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). Please contact herefor information on webinar training or for business ideas.

Website Stats

8,167,428 views

Getting a 7 in IB Maths Exploration Coursework

Getting a 7 in IB Maths Exploration Coursework

I’ve teamed up with Udemy – the world’s leading provider of online courses to create a comprehensive online guide to the exploration. It includes 9 tutorial videos totaling 2 hours 30 minutes of essential information designed to ensure you get the best possible grade.

You can sign up for this course for 40% off the standard price by using the coupon: JULYDISCOUNT. (Expires 20/08/21).

Seventeen full investigation questions – each one designed to last around 1 hour, and totaling around 40 pages and 600 marks worth of content. There is also a fully typed up mark scheme. Together this is around 120 pages of content.

A 50 page pdf guide full of advice to help with modelling explorations – focusing in on non-calculator methods in order to show good understanding.

Modelling Guide includes:

Linear regression and log linearization, quadratic regression and cubic regression, exponential and trigonometric regression, comprehensive technology guide for using Desmos and Tracker.

A 55 page pdf guide full of advice to help with modelling explorations – focusing in on non-calculator methods in order to show good understanding.

Statistics Guide includes: Pearson’s Product investigation, Chi Squared investigation, Binomial distribution investigation, t-test investigation, sampling techniques, normal distribution investigation and how to effectively use Desmos to represent data.

Full revision notes for SL Analysis (60 pages), HL Analysis (112 pages) and SL Applications (53 pages). Beautifully written by an experienced IB Mathematics teacher, and of an exceptionally high quality. Fully updated for the new syllabus. A must for all Analysis and Applications students!