But what I held in my hand was a strict and precise solution of my equations!

I ran my eye through page after page of calculations that took my breath away with their originality and sheer beauty. Whoever had done it possessed an immense mathematical knowledge to be envied by the world's foremost mathematicians. Almost all the modern armoury of mathematics had been employed: the theory of linear and non-linear differential and integral equations, the theory of the functions of a complex alternating current, and those of groups, and of plurality, and even such apparently irrelevant systems as topology, number theory and mathematical logic.

I nearly cried out in delight when at the end of a synthesis of countless theorems, intermediate calculations, formulae and equations the final solution emerged-a mathematical formula taking up three whole lines.

And to add a touch of the exquisite, the unknown mathematician had given himself the trouble of resolving the long formula into a simpler one. He had found a brief and precise form containing only the more elementary algebraic and trigonometric expressions.

At the very end, on a small inset, there was a graphic representation of the solution.

I could wish for nothing better. An equation which I thought could not be solved in the final form had been solved.

When I had recovered a little from my initial surprise and admiration I went through the photo copies again. Now I noticed that he who had solved my problem had been writing in great hurry and very closely as though trying to save on every scrap of paper and every second of time. Altogether he had written twenty-eight pages and I pictured mentally what a titanic work that had been! Try and pen a letter of twenty-eight closely-written pages in one day or just copy, without following the meaning, twenty-eight pages out of a book, and you will surely find it a hellish job.

But what I had in front of me was not a letter to a friend or a chapter copied out of a book. It was the solution of a most intricate mathematical problem-done in twenty-four hours.