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106

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Not especially famous, long-open problems which anyone can understand

Jun 24 at 9:59 mrtaurho 103

84

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answers

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ca.classical-analysis-and-odes galois-theory integration closed-form-expressions

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58

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7

answers

3k

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ca.classical-analysis-and-odes mathematical-philosophy closed-form-expressions conjectures soft-question

Jun 13 '13 at 18:25 Community♦ 1

42

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2

answers

2k

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nt.number-theory co.combinatorics sequences-and-series transcendental-number-theory oeis

Sep 20 '13 at 11:54 Community♦ 1

41

votes

2

answers

14k

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nt.number-theory ca.classical-analysis-and-odes irrational-numbers

Nov 13 '15 at 13:36 BigM 1,533

33

votes

1

answer

4k

views

How to calculate [10^10^10^10^10^-10^10]?

computational-number-theory

Oct 27 '11 at 1:09 GH from MO 76.1k

29

votes

5

answers

1k

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When are some products of gamma functions algebraic numbers?

ca.classical-analysis-and-odes nt.number-theory cv.complex-variables

Dec 26 '17 at 5:35 Raimundas Vidunas 41

28

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3

answers

6k

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nt.number-theory open-problems transcendental-number-theory transcendence

Mar 14 '19 at 20:54 litepresence 101

28

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0

answers

845

views

On certain representations of algebraic numbers in terms of trigonometric functions

nt.number-theory algorithms algebraic-number-theory computability-theory galois-theory

Jan 20 '15 at 16:14 Vladimir Reshetnikov 5,763

27

votes

1

answer

564

views

Decidability of equality of expressions built using 1,+,-,*,/,^

decidability algorithms peano-arithmetic

Jun 14 '14 at 18:57 Oksana Gimmel 1,569

26

votes

3

answers

1k

views

Largest possible volume of the convex hull of a curve of unit length

convex-geometry combinatorial-geometry calculus-of-variations

Aug 23 '14 at 13:03 Joseph O'Rourke 138k

24

votes

3

answers

825

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Does every convex polyhedron have a combinatorially isomorphic counterpart whose faces all have rational areas?

mg.metric-geometry discrete-geometry convex-polytopes polyhedra rational-points

Oct 9 '17 at 12:58 Tony Huynh 24.9k

24

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2

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596

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Order type of the smallest set containing the identity function and closed under exponentiation

order-theory ordinal-numbers exponential-polynomials set-theory

May 24 '13 at 9:51 Community♦ 1

23

votes

3

answers

1k

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Is it possible to construct an infinite subset of $\Bbb R$ that is not order isomorphic to any proper subset of itself?

set-theory order-theory linear-orders

May 26 '13 at 20:26 Community♦ 1

23

votes

1

answer

1k

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Busy Beaver modulo 2

computability-theory sequences-and-series oeis

Jul 23 '13 at 9:18 Kaveh 4,774

19

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5

answers

6k

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Rational points on a sphere in $\mathbb{R}^d$

nt.number-theory arithmetic-geometry rational-points

May 5 '17 at 13:00 Joseph O'Rourke 138k

19

votes

3

answers

829

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Is this combination of generalized polygamma and dilogarithm actually zero? $\Im\;\psi^{(-2)}(1+i)+\frac1{4\pi}\text{Li}_2(e^{-2\pi})-\log\sqrt{2\pi}+\frac{5\pi}{24}+\frac12$

special-functions polylogarithms gamma-function closed-form-expressions ca.classical-analysis-and-odes

Jan 13 '15 at 0:53 Gene S. Kopp 2,100

19

votes

1

answer

2k

views

On a Conjecture of Schinzel and Sierpinski

nt.number-theory analytic-number-theory

Jul 25 '11 at 20:26 Community♦ 1

18

votes

4

answers

4k

views

Is $x \, \tan(x)$ integrable in elementary functions?

ca.classical-analysis-and-odes real-analysis mathematics-education integration teaching

Jun 15 '14 at 0:14 Benjamin Dickman 6,675

17

votes

2

answers

311

views

Is it possible to reconstruct an order type from its initial segments?

order-theory linear-orders set-theory

May 6 '13 at 22:31 Community♦ 1

16

votes

2

answers

998

views

Integer lattice points on a hypersphere

ag.algebraic-geometry combinatorial-geometry mg.metric-geometry geometry

May 23 '13 at 0:26 Laila Podlesny 386

16

votes

2

answers

1k

views

Is it possible to generalize functions like $x^y, \ln x, \sin x, \arctan x$ to surreal numbers or surcomplex numbers?

ca.classical-analysis-and-odes lo.logic set-theory surreal-numbers surreal-analysis

May 30 '13 at 18:53 J. M. isn't a mathematician 3,455

16

votes

1

answer

1k

views

Number of distinct values taken by $\alpha$ ^ $\alpha$ ^ $\dots$ ^ $\alpha$ with parentheses inserted in all possible ways, $\alpha\in\mathbf{Ord}$

ordinal-numbers co.combinatorics oeis set-theory analytic-number-theory

Aug 1 '12 at 6:53 Community♦ 1

15

votes

2

answers

2k

views

Is there an algebraic number that cannot be expressed using only elementary functions?

nt.number-theory algebraic-number-theory galois-theory

Aug 19 '14 at 20:03 Community♦ 1

14

votes

0

answers

468

views

Does every convex polyhedron have a combinatorially isomorphic counterpart whose angles between edges are rational multiples of $\pi$?

mg.metric-geometry convex-polytopes convex-geometry combinatorial-geometry polyhedra

Oct 11 '17 at 22:38 Mohammad Ghomi 4,705

13

votes

1

answer

387

views

An elementary expression for $_3F_2(1,1,9/4;2,2;-1)$

ca.classical-analysis-and-odes hypergeometric-functions sequences-and-series closed-form-expressions conjectures

May 29 '13 at 20:47 Community♦ 1

13

votes

2

answers

581

views

How many subsets of $\mathbb{R}$ are order isomorphic to $\mathbb{Q}$?

lo.logic gn.general-topology set-theory order-theory linear-orders

May 26 '13 at 16:31 Community♦ 1

13

votes

0

answers

393

views

Integer-valued power towers

nt.number-theory transcendental-number-theory real-algebra

Aug 25 '13 at 12:25 Michael Hardy 8,978

12

votes

2

answers

342

views

A sequence based on Catalan–Mihăilescu problem

nt.number-theory diophantine-equations conjectures sequences-and-series

May 11 '13 at 15:22 Mike Bennett 2,236

12

votes

4

answers

365

views

Smallest containing simplex

mg.metric-geometry discrete-geometry convex-geometry

Jul 3 '18 at 1:20 user530104 11

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Not especially famous, long-open problems which anyone can understand

Is it possible to express $\int\sqrt{x+\sqrt{x+\sqrt{x+1}}}dx$ in elementary functions?

How closed-form conjectures are made?

Numbers that are generic w.r.t. exponentiation

Irrationality of $ \pi e, \pi^{\pi}$ and $e^{\pi^2}$

How to calculate [10^10^10^10^10^-10^10]?

When are some products of gamma functions algebraic numbers?

Work on independence of pi and e

On certain representations of algebraic numbers in terms of trigonometric functions

Decidability of equality of expressions built using 1,+,-,*,/,^

Largest possible volume of the convex hull of a curve of unit length

Does every convex polyhedron have a combinatorially isomorphic counterpart whose faces all have rational areas?

Order type of the smallest set containing the identity function and closed under exponentiation

Is it possible to construct an infinite subset of $\Bbb R$ that is not order isomorphic to any proper subset of itself?

Busy Beaver modulo 2

Rational points on a sphere in $\mathbb{R}^d$

Is this combination of generalized polygamma and dilogarithm actually zero? $\Im\;\psi^{(-2)}(1+i)+\frac1{4\pi}\text{Li}_2(e^{-2\pi})-\log\sqrt{2\pi}+\frac{5\pi}{24}+\frac12$

On a Conjecture of Schinzel and Sierpinski

Is $x \, \tan(x)$ integrable in elementary functions?

Is it possible to reconstruct an order type from its initial segments?

Integer lattice points on a hypersphere

Is it possible to generalize functions like $x^y, \ln x, \sin x, \arctan x$ to surreal numbers or surcomplex numbers?

Number of distinct values taken by $\alpha$ ^ $\alpha$ ^ $\dots$ ^ $\alpha$ with parentheses inserted in all possible ways, $\alpha\in\mathbf{Ord}$

Is there an algebraic number that cannot be expressed using only elementary functions?

Does every convex polyhedron have a combinatorially isomorphic counterpart whose angles between edges are rational multiples of $\pi$?

An elementary expression for $_3F_2(1,1,9/4;2,2;-1)$

How many subsets of $\mathbb{R}$ are order isomorphic to $\mathbb{Q}$?

Integer-valued power towers

A sequence based on Catalan–Mihăilescu problem

Smallest containing simplex