That’s the provocative question posed by American Physicist Michio Kaku in this fascinating 5 minute interview which takes in the ideas of Newton, Einstein and modern ideas on String Theory. It addresses the fundamental questions in maths ToK – is mathematics invented or discovered? What explains the “unreasonable effectiveness” of mathematics in the universe?

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.

Mathematician Eugene Wigner (quoted above) has called this seemingly fundamental relationship between mathematics and our world as nothing short of miraculous. Why should the motion of planets, the interaction of subatomic particles, the energy of a Black Hole, the growth of populations, the energy in a spring all be described by mathematical equations?

Since the invention of quantum mechanics in the 1920s, mathematicians have been searching for a grand unified theory – a so called Theory of Everything – which can describe the entire universe through a single mathematical equation. We have quantum mechanics which describes the sub-atomic world with remarkable accuracy, and general relativity which does equally well with describing the macroscopic world. However the 2 theories break down when objects are both massive and subatomic (such as the singularity in a Black Hole or the conditions at the birth of the Universe) – hence the need for a single unified theory that can bridge this gap.

Another Michio Kaku video talking through the problem with describing the singularity at the heart of a Black Hole

This blog was inspired by a video posted on Larry Ferlazzo’s ToK site – which has hundreds of links and ideas for ToK maths articles in the news – well worth reading!

All content on this site has been written by Andrew Chambers (MSc. Mathematics, IB Mathematics Examiner).

New website for International teachers

I’ve just launched a brand new maths site for international schools – over 2000 pdf pages of resources to support IB teachers. If you are an IB teacher this could save you 200+ hours of preparation time.