In volume 17 numer 2 of this Bulletin we published the catalan translation of A Socratic dialogue on mathematics, the small masterpiece of Alfred Rényi (Budapest, 1921--1970), initially published in Hungarian in 1962. The success of this dialogue encouraged him to write a second dialogue (to which a third one would follow later on) which we are now offering in Catalan to our readers.
The central character of this dialogue is Archimedes, the greatest mathematician of antiquity and one among the greatest of all times, who was born and died in the island of Sicily in the 3rd century BC. His conterpart is King Hieron II of Siracusa (the capital of Sicily), and the dialogue is supposed to take place during the roman army's siege to Siracusa in 212 BC, one of the episodes of the 2nd Punic war. Here Rényi allows himself a historical licence, because it is known that Hieron died 3 years before the roman's siege (Rényi is aware of this fact, as he himself declares in the Postcript to his book Dialogues on mathematics). It is believed that Archimedes died during the roman's assault to Siracusa that ended the siege.
In this dialogue Rényi does not claim to be reconstructing Archimedes' personality, as very little is known about him and his real life. He rather takes the historical circumstances, with his characteristic skill, and puts in Archimedes' words his personal view of the debate "pure mathematics vs. applied mathematics" (a very strong debate in Hungary at the time when he wrote the dialogue, but probably much weaker today). Rényi clearly denies the existence of an applied mathematics as a different kind of mathematics, and believes that the difference lies in the scholar's attitude. He also puts forward other issues concerning the money given for research towards to military applications (the easier it is to obtain it, the debate about the ownership of the results), issues which are still under discussion at the beginning of the XXIst century.
Rényi puts forward a solution to a much debated question: Why is there no documental proof of Archimedes' practically-oriented work? Did he actually produce any such work? As a matter of fact, no serious treatise of the history of mathematics does attribute to him the kind of artifacts that tradition has associated with him, and which are mentioned in the dialogue. It is true that all history texts assert that Archimedes did help in the defence of Siracusa against the Roman assault, and that he died in it. Rényi's explication is that Archimedes did not want any of his destructive machines to be preserved simply because he felt guilty of the death they produced. But this does not explain why there is no proof either of other machines that helped in ordinary life, of which some are also mentioned in the dialogue. One should point out that many of Archimedes' theoretical works touch also the theoretical basis of applied problems.
Instead of looking for historical accuracy, we should admire a piece of literary art, where the author construes two lively personalities and where, through the dialogue, he conveys to us his own opinions on the applications of mathematics. As in the Socratic dialogue, Rényi insists in giving mathematicians a certain responsibility in the social affairs and in the solution of collective problems, even the worst ones such as war and death.