x Preface from center to center spreading his mathematical pollen. “Prove and Conjecture!” was his constant refrain. Were we, in those halcyon days, students of Uncle Paul. I think the word inadequate and inaccurate. Better to say that we were dis- ciples of Paul Erd˝ os. We (and the list is long indeed) had energy and talent. Paul, through his actions and his theorems and his conjectures and every fibre of his being, showed us the Temple of Mathematics. The Pages of The Book were there, we had only to open them. Does there exist for all suﬃciently large n a triangle free graph on n ver- tices which does not contain an independent set of size √ n ln n? We had no doubts—the answer was either yes or no. The answer was in The Book. Pure thought—our thought—would allow its reading. I would sit with Uncle Paul and discuss an open problem. Paul would have a blank pad of paper on his lap. “Suppose,” he would say in his strong Hungarian accent,1 “we set p = ln n n .” He would write the formula for p on the blank page and nothing else. Then his mind sped on, showing how this particular value of p led to the solution. How, I wondered, did Uncle Paul know which value of p to take? The final form of mathematics, the form that students see in textbooks, was described by Bertrand Russell: Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and aus- tere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry. 1 The documentary film “N is a Number” by George Csicsery [Csi93], available on the web, shows Uncle Paul in action.

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