13 problems

Conjecture concerning YBC 7289. The scheme

Conjecture on Hardy's separation of Ramanujan's letter page. Hardy separated the page of Ramanujan's letter containing the Rogers--Ramanujan identities to show them to others, and…

The Snell–Cusa inequalities are convergence-improving inequalities: they produce at least twice the accuracy of Archimedes' original procedure for bounding $\pi$. Historical conjec…

Theodorus studied the irrational square roots represented by the successive sides of right triangles in his spiral, including the square roots of $3,5,\ldots,17$. Theodorus's histo…

Gödel–Hilbert programme conjecture. Gödel may have intended to argue that, for every system of the specified kind, the sentence $G$ is axiomatically undecidable but is decidable vi…

Let $p(x)=x^3+2x^2+10x-20$, let $x_5=1+22/60+7/60^2+42/60^3+33/60^4+4/60^5$, and let $k$ be an integer. Fibonacci's selected-checks conjecture. Fibonacci may have calculated only ……

Let $p(x)=x^3+2x^2+10x-20$, let $x_5=1+22/60+7/60^2+42/60^3+33/60^4+4/60^5$, and let $k$ be an integer. Fibonacci's computational-effort conjecture. Fibonacci may have avoided calc…

Peano's early conception of the infinite was gradually modified and definitively replaced by Cantor's theory of the transfinite in 1899. The 1895 correspondence conjecture. Althoug…

Conjecture. Grothendieck realized that his tame topology was not the right framework for understanding forms in this broad sense, and therefore saw the necessity of producing a new…

The theory of conic sections and the practical observations of sundials are the relevant mathematical objects. De la Hire's conjecture. The theory of conic sections originated in t…

The solid in Albrecht Dürer's Melencolia I has a face represented by a drawing from Dürer's sketchbook found by Weitzel; the drawing includes a rhombus whose angle is estimated as…

A Pythagorean triple is a triple of positive integers that can occur as the side lengths of a right triangle, equivalently satisfying $a^2+b^2=c^2$. Van der Waerden's conjecture. P…

In the early nineteenth century, consider the mapping by reciprocal radii, also called inversion, between geometric objects such as circles and lines or spheres and planes. Steiner…