Fermat’s Theorem – one of the most famous and long running puzzles in mathematics is a great way to introduce proof, the history of mathematics and also to show how apparent work on an entirely abstract concept can actually drive the development of techniques which have real world applicability. The (much abridged!) story is that Fermat, a 17th century mathematician scribbled that he had a proof that the statement at the top of page was correct – ie. that whilst the equation holds when n = 2 (for pythagorian triples), for n greater than 2 there is no solution with positive whole numbers. Mathematicians spent the next 358 years trying to find that same proof (and now believe that Fermat was actually mistaken), before Andrew Wiles finally proved it in 1995 using mathematics from elliptical curves.

A seemingly simple statement had occupied some of the best mathematical minds for over 3 centuries – everyone agreed that it probably was true – but to go from probably true, to 100% certainty – that knowledge gap required a monumental amount of effort. How many other things can we genuinely say we are 100% certain of outside mathematics?

See the Horizon documentary on Fermat’s Last Theorem with Simon Singh and Andrew Wiles:

IB Revision

If you’re already thinking about your coursework then it’s probably also time to start planning some revision, either for the end of Year 12 school exams or Year 13 final exams. There’s a really great website that I would strongly recommend students use – you choose your subject (HL/SL/Studies if your exam is in 2020 or Applications/Analysis if your exam is in 2021), and then have the following resources:

The Questionbank takes you to a breakdown of each main subject area (e.g. Algebra, Calculus etc) and each area then has a number of graded questions. What I like about this is that you are given a difficulty rating, as well as a mark scheme and also a worked video tutorial. Really useful!

The Practice Exams section takes you to ready made exams on each topic – again with worked solutions. This also has some harder exams for those students aiming for 6s and 7s and the Past IB Exams section takes you to full video worked solutions to every question on every past paper – and you can also get a prediction exam for the upcoming year.

I would really recommend everyone making use of this – there is a mixture of a lot of free content as well as premium content so have a look and see what you think.

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:

Pearson’s Product: Height and arm span

How to calculate standard deviation by hand

Binomial investigation: ESP powers

Paired t tests and 2 sample t tests: Reaction times