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Fedor Petrov's answer of my preceding question shows that my question reduces to the famous Hadamard conjecture about Hadamard matrices of order $4k$. So I decided to study this conjecture and I got …

The following conjecture is known as "Table problem on $\Bbb S^2$" Conjecture (Table problem on $\Bbb S^2$): Suppose $x_1, x_2,x_3,x_4 \in\Bbb S^2 \subseteq \Bbb R^3$ are the vertices of a squar …

According to Wikipedia (last edited on 31 March 2017, at 03:48.) the Hadamard conjecture is open still.

In On the number of inscribed squares of a simple closed curve in the plane it is shown that Theorem: For every positive integer $n$ there is a simple closed curve in the plane (which can be ta …

I have a question on the Total Coloring Conjecture in graph theory. This conjecture states that $$\chi^"(G)\leq \Delta +2,$$ where $\Delta$ is the maximum degree of the graph and $\chi^"(G)$ denotes …

Today I read about Gromov's definition of minimal volume for smooth manifolds. $$\min {\rm Vol}(M):=\inf_{|K_g|\leq1}\{{\rm Vol}(M,g)\}.$$ Gromov's conjecture states that for every closed simply con …