justanothermathmo

The Maximum Modulus Principle

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

Statement

No Diffeomorphism Between R^n and R^m

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…

Plato’s Realm Of Forms Tells Us Nothing About Mathematics

Spatial Reasoning and Mathematics

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

The Ramanujan Summation Delusion — Or Why 1 + 2 + 3 + ⋯ + ∞ ≠ -1/12

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

What is Modern Mathematics? (For The Non-Mathematician)

Are Hong Kong’s Liberties doomed?

I fear that they are

Probability: A Philosophical Perspective, Part I

Should Hong Kong be Independent?

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…