When H. Poincaré first published in 1902 his book La Science et Vhypothèse, it became a bestseller. The first chapter of this book was devoted to the nature of the mathematical reasoning. Poincaré discussed an old philosophical controversy whether the mathematical knowledge could be reduced to long chains of tautological transformations of some basic ("synthetic") truths or it contained something more. He argued that the creative power of mathematics was due to a free choice of the initial… Expand