I have a predilection for unusual relationships between theorems.

• On the Constant Rank Theorem and the Frobenius Theorem for differential equations.

• Minimax Theorems V.S. Fixed Point Theorems.

• Equivalence between Brouwer fixed-point theorem and Borsuk-Ulam theorem. Is there a simple proof of equivalence between them?

I like to discover elegant proofs by unconventional ways

• A simple way to obtain $\prod_{p\in\mathbb{P}}\frac{1}{1-p^{-s}}=\sum_{n=1}^{\infty}\frac{1}{n^s}$.

• On a topological proof of the infinitude of prime numbers.

• Some questions about Hilbert matrix

Naive questions are a great opportunity to share knowledge.

• Why the $\nabla f(x)$ in the direction orthogonal to $f(x)$?

• How does a non-mathematician go about publishing a proof in a way that ensures it to be up to the mathematical community's standards?

The accuracy is inherent in mathematics.

• How to prove that a compact set in a Hausdorff topological space is closed?

• how to prove $(-1)\cdot(-1)=1$ based only on the field axioms?

"An expert is a man who has made all the mistakes, which can be made, in a very narrow field."

                                    Niels Bohr

"A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one."

                                    Paul Halmos

"Information: the negative reciprocal value of probability."

                                   Claude Shannon