### Algebra 1 *versus* Algebra 2

#### Posted by David Corfield

In Delphi, Colin McLarty performed some myth-busting for us. Many of you will have heard of Paul Gordan’s supposed reaction to a result of David Hilbert in the theory of invariants:

This is not Mathematics, it is Theology!

Often this is taken as one of the reactionary old guard standing in the way of the new algebra. However, Colin does a great job explaining how the true story is far more subtle.

Hilbert in 1888 said he found his proof “with the stimulating help of” this very professor Gordan.

Rather than recapping his argument, we may as wait until it appears. Here I want to know more about what happens next. In particular, I’d like to know whether Gian-Carlo Rota’s distinction between *Algebra 1* and *Algebra 2* holds water. He does this somewhere in English, Chapter III of Indiscrete Thoughts I believe.

Online, all I can find is in Italian. Here Rota picks out key figures in each:

Algebra 1: algebraic geometry and algebraic number theory, represented by Kronecker, Hilbert, Weil, …

Algebra 2: ‘Combinatoria Algebrica’ - algebraic combinatorics, represented by Boole, Capelli, Young, Gordan, Hall, Birkhoff, …

Does this chime with anyone?

Posted at July 28, 2007 5:45 PM UTC
## Re: Algebra 1 versus Algebra 2

I always that Gordan’s quote was a joke that was being interpreted as uncharitably as possible for propaganda purposes – propaganda for a cause that had long been won, but the quote and its interpretation lingered on.