1Experimental methods in proofs

The presence of experimental methods in mathematics has been the leit-motiv of the so called, by Imre Lakatos in [12], renaissance of empiricism in the philosophy of mathematics. Among the efforts of reviving the philosophy of mathematics, as urged by Reuben Hersh in [9], in the Seventies the empiricist trend was the most vociferous and fashionable. It could rely on, and was enhanced by the novelties introduced by the computer, namely much larger searches and the formation of conjectures, either by numerical computations or by computer graphics. But as a thesis on the nature of mathematics it had to find confirmation and roots in the history of mathematics. Prominent among others were Hilary Putnam [14] and Imre Lakatos [11]; they didn’t rescue from oblivion old philosophies claiming the empirical nature or origin of mathematical objects; they proposed the term “quasi-empirical” to characterize non-deductive methods of discovery and validation in mathe-matics. The term was taken from Euler, via Polya