# A Mathematical Romance

(With apologies to pure mathematicians — to my cluttered head, any subject that follows logical arguments, beginning from well specified axioms, and even incorporating self-consistent approximations, is mathematics.)

The Boltzmann equation is an integro-differential equation that governs the probability density function in phase space of a collection of particles interacting with each other through instantaneous collisions. It was proposed by Boltzmann in his attempts to arrive at a continuum theory for gases beginning from a molecular standpoint.

Solution of the Boltzmann equation was an outstanding problem at the turn of the 20th century. Yup, 100 years ago. But stay with me. It was solved independently by Sydney Chapman and David Enskog, who employed different methods. Chapman was already an established mathematical physicist, known to have been working on this problem, so his achievement was not surprising. Enskog, on the other hand, solved it as part of his Ph. D. thesis. In Sweden.

Swedish scientists were not impressed by Enskog’s work, which they perceived was in an esoteric area of little practical relevance. He received a mediocre grade for his doctoral thesis. This made it difficult for Enskog to pursue an academic career in Sweden. He retreated to teaching in an high school. About ten years later, by which time his contribution was being recognized widely, Enskog tried again and applied to two different Universities. The Stockholm University rejected his application, while KTH gave him the offer only because Chapman (a Britisher), on a lucky visit to Sweden, interceded with the Swedes. However, years of mundane work had taken their toll, and after getting the position, Enskog occupied himself mostly with teaching and did not produce any notable research.

Today the Boltzmann equation is most routinely solved through the Chapman-Enskog method.

Enskog died in 1947 two days after he was elected to the Swedish Academy of Sciences.

But this is a tragedy. Not a romance. It is Wikipedia’s story. It is also the story of many thinkers who were ahead of their time or at the wrong place or both.

Sydney Chapman published his* magnum opus “The Mathematical Theory of non-Uniform Gases” in 1939. He chose to expose the subject employing Enskog’s methods rather than his own, because, as he said in the Preface “… the work of Enskog showed more regard for mathematical form and elegance”.

Chapman dedicated the book — his magnum opus — to David Enskog.

That was generosity, hallmark of great minds. Uncommon, unfortunately, amongst scientists. Uncommon enough that much of the World still knows — and makes movies — about G. H. Hardy recognizing and nurturing Ramanujam’s genius.

What is not that well known is that Sydney Chapman was Hardy’s Ph. D. student.

That is the romance.