The Dimension of a Point that isn’t there

A slice of Swiss cheese has one-dimensional holes; a block of Swiss cheese has two-dimensional holes. What is the dimension of a point? From classical geometry we have the definition ``A point is that which has no parts'' --- also sprach Euclid. A point has dimension zero, a line has dimension one, a plane has … Continue reading The Dimension of a Point that isn’t there →

Making the Best of Waiting in Line

Queueing is a bore and waiting to be served is one of life's unavoidable irritants. Whether we are hanging onto a phone, waiting for response from a web server or seeking a medical procedure, we have little choice but to join the queue and wait. It may surprise readers that there is a well-developed mathematical … Continue reading Making the Best of Waiting in Line →

Differential Forms and Stokes’ Theorem

The theory of exterior calculus of differential forms was developed by the influential French mathematician Élie Cartan, who did fundamental work in the theory of differential geometry. Cartan is regarded as one of the great mathematicians of the twentieth century. The exterior calculus generalizes multivariate calculus, and allows us to integrate functions over differentiable manifolds … Continue reading Differential Forms and Stokes’ Theorem →

Goldbach’s Conjecture: if it’s Unprovable, it must be True

The starting point for rigorous reasoning in maths is a system of axioms. An axiom is a statement that is assumed, without demonstration, to be true. The Greek mathematician Thales is credited with introducing the axiomatic method, in which each statement is deduced either from axioms or from previously proven statements, using the laws of … Continue reading Goldbach’s Conjecture: if it’s Unprovable, it must be True →