Decades ago, Gregory Chaitin reminds us, mathematicians were not forced by the rules of the academic establishment to keep producing papers, so they could write key books:

*Gregory Chaitin:* And people don’t write books. In the past, some wonderful mathematicians like G. H. Hardy (1877–1947, *pictured in 1927)* would write wonderful books like *A Mathematician’s Apology* (1940) or his *book on number theory* (1938).

Note:Hardy was the mathematician who received gifted young mathematician Srinivasa Ramanujan’s letter from India and “ in 1914, Hardy brought Ramanujan to Trinity College, Cambridge, to begin an extraordinary collaboration.” Ramanujan (1887–1920) was prompted to write to Hardy after reading one of his books.(MacTutor)Ramanujan was plagued by ill health and Hardy recounted at one point: “I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. ‘No,’ he replied, ‘it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.”

On broader issues, Hardy also said, “I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our ‘creations,’ are simply the notes of our observations.” –

A Mathematician’s Apology. So he seems akin to those who think that mathematics is discovered, not invented.

Here’s a short clip from a film made about Ramanujan’s letter and its consequences:

Chaitin himself succeeded with significant work (see Chaitin’s Unknowable Number) by working in time spared from IBM research rather than the academic rat race.