"I especially liked mathematics with the accuracy and evidence of my reasoning"
DESCARTES Rene (Descartes)
BIOGRAPHY of Descartes Rene (1596-1650) Rene Descartes was born on the last day of March 1596 in the small town of Lae in the province of Touraine, in a not very noble, but wealthy noble family.
He was born a frail, weak child.
A few days later, the mother died of consumption.
It seemed that the boy's fate was sealed.
Fortunately, the attached nurse came out to Rene, saved his life and improved his health.
At the age of eight, Rene was placed under the full care of one of the best Jesuit colleges, which had just been founded under the special patronage of King Henry IV.
Taking care of strengthening its influence in the state, the Jesuit order paid great attention to secular schools, the correct preparation of curricula and programs, the reasonable division of students into classes depending on their academic success.
In schools, the Jesuits sought to create favorable conditions for the development of students ' abilities, instilling at the same time obedience, love and respect for the order.
Subsequently, Descartes gratefully recalled the concerns of the teachers of the college.
Paradoxically, it is the Jesuits, Descartes ' teachers, who will become his sworn enemies: they will persecute his philosophical teaching, will not allow him to work not only in his homeland, but also in the neighboring Protestant Holland.
The main subjects in the college were considered Latin, theology and philosophy.
Since childhood, Descartes loved to solve problems and devoted all his free time to studying mathematics.
Fortunately, Descartes was taught this subject at school.
Descartes himself considered mathematics classes at the college to be "trinkets" and therefore independently engaged in a deeper study of it.
"I have abandoned the special study of arithmetic and geometry," Descartes wrote, " in order to devote myself to research in the field of universal mathematics."
But the sciences of that time could not satisfy the inquisitive mind of Descartes and led him to skepticism.
Only in mathematics did he find some satisfaction, but even here he was surprised "how nothing sublime was built on such a basis of the hardness of granite."
Disappointed in the wisdom of the school, Descartes decided "not to look for another science, except for the one that he could find, in himself or in the great book of the universe."
And so, due to the noble traditions, he prepares himself for a military career, devoting a lot of time to strengthening poor health through physical exercises and learning to own weapons.
sometimes he is seen among the gay cavaliers of Paris leading an idle lifestyle; then, after meeting his schoolmate, the mathematician and philosopher monk Mersenne, he suddenly, secretly from relatives and drinking companions, renting a quiet house in the Saint Germain suburb of Paris, is engaged in science; then he is dissatisfied with the existing political situation in France, puts on the uniform of a Dutch volunteer and begins to wander around Europe, participating in the bloody vicissitudes of the Thirty Years ' War that has just begun.
Military fate throws him to Bavaria, to Bohemia, near Prague.
Idle parking in winter quarters in Bavaria became for Descartes a time of intense work of thought, which led to the discovery of the main method, the first fruit of which was analytical geometry.
Finally, tired of the hustle and bustle of military life, twenty five year old Descartes leaves the army.
But he is in no hurry to return to his homeland, which is agitated by the latest outbreaks of religious strife.
As a traveling nobleman, he appears at the palaces of The Hague and Brussels, goes to Italy.
It was only in 1625 that Descartes returned to Paris for a short time.
Here he again converges with Mersenne, the circle of his learned friends expands, and at the same time the reputation of the philosopher grows.
Friends insist on the publication of Descartes ' views, expecting from them a revolution in the philosophical system.
But the Jesuits oppose Descartes ' philosophy, threaten him with violence and force him to leave France.
Descartes is forced to seek solitude in Holland, where, according to him, in the crowd of the active Dutch people, "more caring about their own affairs and less curious about others," he could work quietly.
Descartes lived in Holland for a total of about twenty years, moving from place to place, opening up only to especially close friends.
In Holland, Descartes devoted himself entirely to scientific studies in philosophy, mathematics, physics, astronomy, physiology, published his famous works: "Rules for the guidance of the mind", "A Treatise on light", "Metaphysical reflections on the first Philosophy", "The Beginnings of Philosophy", "Description of the human body" and others.
The most famous work was Descartes '"Reasoning about the Method", which was published in 1637.
But four years before its publication, Descartes wrote to his friend Mersenne that his work was finished and he postponed it for a while to make some corrections later and then publish it.
Fearing the persecution of the Inquisition, Descartes excludes from his work, where possible, everything that can cause dissatisfaction with the church.
The very name of his work has also changed.
Now it sounds like this: "A discussion about a method to guide your mind well and find the truth in the sciences.
In addition, Dioptrics, Meteors and Geometry, which are an application of this method."
The book was written not in Latin,but in French.
The author sought to ensure that a wider audience could get acquainted with his work, who, as Descartes writes, "will judge my opinions better than those who believe only ancient books."
Fierce disputes arise around the philosophical teachings of Descartes.
The disputants do not skimp on colorful epithets.
For some, he is the Archimedes of our century, the Atlas of the universe, the mighty Hercules, for others Cain, a tramp, an atheist, the disputes themselves did not touch the scientist much.
The only thing he feared was the disapproval of the powerful Jesuit order.
The terrible crimes of the Inquisition are still fresh in my memory.
At the turn of the seventeenth and eighteenth centuries, Giordano Bruno was burned alive in the Flora Square.
Twenty years later, in Toulouse, the philosopher Lucilio Vanini, before burning him at the stake, had his tongue torn out by ticks.
The great Galileo was condemned by the" holy " Inquisition.
Descartes knew all this and painfully experienced it.
And, of course, he was afraid of the persecution of the Jesuits.
Even in Holland, where the Jesuit Order had not yet penetrated, opponents, mainly Protestant theologians, began to speak out against Descartes, accusing him of materialism and atheism.
Although Descartes was not an atheist, moreover, in his "Arguments" he even proved the existence of God and the immortality of the human soul, nevertheless he recognized matter and motion.
This is exactly what the theologians opposed, because they saw the danger of Cartesian philosophy for Christian teaching.
Descartes became a target for the furious attacks of the churchmen.
And later the works of Descartes were awarded to be burned as heretical.
All these troubled years Descartes continued to live in Holland, occasionally visiting France, but each time not staying in it for a long time.
The last time he was in his homeland was in 1648.
And two years later he died.
Although, perhaps, he could have lived even longer if a flighty representative of the august family had not interfered in his fate.
Just at that time, Sweden was ruled by the twenty year old Queen Christina.
The young ruler had extraordinary abilities.
She spoke six languages.
She was an excellent shot, could tirelessly chase the beast.
She was used to cold and heat.
I slept for five hours a day and got up very early.
In addition, this new Amazon was interested in philosophy.
She was particularly interested in Descartes ' philosophy.
And the energetic queen decided to invite the scientist to Sweden.
Without waiting for Descartes ' consent, she sent an admiral's ship for him, which brought Descartes to Stockholm in 1649.
Descartes hoped to study science calmly after his arrival in Sweden, without fear of persecution of the churchmen.
But the arrival in this northern country was fatal for the scientist.
Accepted with honor, Descartes had to study philosophy with the queen every day.
Despite the winter cold, classes began every time at five o'clock in the morning.
This was difficult for Descartes, who was used to a warm climate.
Besides, he was so fond of lying in bed almost until noon.
At the same time, Descartes was obliged to work hard on the statute of the Academy of Sciences organized by the Queen.
One day, on his way to the palace, Descartes caught a cold, pneumonia began.
Bloodletting, which was used at that time, did not help, and on February 11, 1650, Descartes died.
"It's time to go, my soul," were his last words.
Descartes ' philosophical studies are closely connected with his mathematical and physical works.
Descartes showed for the first time how mathematics can be applied to the visual representation and mathematical analysis of the most diverse phenomena of nature and society.
He proposed to depict the connections between natural phenomena with curved lines, and to write down the latter with algebraic equations.
Having based his philosophy on the concept of moving matter, Descartes introduced motion into mathematics.
If before Descartes mathematics had a metaphysical character, operating with constant quantities, then with Descartes ' works, dialectics entered mathematics, and at the same time into all natural science.
In Descartes ' works on mathematics, variables appear for the first time and it is indicated how strict laws of geometry can be translated into algebraic language and used in solving various problems that at first glance are far from mathematics.
Thus, Descartes is the discoverer of analytical geometry, which is based on the method of coordinates invented by him.
This method, as is known, was used before Descartes.
It received significant development from Fermat.
Nevertheless, it became much more important for Descartes, since with the help of this method, Descartes was able to indicate new directions in the further development of mathematics.
To the mathematical genius of the thinker we owe the introduction into use of the now familiar designations with the help of Latin letters of constant and variable magnitudes, as well as the designation of degrees.
Thanks to Descartes, algebra, both in its basic methods and in symbolism, has assumed the character that is inherent in it at the present time.
Descartes attached special importance to mathematics.
He proceeded from the conviction that mathematics should be a model for any other science.
In his opinion, only that science can be considered true, which follows mathematics in its construction, since all the conclusions of mathematics are logically necessary, giving full reliability.
ACHIEVEMENTS IN MATHEMATICS Descartes ' mathematical studies are closely related to his works on philosophy and physics.
In" Geometry " (1637), Descartes first introduced the concept of a variable and a function.
A variable appeared in Descartes as a segment of variable length and constant direction (the current coordinate of a point describing a curve with its movements) and as a continuous numerical variable running through the set of numbers that make up the coordinate segment.
The dual image of the variable caused the interpenetration of geometry and algebra, which Descartes sought.
Descartes algebra in contrast to the algebra of F. Vieta, always has one main element - a linear segment, operations on which lead again to a certain segment.
These segments are equivalent in properties to real numbers.
In Descartes, the real number acted as the ratio of the length of the segment to the unit, although only I. Newton formulated such a definition of the number.
Negative numbers received a real interpretation from Descartes in the form of directed coordinates.
Descartes introduced the now generally accepted signs for variables and desired quantities, for letter coefficients, as well as degrees.
Descartes ' records of algebra formulas almost do not differ from modern ones.
Of great importance for the formulations of general algebra theorems was the recording of equations in which one of the parts is zero.
Descartes initiated scientific studies of the properties of equations; formulated the position that the number of real and complex roots of an equation is equal to its degree (this is the main theorem of algebra, which was strictly proved by K. Gauss at the end of the XVIII century, and expressed by A. Girard).
Descartes formulated the rules of signs for determining the number of positive and negative roots of an equation; he raised the question of the boundaries of the real roots and the reducibility of the polynomial.
Descartes proved that the equation of the 3rd degree is solvable in square radicals and is solved using a compass and a ruler when the left part of it is reducible.
In analytical geometry, which was developed simultaneously with Descartes by P. Fermat, the main achievement of Descartes was the method of rectilinear coordinates created by him.
Descartes included "geometric" lines in the field of study, which can be described by one or more continuous movements of articulated mechanisms.
He found that the degree of the curve equation does not depend on the choice of a rectangular coordinate system.
In Geometry, Descartes outlined an algebraic method for constructing normals and tangents to plane curves and applied it to curves of the 4th order, Descartes ' ovals.
Having laid the foundations of analytical geometry, Descartes himself did not advance far in this field.
His coordinate system was imperfect: negative abscissas were not considered in it.
The questions of the analytical geometry of three dimensional space remained almost untouched.
Nevertheless, Descartes '"Geometry" had a huge impact on the development of mathematics, and for almost 150 years algebra and analytical geometry developed mainly in the directions indicated by Descartes.
It is known from Descartes ' correspondence that he made other discoveries, in particular in the field of infinitesimal calculus: calculating the area of a cycloid using the indivisible method; drawing a tangent to a cycloid and its varieties based on the idea of an instantaneous center of rotation; determining the properties of a logarithmic spiral; an approximate solution to the problem of determining a curve by this tangent property.
It can be seen from Descartes ' manuscripts that he knew the relation between the numbers of faces, vertices and edges of polyhedra discovered later by L. Euler - an important result in the topology of surfaces.
The following coordinates, product, parabola, leaf, oval are named after Descartes.
Descartes clarified Galileo's law of inertia.
A body that is not affected by any forces will move evenly and rectilinearly, and not in a circle.
Descartes has already seen that the movement of the planet is an accelerated movement.
Following Kepler, Descartes believed that the planets behave as if there is an attraction of the sun.
In order to explain attraction, he constructed a mechanism of the Universe in which all bodies are set in motion by shocks.
Descartes ' world is completely filled with the thinnest invisible matter.
Deprived of moving in a straight line, the transparent flows of this medium formed systems of large and small vortices in space.
Vortices, picking up larger, visible particles of ordinary matter, form the cycles of celestial bodies.
They mold them, rotate them and carry them in orbits.
The Earth is also located inside the small vortex.
The circulation tends to pull the transparent vortex outwards.
At the same time, the particles of the vortex drive the visible bodies to the Earth.
According to Descartes, this is gravity.
Descartes ' system was the first attempt to mechanically describe the origin of a planetary system.
REFERENCES 1.
Bell E. T. The Creators of Mathematics.
- Moscow: Nauka, 1979.
2. Smyshlyaev V. K.
About mathematics and mathematicians.
- Yoshkar Ola: Nauka, 1977.
3. Matviyevskaya G. P. Rene Descartes , Moscow: Prosveshchenie, 1987.
