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 Oct 17 accepted Lower bound on the rank of the elliptic curve $y^{2} = x^{3} + A x^{2} + B x$ Oct 16 awarded Popular Question Oct 16 revised Proofs that every mathematician should know? added 1 characters in body Oct 15 revised What is the connectivity between Boltzmann's entropy expression and Shannon's entropy expression? changed "connectivity" to "connection" Sep 6 revised Proving $|e^{iθ}|=1$ edited title Aug 28 comment Can 3 planes fail to intersect even if none of the planes are parallel? The letter 'A' seems to be a good hint. Aug 22 comment Upper bound for the quality of an $abc$-triple Actually, I asked it on MO when I got no answers here. Aug 21 revised Lower bound on the rank of the elliptic curve $y^{2} = x^{3} + A x^{2} + B x$ added 24 characters in body Aug 20 asked Lower bound on the rank of the elliptic curve $y^{2} = x^{3} + A x^{2} + B x$ Aug 14 comment Could you explain why $\frac{d}{dx} e^x = e^x$ “intuitively”? "The more bacteria exist in a colony, the faster the colony will grow" is false. Competition for resources adds a negating term which depends on the concentration of bacteria: $dB/dt = B - f(B)$. This makes all of the difference. Jul 24 comment Is this proof about $\pi$ is irrational correct? This is Niven's proof. The integral (1) should be from $0$ to $\pi$. Also, the word is "contradicts" not "contracted". Jul 17 comment How to convince a math teacher of this simple and obvious fact? A proof by contradiction aims to develop an absurdity. Jul 16 awarded Good Answer Jul 16 awarded Mortarboard Jul 16 awarded Nice Answer Jul 16 answered How to convince a math teacher of this simple and obvious fact? Jul 6 awarded Good Answer Jun 29 comment Bott periodicity and homotopy groups of spheres It depends on the values of $k$ and $n$. It is trivial to compute the groups for $0 \leq k \leq n$, but rather non-trivial for $k > n$. Jun 27 revised Proof for Sum of Sigma Function added 2 characters in body Jun 24 awarded Nice Question