# Mathematics – a part of physics.

Physics – experimental science, a part of science. Mathematics – is the part of physics where experiments are cheap.

Jacobi identity (which forces the heights of a triangle intersect at one point) – the same experimental fact is that the Earth is round (that is, homeomorphic to a ball). But it can be discovered with less.

In the middle of the twentieth century was an attempt to divide physics and mathematics. The consequences were disastrous. Whole generations of mathematicians grew up without knowing half of their science and, of course, do not have any idea of any other science. They began teaching their ugly scholastic pseudomathematics first students, then to schoolchildren (forgetting Hardy’s warning that ugly mathematics has no permanent place under the sun).

Since neither to teach, nor to applications in any other science scholastic, cut off from physics, mathematics is not fitted, the result was a general hatred for mathematicians – and by the unfortunate students (some of which eventually became ministers), and on the part of users .

Ugly building built tortured inferiority complex-educated mathematicians, who failed to timely meet with physics, like slender axiomatic theory of odd numbers. It is clear that such a theory can create and make students admire the perfection and internal consistency of the resulting structure (in which, for example, the sum of an odd number of terms and the product of any number of factors). Even numbers from this sectarian point of view, you can either be declared a heresy, or in time to introduce the theory supplemented (after the needs of physics and the real world), some of the “ideal” objects. Learn more at .

Unfortunately, it was an ugly twisted construction prevailed in mathematics teaching mathematics for decades. Having originated in France, it is a perversion spread quickly on learning the basics of mathematics students at first, and then the students of all disciplines (first in France and later in other countries, including Russia).

French primary school pupil to the question “what is 2 + 3″ replied: “3 +2, since addition is commutative.” He did not know what is the amount, and did not even realize what he was asked!

Another French student (in my opinion, quite reasonable) defined mathematics as follows: “there is a square, but it is still to be proved.”

In my teaching experience in France, the idea of mathematics students (even of studying mathematics at École Normale Supérieure – these clearly intelligent but mutilated children I feel sorry most of all) – as pathetic as this student.

For example, these students have never seen a paraboloid and a question of the form of the surface given by the equation xy = z2, causing mathematicians studying at ENS, stupor. Drawing a curve given by parametric equations (like x = t3 – 3t, y = t4 – 2t2) – totally impossible problem for students (and perhaps even the majority of French professors of mathematics).

Beginning with the first textbook analysis L’Hospital (“analysis to understand the curves”) and up to about Goursat’s textbook, the ability to solve such problems was considered (along with knowledge of the multiplication tables), a necessary part of the craft of every mathematician.

Mentally challenged zealots of “abstract mathematics” thrown out of the teaching of all the geometry (in mathematics through which often communicates with physics and reality.) Textbooks Goursat, Hermite, Picard were recently dumped by the student library of the Universities Paris 6 and 7 (Jussieu) as obsolete and, therefore, harmful (only by my intervention to save them.)

Students ENS, courses on differential and algebraic geometry (read by respected mathematicians) were no strangers to the Riemann surface of the elliptic curve y2 = x3 + ax + b, nor even with the topological classification of surfaces (not to mention the elliptic integrals of the first kind and the group property elliptic curve, ie, the addition theorem of Euler-Abel) – They were only taught Hodge structures and Jacobi varieties!

How could this happen in France, which gave the world Lagrange and Laplace, Cauchy and Poincaré, Leray and Thom? It seems to me a reasonable explanation was given by IG Petrovsky, who taught me in 1966: real mathematicians do not gang up, but the weak need gangs to survive. They can unite on various grounds (whether sverhabstraktnost, anti-Semitism or “applied and industrial” problems), but the essence is always the solution of social problems – self-preservation in a more professional environment.

Let me remind you, by the way, a warning of Louis Pasteur – never have been and never will be any “applied science”, there are only applications of Sciences (very useful!).

At the time, I treated Petrovsky said with some doubt, but now I am more and more convinced of how right he was. A significant part of the sverhabstraktnoy reduced simply to industrialization shameless grabbing discoveries from discoverers and their epigones, systematically assigning obobschatelyam. Just as America is not named after Columbus, mathematical results are almost never called by the names of their discoverers.