User Jeff Strom

102 votes

nontrivial theorems with trivial proofs

answered Jun 20, 2010 at 14:24

97 votes

Why do we teach calculus students the derivative as a limit?

real-analysis ho.history-overview teaching limits-and-convergence

answered Sep 27, 2010 at 13:58

69 votes

Can a subset of the plane have nontrivial $H_2$ or $\pi_2$?

at.algebraic-topology counterexamples

answered Dec 9, 2014 at 21:32

54 votes

Can a mathematical definition be wrong?

soft-question mathematical-philosophy definitions ho.history-overview big-list

answered Aug 6, 2010 at 23:36

39 votes

What are some noteworthy "mic-drop" moments in math?

soft-question big-list

answered Mar 11, 2019 at 0:22

36 votes

In a topological space if there exists a loop that cannot be contracted to a point does there exist a simple loop that cannot be contracted also?

at.algebraic-topology gn.general-topology homotopy-theory

answered Aug 9, 2019 at 1:23

33 votes

Accepted

Is every real n-manifold isomorphic to a quotient of $\mathbb{R}^n$?

gt.geometric-topology gn.general-topology manifolds

answered Nov 13, 2010 at 21:50

32 votes

Accepted

Suspension of a topological space

at.algebraic-topology gt.geometric-topology manifolds

answered Jun 3, 2021 at 0:57

30 votes

The role of the mean value theorem (MVT) in first-year calculus

real-analysis mathematics-education teaching

answered Jul 11, 2010 at 23:05

28 votes

Main statement as theorem or corollary

terminology mathematical-writing definitions

answered Jan 15, 2018 at 14:09

27 votes

Accepted

Interesting Calculus Questions/Exercises

ca.classical-analysis-and-odes soft-question big-list teaching

answered Jan 21, 2011 at 21:10

25 votes

Accepted

Image of a map on cohomology rings

at.algebraic-topology cohomology

answered Sep 25, 2019 at 0:01

25 votes

Why is it so hard to compute $\pi_n(S^n)$?

at.algebraic-topology homotopy-theory

answered Oct 21, 2014 at 17:46

24 votes

Accepted

Homotopy equivalent Postnikov sections but not homotopy equivalent

at.algebraic-topology homotopy-theory homology

answered Jul 30, 2020 at 17:14

21 votes

Accepted

Whitehead theorem for cohomotopy

at.algebraic-topology

answered May 13, 2014 at 0:49

20 votes

Accepted

Divisibility in the homotopy groups of spheres?

at.algebraic-topology homotopy-theory

answered Nov 25, 2019 at 3:52

19 votes

Advantages of working with CW complexes/spaces over Kan complexes/simplicial sets?

homotopy-theory soft-question simplicial-stuff at.algebraic-topology

answered Jul 13, 2010 at 0:50

17 votes

An abstract nonsense proof of the Hurewicz theorem

homotopy-theory simplicial-stuff

answered Oct 11, 2017 at 2:47

16 votes

The most outrageous (or ridiculous) conjectures in mathematics

ho.history-overview big-list

answered Jan 21, 2017 at 1:05

14 votes

Teaching Steenrod Operations

at.algebraic-topology homotopy-theory cohomology simplicial-stuff teaching

answered Nov 2, 2017 at 18:18

13 votes

Accepted

In a fibration, can a deformation retraction of the base be lifted to the total space?

at.algebraic-topology

answered Aug 14, 2014 at 1:24

13 votes

Proof synopsis collection

big-list intuition gm.general-mathematics

answered Oct 28, 2010 at 0:03

13 votes

What is the intuition behind the Freudenthal suspension theorem?

at.algebraic-topology gt.geometric-topology intuition

answered Feb 23, 2011 at 20:14

12 votes

Why should one still teach Riemann integration?

ca.classical-analysis-and-odes soft-question measure-theory integration teaching

answered Jan 21, 2011 at 20:52

12 votes

Why does homotopy behave well with respect to fibrations and homology with respect to cofibrations?

big-picture homotopy-theory at.algebraic-topology

answered Feb 24, 2011 at 21:30

12 votes

Counterexamples in algebraic topology?

at.algebraic-topology examples

answered Feb 14, 2011 at 1:44

12 votes

Categories First Or Categories Last In Basic Algebra?

mathematics-education homological-algebra ct.category-theory

answered Oct 4, 2010 at 21:04

9 votes

when cup product is a zero homomorphism

at.algebraic-topology

answered Aug 4, 2010 at 21:49

9 votes

Homotopic maps out of cofibration sequences

at.algebraic-topology ct.category-theory model-categories

answered Nov 10, 2011 at 1:27

9 votes

Accepted

continuous images of open intervals

gn.general-topology

answered May 25, 2014 at 1:11

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127 Answers

nontrivial theorems with trivial proofs

Why do we teach calculus students the derivative as a limit?

Can a subset of the plane have nontrivial $H_2$ or $\pi_2$?

Can a mathematical definition be wrong?

What are some noteworthy "mic-drop" moments in math?

In a topological space if there exists a loop that cannot be contracted to a point does there exist a simple loop that cannot be contracted also?

Is every real n-manifold isomorphic to a quotient of $\mathbb{R}^n$?

Suspension of a topological space

The role of the mean value theorem (MVT) in first-year calculus

Main statement as theorem or corollary

Interesting Calculus Questions/Exercises

Image of a map on cohomology rings

Why is it so hard to compute $\pi_n(S^n)$?

Homotopy equivalent Postnikov sections but not homotopy equivalent

Whitehead theorem for cohomotopy

Divisibility in the homotopy groups of spheres?

Advantages of working with CW complexes/spaces over Kan complexes/simplicial sets?

An abstract nonsense proof of the Hurewicz theorem

The most outrageous (or ridiculous) conjectures in mathematics

Teaching Steenrod Operations

In a fibration, can a deformation retraction of the base be lifted to the total space?

Proof synopsis collection

What is the intuition behind the Freudenthal suspension theorem?

Why should one still teach Riemann integration?

Why does homotopy behave well with respect to fibrations and homology with respect to cofibrations?

Counterexamples in algebraic topology?

Categories First Or Categories Last In Basic Algebra?

when cup product is a zero homomorphism

Homotopic maps out of cofibration sequences

continuous images of open intervals