Discussion of axioms, proof theory, logic systems, and the philosophy of mathematics.

Structures, symmetry, equations, primes, and the hidden patterns of numbers.

Shapes, vectors, and the language of dimension—from Euclid to relativity.

Limits, change, and motion; the mathematics behind continuous systems.

Data, uncertainty, inference, and the mathematics of prediction.

Numerical methods, modelling, and algorithms in real-world problems.