### 1.2.4.6 The Constructionist School

This is the name given to the school dedicated to the work of Kronecker and Brouwer. The definition of mathematics is the natural numbers. Everything else has to be constructed. The problem with this school was it took so long to prove anything although it did tighten up many woolly or fuzzy concepts.

Hilbert was particularly alarmed: What Weyl and Brouwer do is to seek to save mathematics by throwing overboard all that which is troublesome......If we would follow such a reform as they suggest, we would run the risk of losing a great part of our most valuable treasure!

What Hilbert did, we shall now see.