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25 Questions

Views Newest Activity Votes

votes

answers

638

views

Are there non-standard counterexamples to the Fermat Last Theorem?

Oct 31 '17 at 20:54 Carl Mummert 68.4k

votes

answer

455

views

Are there spaces that 'look the same' at every point, but are not homogeneous?

geometry differential-geometry riemannian-geometry

May 28 '15 at 11:08 levap 48.4k

votes

answer

900

views

What is the reflection across a parabola?

complex-analysis geometry geometric-construction reflection

Nov 17 '16 at 17:20 mercio 44.9k

votes

answers

248

views

How many different products can be formed by multiplying $n$ numbers at most once?

combinatorics number-theory

Jun 30 '17 at 21:11 Artimis Fowl 840

votes

answers

179

views

Is there a clever way to find a smaller number that produces the Euclidean algorithm of given length?

number-theory elementary-number-theory modular-arithmetic euclidean-algorithm

May 10 '16 at 0:13 Conifold 7,105

votes

answers

695

views

Why do we know that Gödel sentences are true in the standard model of set theory, but do not know if the continuum hypothesis is?

logic set-theory model-theory

Jul 1 '15 at 5:12 Community♦ 1

votes

answer

383

views

Is Archimedes's method for computing volumes equivalent to Cavalieri's?

integration geometry

May 4 '15 at 22:36 Conifold 7,105

votes

answers

28k

views

Are triangles the strongest shape?

geometry optimization calculus-of-variations

Jun 15 '17 at 13:52 Andrew T Keener 1

votes

answer

255

views

How do inconsistent arithmetics get around Gödel incompleteness?

logic model-theory axioms incompleteness

Nov 12 '15 at 13:36 Community♦ 1

votes

answer

457

views

Why is the powerset axiom more acceptable than the axiom of choice?

soft-question set-theory model-theory axiom-of-choice

Aug 20 '14 at 23:25 Community♦ 1

votes

answer

341

views

Is there a theory of integration in elementary terms for definite integrals?

calculus integration definite-integrals closed-form elementary-functions

Aug 19 '14 at 20:41 Community♦ 1

votes

answer

views

Functions with every point being a Lebesgue point

real-analysis integration measure-theory lebesgue-integral lebesgue-measure

Jul 8 '14 at 13:51 George 1,233

votes

answers

103

views

What is the multiplicative order of a product of two integers $\mod n$?

group-theory number-theory modular-arithmetic prime-factorization

Sep 2 at 22:41 Conifold 7,105

votes

answer

248

views

Circle inversion and the Pappus chain paradox

geometry circles transformation mobius-inversion

Jan 29 '18 at 0:43 Conifold 7,105

votes

answers

243

views

Can one prove existence of incommensurables without the Pythagorean theorem?

geometry logic model-theory irrational-numbers

Aug 30 '14 at 1:38 Community♦ 1

votes

answer

355

views

Partial order on cardinalities without the axiom of choice

reference-request logic set-theory cardinals axiom-of-choice

Jun 18 '14 at 0:09 Community♦ 1

votes

answer

124

views

Are all rationally parametrized plane curves algebraic? How does one find their degree?

algebraic-geometry polynomials algebraic-curves plane-curves

Jan 31 '16 at 23:42 Conifold 7,105

votes

answer

356

views

Finding covering system of congruences with prescribed moduli

number-theory elementary-number-theory

May 26 '14 at 23:12 Conifold 7,105

votes

answers

views

Can existence of aleph one be proved without the power set axiom? [duplicate]

logic set-theory

May 24 '14 at 22:08 Conifold 7,105

votes

answer

568

views

Can hyperreal numbers be studied 'naively', like surreal numbers?

logic nonstandard-analysis

Jun 22 '18 at 8:36 Mikhail Katz 30.9k

votes

answer

688

views

What is the dual space in the strong operator topology?

functional-analysis operator-theory hilbert-spaces banach-spaces

Sep 2 '16 at 0:24 Conifold 7,105

votes

answer

187

views

Banach valued sequence spaces $\ell^p(X)$

functional-analysis reference-request banach-spaces lp-spaces

Dec 13 '15 at 8:01 Community♦ 1

votes

answers

views

Is there an intuitive reason why hippopede, the intersection curve of a sphere and a cylinder, is traced by composing two rotational motions?

geometry differential-geometry intuition recreational-mathematics kinematics

Jan 22 '15 at 21:52 Community♦ 1

votes

answer

246

views

Are order isomorphic real closed fields isomorphic?

field-theory model-theory ordered-fields

Aug 7 '14 at 21:59 Community♦ 1

vote

answer

109

views

Is there a formalisation of set theory where unions can be taken over some classes that are not a priori known to be sets?

logic set-theory

Jun 16 '14 at 22:09 Community♦ 1

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25 Questions

Are there non-standard counterexamples to the Fermat Last Theorem?

Are there spaces that 'look the same' at every point, but are not homogeneous?

What is the reflection across a parabola?

How many different products can be formed by multiplying $n$ numbers at most once?

Is there a clever way to find a smaller number that produces the Euclidean algorithm of given length?

Why do we know that Gödel sentences are true in the standard model of set theory, but do not know if the continuum hypothesis is?

Is Archimedes's method for computing volumes equivalent to Cavalieri's?

Are triangles the strongest shape?

How do inconsistent arithmetics get around Gödel incompleteness?

Why is the powerset axiom more acceptable than the axiom of choice?

Is there a theory of integration in elementary terms for definite integrals?

Functions with every point being a Lebesgue point

What is the multiplicative order of a product of two integers $\mod n$?

Circle inversion and the Pappus chain paradox

Can one prove existence of incommensurables without the Pythagorean theorem?

Partial order on cardinalities without the axiom of choice

Are all rationally parametrized plane curves algebraic? How does one find their degree?

Finding covering system of congruences with prescribed moduli

Can existence of aleph one be proved without the power set axiom? [duplicate]

Can hyperreal numbers be studied 'naively', like surreal numbers?

What is the dual space in the strong operator topology?

Banach valued sequence spaces $\ell^p(X)$

Is there an intuitive reason why hippopede, the intersection curve of a sphere and a cylinder, is traced by composing two rotational motions?

Are order isomorphic real closed fields isomorphic?

Is there a formalisation of set theory where unions can be taken over some classes that are not a priori known to be sets?