"All limits, especially national ones, are contrary to the nature of mathematics… Mathematics knows no races… For mathematics the whole cultural world is a single country" – David Hilbert, the foremost mathematician of the 20th century, speaking as the Nazis neared power in his native Germany.

Writing “proofs by induction” – video clip

“Proof by induction” means that we prove a claim referring to a whole number called n true for all values of n by two steps

• proving it’s true for n=1

• proving that if it is true for any particular value k of n, then it must be true for the next value, k+1.

The two steps together produce a “domino effect” guaranteeing the truth of the claim for 1, then for 2, then for 3, then for 4, and so on for ever.

This short video clip shows how to write out proofs by induction clearly and briefly.