# Tag Info

### Why do we make such big deal about the 'unsolvability' of the quintic?

I think that a large part of the difficulty we have in understanding why this result is considered important is that it is psychologically difficult to put oneself into the shoes of mathematicians of ...
• 79.4k
Accepted

### Ideas for introducing Galois theory to advanced high school students

I have now twice taught Galois theory to advanced high school students at PROMYS. This is a six week course, meeting four times a week, for students who already are comfortable with proofs and, in ...

### Why do we make such big deal about the 'unsolvability' of the quintic?

It is not a big deal anymore (edit: I mean in modern math, not for teaching undergraduate math courses) and has not been for a long time. It was important historically because of the math that came ...
• 49.9k
Accepted

### Grothendieck says: points are not mere points, but carry Galois group actions

Suppose $k$ is a field, not necessarily algebraically closed. $\text{Spec } k$ fails to behave like a point in many respects. Most basically, its "finite covers" (Specs of finite etale $k$-algebras) ...
• 115k
Accepted

### What is the dimension of the mathematical universe?

My co-authors and I introduced a notion of dimension for forcing extensions in the following paper: Hamkins, Joel David; Leibman, George; Löwe, Benedikt, Structural connections between a forcing ...

### Why do we make such big deal about the 'unsolvability' of the quintic?

Perhaps it's not a big deal that's it's true; but it's a big deal that we can know and prove that it's true. I don't mean because the ability to prove that it's true implies the ability to do other, ...
• 441
Accepted

### Does any cubic polynomial become reducible through composition with some quadratic?

You should refer to Lemma 10 (page-233) in this paper by Schinzel where he proves that for any polynomial $F(x)$ of degree $d$ we have a polynomial $G(x)$ of degree $d-1$ such that their ...
• 1,032
Accepted

### How are motives related to anabelian geometry and Galois-Teichmuller theory?

Two clarifications: For anabelian geometry, you should ask how much information about a variety is contained in the Galois action on its etale fundamental group. While it's true that the motivic ...
• 138k

### Why do we make such big deal about the 'unsolvability' of the quintic?

Mathematically, there is nothing special about radicals: solving algebraic equations by radicals is only one example of mathematical problems among others that are self-contained, comprehensive, ...
• 1,061