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First of all, briefly introduce life.
Second, representative works
Thirdly, Descartes and philosophy.
Fourthly, Descartes and geometry.
Five, other mathematical achievements
First of all, briefly introduce life.
Rene descartes, 1596 was born in Dulan, France on March 3 1. Descartes is a great philosopher, physicist, mathematician, physiologist, the founder of analytic geometry, and the founder of modern philosophy and rationalism. When he was young, rene descartes's philosophy and mathematical thoughts had a far-reaching impact on history. People carved a sentence on his tombstone: "Descartes, the first person who fought for and guaranteed rational rights for mankind since the European Renaissance."
Descartes1March 3, 5961was born in a noble family in Toulon-Lyle, France. His father hoped Descartes would become a theologian in the future, so when Descartes was eight years old, he sent him to the Jesuit school in Lafleur for a classical education. In order to take care of his weak body, Descartes was allowed to go to bed early and get up early to study, which made him develop the habit of lifelong meditation and withdrawn personality.
First of all, briefly introduce life.
Descartes 16 12 went to the University of Poitiers to study the introduction of Descartes' law, and received his doctorate four years later. After Descartes finished his studies in 16 16, he deviated from his family's professional tradition and began to explore the road of life. He joined the army and wanted to take the opportunity to travel around Europe and broaden his horizons. During this period, he got to know the famous scholar Isaac Pickermann and became interested in mathematics. With Pickman's association, Descartes had a full understanding of his mathematical and scientific abilities. In order to acquire real knowledge, he began to seriously explore whether there was a universal method similar to mathematics.
Descartes 162 1 year retired, 1628 moved to the Netherlands and lived there for more than 20 years. During this period, Descartes conducted in-depth research in the fields of philosophy, mathematics, astronomy, physics, chemistry and physiology, and kept close contact with major European scholars through the mathematician Father Mei Sen. Almost all his major works were completed in the Netherlands. He wrote and published many important collections in Holland, including Methodology, Metaphysical Meditation and Philosophical Principles.
Second, masterpieces.
Thirdly, Descartes and philosophy.
1, "I think, therefore I am"
2. Evidence of the existence of God
3. Proof of the existence of external things
4. "Natural concept" and rational deduction
5. Mind-matter dualism
6. Psychosomatic sympathy theory
1, "I think, therefore I am"
Through universal doubt, we finally established an unquestionable thing, that is, "doubt" itself. Doubt is thought, and thought must have thinkers, which leads to the philosophical first principle of "I think, therefore I am".
"I" is a pure spiritual subject, and the only essential attribute of "I" is thinking.
"Strictly speaking, I am just a thinking thing, that is, I am just a brain, a reason or a reason."
2. Evidence of the existence of God
"I think, therefore I am" establishes self-consciousness as the first principle of philosophy, but how to get out of the narrow self and re-establish the external world that is denied in general suspicion? Only through God can this theoretical problem be solved.
3. Proof of the existence of external things
The third principle of Descartes' metaphysics is "material existence".
We determine "I think" by general suspicion. Although this method of doubt is effective, it also causes the greatest doubt about the existence of the material world.
However, when we prove the existence of God, the problem is solved. As mentioned above, God is the most perfect entity, so I am sure that God will never deceive me or lead me astray.
Since we know that God is complete, it is impossible to deceive us, so our greatest doubts are uprooted. In other words, I am now convinced of the existence of the material world, because I have determined the reality and integrity of God.
4. "Natural concept" and rational deduction
The concept of nature is the source and premise of knowledge that rationalists always adhere to, and the whole epistemological system of rationalism is based on the concept of nature and rational deduction.
5. Mind-matter dualism
On the one hand, God ensures the clarity of the spiritual world (conceptual system), on the other hand, it also ensures the authenticity and reliability of the material world, and he also ensures the mutual independence of the two worlds. (Dualism)
Fourthly, Descartes and geometry.
The core of Descartes' thought is to reduce geometric problems to algebraic problems, calculate and prove them by algebraic methods, and finally solve geometric problems. According to this idea, he founded what we now call analytic geometry.
Analytic geometry shows that geometric problems can not only be reduced to algebraic form, but also be discovered and proved by algebraic transformation. The appearance of analytic geometry has changed the trend of separation between algebra and geometry since ancient Greece, unified the "number" and "shape" which are opposite to each other, and combined geometric curves with algebraic equations. Descartes' creation laid the foundation for the creation of calculus, thus opening up a broad field of variable mathematics.
Five, other mathematical achievements
2. Euler-Descartes formula
Euler-Descartes formula: the content of this formula is: on any convex polyhedron, let V be the number of vertices, E be the number of edges and F be the number of faces, then V? E+F = 2. This formula was first proved by the French mathematician Descartes around 1635, but no one knows it. Post-Swiss mathematician Leonhard? Euler independently proved this formula in 1750. 1860, Descartes' work was discovered, and then this formula was called Euler-Descartes formula.
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