul 30, 2023 at 4:03 | history | edited | plm | CC BY-SA 4.0 |
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| Jul 30, 2023 at 0:40 | history | asked | plm | CC BY-SA 4.0 |