We prove the maximum modulus principle from complex analysis! (more advanced material, approx second year mathematics undergraduate)

As I am learning about manifold theory, I thought I’d share a neat and short proof that R^n and R^m aren’t diffeomorphic. This means there is no continuous, bijective and infinitely differentiable function from R^n to R^m whose inverse is also bijective and…

What happens when Pythagoras meets calculus? Mathematics elegantly combines abstract and spatial…

Here’s why the Ramanujan summation is misunderstood. Its origin is a human desire for beauty, rather than a strictly accurate mathematical truth.

I fear that they are

Living in Hong Kong at the time of the 2014 Umbrella Movement, I was shocked by the unprecedented size and violence of the protests. While protests are common in Hong Kong, never before had they caused so much disruption nor provoked such a heavy response from the…