performance of it, in analysis, description of its objects, etc. Of course acoustics, which uses mathematics, is part of physics and music.

Some people think that mathematics is a simple game that alone and coldly interests the intellect. This would mean forgetting, according to Poincaré, the sensation of mathematical beauty, the harmony of numbers and forms, as well as the geometric elegance. This is certainly a sensation of esthetic pleasure that all true mathematicians have felt and of course that belongs to the field of the sensitive emotion. Beauty and mathematical elegance consist of all the elements, harmoniously settled in such a way that our mind could embrace them completely, effortlessly and at the same time maintain their details. This harmony, Poincaré continues, is, immediately, a satisfaction of our esthetic needs and an aid for the mind that sustains and guides. And, at the same time, when putting under our vision a complete orderly whole, makes us see a law or mathematical truth. This is the esthetic sensibility that plays a role of a delicate filter, which explains sufficiently why the one who lacks it will never be a true creator, concludes Poincaré.

The genius of Mozart consisted of choosing the best or more beautiful musical sentences in the whole enormous range of possibilities to create his music. Poincaré mentions that the creation of new mathematics doesn’t consist of making new combinations of well-known mathematical entities at random, but only in taking the useful combinations, which are a small proportion. If only the routine of applying rules was to be taken into account, the obtained combinations would be exaggeratedly numerous, useless or strange. The inventor’s or creator’s work consists of choosing the useful combinations. The rules or the procedures that lead to this election are extremely fine and delicate. It is almost impossible, says Poincaré, to establish these rules or procedures. It is a feeling thing rather than a formulation thereof. Under these conditions one can imagine a machine or computer applying them mechanically. It would happen the same thing as with Mozart’s game.

Poincaré writes at the beginning of the 20th century that a mathematical proof is not a simple juxtaposition of syllogisms, but syllogisms placed with certain order, and that the order in which they are placed is much more important than the syllogisms by themselves. He comments that he is not afraid of forgetting some of these since each one of them will take their place in the arrangement without the smallest effort. Also, he describes the creation process: First he carries out a conscious work about the problem, later he allows to mature those ideas in the subconscious, then the solution appears, maybe when least expected, and finally this is written.

Most mathematics is created by simple curiosity. But this simple curiosity is only possessed by the great mathematicians. One of the most difficult problems for a novice in mathematics (or not so novice) is that of finding a problem. It happens often that almost the whole emotion of the creation and penetration is concentrated on formulating the appropriate question. It could be said that this is more than half of the work and often the one that requires inspiration. This is a great difference to research in other areas of knowledge, and it is precisely for this reason that the mathematical research is extremely difficult. The answer can also be difficult, it can require a lot of genius, it can use well-known techniques and