This week’s SUMS talk is by Cambridge student David Vasak. Abstract: One of the core insights of relativity is that the world is 4 dimensional. Why then do we persist in teaching most of modern physics using 3 dimensional operations, like divergence, gradient and curl? We will discuss a more geometric approach to calculus, generalising the intuitions most students of mathematics have picked up in low dimensional situations. The payoff will be a beautifully simple description of Maxwell’s equations in language even pure mathematicians can love. Along the way, time permitting, we will touch on subjects as varied as complex analysis and the deformations of coffee cups into donuts.