New posts in conjectures

Numbers that are clearly NOT a Square

elementary-number-theory diophantine-equations factorial square-numbers conjectures

Conjecture: $\int_0^1\frac{3x^3-2x}{(1+x)\sqrt{1-x}}K\big(\!\frac{2x}{1+x}\!\big)\,dx\stackrel ?=\frac\pi{5\sqrt2}$

calculus integration closed-form conjectures elliptic-functions

A conjectured continued fraction for $\phi^\phi$

number-theory continued-fractions conjectures golden-ratio

Examples of falsified (or currently open) longstanding conjectures leading to large bodies of incorrect results.

soft-question math-history big-list conjectures

A false conjecture by Goldbach

elementary-number-theory conjectures

How to show an infinite number of algebraic numbers $\alpha$ and $\beta$ for $_2F_1\left(\frac13,\frac13;\frac56;-\alpha\right)=\beta\,$?

calculus radicals modular-forms hypergeometric-function conjectures

Conjectured closed form for $\int_0^1x^{2\,q-1}\,K(x)^2dx$ where $K(x)$ is the complete elliptic integral of the 1ˢᵗ kind

calculus definite-integrals closed-form conjectures elliptic-integrals

Sum of digits of $a^b$ equals $ab$

number-theory decimal-expansion conjectures

Does this conjecture about prime numbers exist? If $n$ is a prime, then there is exist at least one prime between $n^2$ and $n^2+n$.

number-theory prime-numbers conjectures

How to prove $\int_0^\infty J_\nu(x)^3dx\stackrel?=\frac{\Gamma(1/6)\ \Gamma(1/6+\nu/2)}{2^{5/3}\ 3^{1/2}\ \pi^{3/2}\ \Gamma(5/6+\nu/2)}$?

special-functions gamma-function closed-form conjectures hypergeometric-function

A conjecture regarding prime numbers

number-theory prime-numbers prime-factorization conjectures prime-gaps

What does proving the Collatz Conjecture entail?

open-problem conjectures collatz-conjecture

Is $100$ the only square number of the form $a^b+b^a$?

number-theory modular-arithmetic square-numbers conjectures pythagorean-triples

What is the role of conjectures in modern mathematics?

soft-question terminology education conjectures

Symmetry of bicycle-lock numbers

combinatorics conjectures

The $5n+1$ Problem

combinatorics conjectures collatz-conjecture

Proving a known zero of the Riemann Zeta has real part exactly 1/2

complex-analysis special-functions riemann-zeta conjectures riemann-hypothesis

Prove that there exist infinitely many integers $(n^{2015}+1)\mid n!$

number-theory divisibility factorial conjectures

On Ramanujan's Question 359

trigonometry systems-of-equations radicals conjectures

Is any mathematican more famous for their conjecture(s) than their theorem(s)?

math-history conjectures mathematicians