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Is God a Mathematician?

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

For a more in-depth look at this topic, read, “Is Maths Invented or Discovered?” 

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!

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IB Maths Exploration Guide

IB Maths Exploration Guide

A comprehensive 63 page pdf guide to help you get excellent marks on your maths investigation. Includes:

  1. Investigation essentials,
  2. Marking criteria guidance,
  3. 70 hand picked interesting topics
  4. Useful websites for use in the exploration,
  5. A student checklist for top marks
  6. Avoiding common student mistakes
  7. A selection of detailed exploration ideas
  8. Advice on using Geogebra, Desmos and Tracker.

Available to download here.

IB Revision Notes

IB Revision Notes

Full revision notes for both SL Analysis (60 pages) and HL Analysis (112 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 students!

Available to download here.

IB HL Paper 3 Practice Questions (120 page pdf)

IB HL Paper 3 Practice Questions 

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.

Available to download here.

IB Exploration Modelling and Statistics Guide


IB Exploration Modelling and Statistics Guide

A 60 page pdf guide full of advice to help with modelling and statistics explorations – focusing in on non-calculator methods in order to show good understanding. Includes:

  1. Pearson’s Product: Height and arm span
  2. How to calculate standard deviation by hand
  3. Binomial investigation: ESP powers
  4. Paired t tests and 2 sample t tests: Reaction times
  5. Chi Squared: Efficiency of vaccines
  6. Spearman’s rank: Taste preference of cola
  7. Linear regression and log linearization.
  8. Quadratic regression and cubic regression.
  9. Exponential and trigonometric regression.

Available to download here.

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