The counting of various objects has existed among people since ancient times, but mathematics appeared only when a certain philosophy became its component part. We know that the philosophical basis of the mathematics of the Pythagorean school was the belief that the world was created by the gods precisely with the help of mathematics. It is clear that the Egyptian, Indian, Chinese and other mathematicians had the same ideas much earlier than Pythagoras. The difference between ancient Greek mathematics and all others was that the Greek mathematicians had doubts about the divinity of this area of knowledge. For example, the Pythagorean postulates of geometry about the concepts of points, lines and other figures, in the 5th century BC, were criticized by Zeno of Elea, who stated that the real path of movement cannot consist of points that have no dimensions. There were other conflicts as well. Disciples of Pythagoras somehow discovered that his postulate that «everything is a number» is not always true, the diagonal of a square turned out to be incommensurable with its side, neither in natural numbers nor in fractions. Only in the IV century BC, Eudoxus of Cnidus added the concept of geometric quantities to numbers: length, area, volume. That is, the practice periodically came into conflict with the inventions of theorists.
Euclid in the III century BC in the «Elements» already referred both natural numbers and geometric quantities to mathematical objects. His «Beginnings» is arithmetic and geometry.
Mysticism flourished in Europe in the Middle Ages. The mathematical formulas found by the mathematicians of the Ancient world, of course, were used in practice, and philosophers shared the ancient ideas that mathematics, the truths of which are absolute, lay at the basis of the laws of nature established from above.
European theorists could only argue how many devils can fit on tip of a needle. Film The development of mathematical ideas went on in the states of the East. In the 9th century treatise by Muhammad ibn Musa al-Khwarizmi, which gave the title to the third section of mathematics, algebra, mathematicians — arithmetic in the positional decimal number system and the solution of a quadratic equation. These results were obtained by Brahmagupta and his predecessors no later than the 7th century.
Development of mathematics in Europe, after reading it theorists with ideas from the East, followed the path leading away from everything natural. This is very well shown by Novalis (Friedrich von Hardenberg, 1772-1801). In his «Fragments» it is said: «True mathematics is the real element of the magician. A true mathematician is an enthusiast per se. Without enthusiasm there is no mathematics. The life of gods is mathematics. Pure mathematics is a religion. In the East, true mathematics is at home. In Europe, it has degenerated. into pure technology. «
It must be said that even in arithmetic there are actions that are completely permissible with numbers, but meaningless when these actions are applied to real objects. For example, 4 divided by 0.5 … When operating only with numbers, it will be 8, but if you divide 4 apples by half a person, it will be absurd, because you cannot divide into half a person, and for a whole person there is nowhere to get an additional four apples. You cannot, for example, multiply apples by apples or extract roots from apples. But an example of the most dangerous unnatural formula is the gravity formula Newton , where mass is multiplied by mass, and distance by distance.
The result of applying Newton’s formula is incorrect determination of masses and distances , searches for «dark matter» and other nonsense. In algebra, there is an incredible amount of such absurd application of formulas. Juggling with formulas became entertainment for some people with a mathematical orientation of brain activity, but it became less and less possible to apply their formulas to reality. The belief in the primordial nature of mathematics has not disappeared either, although instead of a primitive creator god sitting on a cloud, philosophers from mathematics invented a kind of «world mind» that created mathematics and, on its basis, an «expanding universe.» relativism and quantum mechanics , which supplanted an objective attitude to reality from physics, originally the science of nature, which has become just a testing ground for mathematicians.
There is a healthy part in mathematics, it is arithmetic with an adjacent part of algebra and geometry. They can and should be used to work with real objects, but in practice, restrictions are necessary when substituting named numbers into formulas. By the way, the maxim of Emmy Noether, an authoritative mathematician, that mathematicians should do mathematics, and not direct