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Sep
10
comment Why Euler-Lagrange equation does not depend on the second derivative of the function?
See en.wikipedia.org/wiki/…
Jun
29
comment Cutting the $2$-dimensional real Projective Space
The projective plane is the quotient of $S^2$ by the antipodal map, and cutting out a non-contractible cycle corresponds to removing the equator in the sphere.
Feb
13
awarded  Citizen Patrol
Feb
13
comment How to bound the maximal consecutive length in a random subset of [n] as function of n?
Concerning the usual reasons: On MathOverflow, we're getting flags claiming that this user's questions come from a take-home exam that is in progress.
Nov
6
awarded  Yearling
Aug
20
awarded  Enlightened
Aug
20
awarded  Nice Answer
Jun
10
comment Guaranteed Checkmate with Rooks in High-Dimensional Chess
@George: Your strategy sounds good, but I'm pretty sure you don't need more than 7 at each corner. The extra shrinking piece also seems unnecessary, so I have a tentative upper bound of 44.
Jun
8
awarded  Constituent
Jun
8
awarded  Caucus
Feb
10
comment The definition of the logarithm.
There is also the lemma-definition that log is the unique continuous homomorphism from $(\mathbb{R}^\times, \times)$ to $(\mathbb{R}, +)$ that has unit slope at 1.
Nov
6
awarded  Yearling
Aug
1
comment Why the moduli space of complex structure in a compact complex manifold is of finite dimension
By Kodaira-Spencer theory, you can compute the space of first-order deformations of the complex structure as a cohomology group. For a fixed choice of complex structure, this space is (more or less) the tangent space of the moduli space of complex structures at the point that describes the chosen complex. structure.
Jul
23
comment Can an algorithm be faster than O(1)?
Your analog computation is still $O(1)$ due to relativistic considerations. From a physical perspective, since the observable universe has finite usable energy, it will always take time bounded away from zero to output the result of a non-null algorithm.
Jul
23
answered $\mathbb{G}_a$ has no nontrivial characters
Jul
23
comment Should I write out stuff?
@Alex J: I interpret the quote as follows: For each theorem that Bourgain proved, he did not need to do a computation to convince himself that it was true. Often, there are structural methods outside computation that you can use to make guesses.
Jul
21
comment Why is it “easier” to work with function fields than with algebraic number fields?
Incidentally, there's nothing formal about the derivative of a polynomial. Given a polynomial map, the derivative is the canonical map from the tangent bundle of the source to the pullback of the tangent bundle of the target.
Jul
14
answered Motivation for supermanifolds
Jul
13
answered Abstract Nonsingular Curves
Jul
10
awarded  Commentator