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age 34
visits member for 1 year, 7 months
seen Jul 11 at 20:03

Apr
3
awarded  Yearling
Jan
5
awarded  Excavator
Jan
5
revised Widely accepted mathematical results that were later shown wrong?
Formatting and punctuation.
Dec
20
comment Is Euclid dead?
Offering people the opportunity to study something is not the same as forcing them to do so. I had to fight tooth and nail to get into appropriate math classes in elementary and middle school—no one forced me to do that!
Dec
20
comment Is Euclid dead?
Linear algebra is useful, but that doesn't make it the right introduction to proof for students. Why do you say linear algebra is "the basic language in which most of mathematics is expressed"? I see neither hide nor hair of it in set theory, formal logic, general topology, etc.
Dec
20
comment Is Euclid dead?
@Federico Poloni, math and science classes are full of "lies told to children" and things left unexplained. What high school number theory or discrete math course would build up from Peano arithmetic or ZF theory? What high school calc 2 class includes a rigorous proof of Stokes's Theorem?
Dec
20
comment Is Euclid dead?
In addition: straightedge and compass constructions are wonderful ways to get hands-on with mathematical proofs.
Dec
20
comment Is Euclid dead?
My middle-school geometry class (age 13) was a proof-based geometry class. We started out with synthetic affine geometry and built up to Euclidean. It was surely not the most rigorous axiomatization of geometry, but it was an excellent class and made every "introduction to proof" class I've encountered since entirely redundant. Every assignment and every test was entirely proof-based, and some were quite challenging to me at the time. Do I remember any geometry? No, not really. Was it one of the most valuable classes I've ever taken? Absolutely.
Oct
7
awarded  Critic
Jul
9
comment What sets of self-maps are the continuous self-maps under some topology?
I'm not surprised that the properties at the end are not sufficient; they're extremely weak. I just haven't been able to come up with others!
Jul
9
awarded  Commentator
Jul
9
comment What sets of self-maps are the continuous self-maps under some topology?
Another thing about the polynomials over infinite fields, and I believe also the holomorphic functions: in those cases $|X|=|\mathscr C|$.
Jul
9
awarded  Supporter
Jul
9
comment What sets of self-maps are the continuous self-maps under some topology?
Could someone explain how this result is more than superficially related to the question? Am I missing something important?
Jul
8
awarded  Citizen Patrol
Jul
8
revised What sets of self-maps are the continuous self-maps under some topology?
Silly typo
Jul
8
revised What sets of self-maps are the continuous self-maps under some topology?
Expand a bit
Jul
8
awarded  Nice Question
Jul
8
comment What sets of self-maps are the continuous self-maps under some topology?
@MartinBrandenburg: unfortunately there isn't much discussion there.
Jul
8
asked What sets of self-maps are the continuous self-maps under some topology?