Imagination and reason in Mathematics

Philosophical Remarks

When did we first fall in love with mathematics? For me, it was in class 6.

My father exposed me to a problem from Euclidean geometry. We were traveling in Kausani.

After days of frustration and failed attempts, I could put together the ‘reason’ that made ‘everything fit together perfectly’. The problem was solved and beauty of ‘pure reason’ revealed itself. It was breathtaking. I fell in love!

This has been the guiding principle in my teaching efforts. At the core of mathematics is ‘reason’. We definitely draw inspiration from real world observations. However, one does mathematics because he or she adores ‘reason’ itself and not the observations.

Years later, I was exposed to Kant’s ‘Critique of Pure Reason’ (thanks to my wife). I was tempted to switch to Philosophy. The promise to go beyond reason was alluring.

Methodology

The philosophical foundation of this eight - week course in beautiful mathematics is therefore well-grounded in these personal experiences. I hope to expose the students to the enchanting beauty of ‘reason’. This is planned in the following manner:

Hence we have the following recipe:

Observation —> Pattern Recognition —> Generalization

Here is a concrete example:

There are two other things, that I would love to try in this course

Cheenta - Filix Level 1 Math Olympiad Starter module.

Day 0 - Warm up with beautiful problems and drawings.

Day 1 - Platonic Solids (Cube, Tetrahedron, Octahedron, projections)

Day 2 - Platonic Solids (Icosahedron, Dodecahedron, projections)

Day 3 - Counting the simplexes

Day 4 - Invariance principle (Euler number)

Day 5 - Invariance principle (Golden ratio)

Day 6 - Algorithms (Fibonacci number generator)

Day 7 - Algorithms (Fibonacci number generator)

Day 8 - General problems from invariance principle

How the sessions are designed?

Key Points

Start here

Math Olympiad Starter Module