"Francois Viet
Pierre Fermat "
RENE DESCARTES
Published
Rene Descartes is better known as a great philosopher than a mathematician.
But it was he who was the pioneer of modern mathematics, and his merits in this field are so important
it is great that he is justly among the great mathematicians of our time.
We donot know much about the life of Descartes, also known by the Latinized name Cartesia (hence Cartesianism).
Descartes was born in France, in the small town of Lae, in the department of Touraine.
After graduating from the Jesuit college for the sons of aristocratic families, he followed the example of his brother and began to study law.
At the age of 22, he left France and served as a volunteer officer in the troops of various military leaders who participated in the Thirteen Years ' War.
During the war, he had to visit Austria, Hungary and the territory of present day Czechoslovakia.
Descartes in his philosophical teaching developed the idea of the omnipotence of the human mind, and therefore was persecuted by the Catholic Church.
Desiring to find a refuge for quiet work on philosophy and mathematics, in which he had been interested since childhood, Descartes settled in Holland in 1629, where he lived almost until the end of his life.
In one of his letters, Descartes described his stay in Holland as follows: "Everyone here, except me, is so busy with their own affairs and income that you can live all your life and no one will be interested in you…
In what other country can you enjoy more freedom, where you can sleep with more peace than here, where poison, betrayal, slander are much less common than in other countries…"
All the major works of Descartes on philosophy, mathematics, physics, cosmology and physiology were written by him in Holland.
Descartes 'mathematical works are collected in his book "Geometry" (1637).
In" Geometry " Descartes gave the basics of analytic geometry and algebra.
Descartes was the first to introduce the concept of a variable function into mathematics.
He turned
note that a curve on a plane is characterized by an equation that has the property that the coordinates of any point lying on this line satisfy this equation.
He divided the curves given by an algebraic equation into classes depending on the greatest degree of an unknown quantity in the equation.
Descartes introduced into mathematics the signs plus and minus to denote positive and negative quantities, the designation of the power sign oo to denote an infinitely large quantity.
For variables and unknown quantities, Descartes adopted the notation a for known and constant quantities —as is known, these notations are used in mathematics to this day.
Descartes initiated the study of algebraic equations.
In particular, he established that the number of real and imaginary roots of an algebraic equation is equal to the degree of the unknown.
This is the most important theorem of algebra, proved much later by Gauss.
It is also known that Descartes ' rule regarding the number of positive roots of an equation with real coefficients, according to which this number is equal to (or less than an even number) the number of changes in the signs in the sequence of coefficients, the equations
Later, on the basis of Descartes ' mathematical achievements, thanks to Leibniz and Newton, the principles of differential calculus were developed.
In physics, Descartes discovered the laws of reflection and deformation of waves and explained the reasons for the appearance of the rainbow.
Despite the fact that Descartes did not advance very far in the field of analytical geometry, his works had a decisive influence on the further development of mathematics.
For 150 years, mathematics has been developing in the ways prescribed by Descartes.
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