(Top to bottom) DeZargues, Descartes, Fermat, Pascal, Newton, Leibniz, 17th century genius
Cai Tianxin, a professor at the School of Mathematics of Zhejiang University and a qiushi distinguished scholar (a guest of the 100th lecture hall), wrote a new book, "Mathematics and Art", which attempts to reveal the similarities and essential attributes between mathematics and art, and he himself has made great achievements in the field of mathematics and poetry. With permission, the third chapter, "The Century of Genius", is compiled for the benefit of the reader.
At the moment of cultivating compound talents, in today's emphasis on basic discipline education, the ideological and academic journey of this group of star-studded seventeenth-century geniuses will surely bring us endless inspiration.
"Mathematics and Art" Cai Tianxin, Responsible editor Hong Yang, published by Jiangsu People's Publishing House in June 2021, priced at 58 yuan
The British philosopher Whitehead studied mathematics at Cambridge University in his early years, and later stayed on as a lecturer for 30 years, after which he was invited to Imperial College London as a professor of applied mathematics for ten years. During this period, Whitehead was so fruitful that he was hired as a professor of philosophy by Harvard University on the other side of the Atlantic after his retirement, and began another brilliant academic career, leaving at the age of 76. Ten years later, he died in Boston.
Whitehead collaborated with his disciple Betrand Rusel (1872-1970, winner of the Nobel Prize in Literature in 1950) to write a three-volume tome, Principia Mathematica (1913), while Science and the Modern World (1925, later renamed Science and the Modern World) was his late masterpiece. In this less than 200-page but almost all-encompassing treatise on natural philosophy, Whitehead calls the 17th century the "century of genius" and names the third chapter in it.
Whitehead collaborated with his disciple Nobel Prize winner Russell to write a three-volume tome, Principia Mathematica.
Century of Genius: "There is not enough time to manipulate the major events of geniuses"
Speaking about the main factors that played a key role in the budding of science in the 17th century, Whitehead points out that the first was the rise of mathematics, followed by an instinctive belief in natural order and rationalism in the late Middle Ages. He also pointed out that the 17th century consistently provided a thinking genius for all areas of human life, and according to leonardo da Vinci, the rise of realist art in the Italian Renaissance was also an important factor in the formation of Scientific Thought among Europeans.
Whitehead went on to say that because there are so many great figures and inventions that have emerged in the "century of genius", it is inevitable that some events will happen at the same time. For example, in 1605, Bacon's book Advances in Scholarship and Cervantes' novel Don Quixote were published at the same time. The first edition of Shakespeare's tragedy Hamlet was released the year before, and a revised edition was published that year. Then Shakespeare and Cervantes died on the same day (23 April) in 1616. In the spring of that year, Harvey also published a theory about blood circulation.
Shakespeare (right) and Cervantes died on the same day on 23 April 1616
In the middle of the year, 1642, when the Englishman Newton was born, the Italian Galileo Galileo died, which was also the 100th anniversary of the publication of the Pole Copernicus's Theory of Celestial Motion. The year before, the Frenchman Descartes published Meditations on Metaphysics, and two years later he published Philosophical Principles. All in all, "this century can be said to be short of time to manipulate the major events of geniuses"
Whitehead lists 12 geniuses of the 17th century in his book, claiming to be premised on the spirit of "nothing but twelve.". Britain held five seats: Bacon, Harvey, Newton, Locke and Boyle, France, the Netherlands and Germany each had two seats, descartes and Pascal, Whigans and Spinoza, Kepler and Leibniz, and the Italian Galileo Galilei.
Bacon: Interested in science, he published The New Instrumental Theory to propose a new inductive approach
Bacon napping (left, Photographed by Cai Tianxin at Trinity College, Cambridge), Bacon once wrote in the Meditations, "Knowledge is power"
Francisco Bacon (1561-1626) of the Englishman. Methodologically, Bacon was the first to realize the opposition between the deductive method of the ancient cumbersome school and the modern inductive observation method. In particular, he was acutely aware that Aristotle's syllogism could no longer meet the development of science and required a new instrumental theory.
Born into a new aristocratic family in London, Bacon, who enrolled at Trinity College, Cambridge University, was diligent in observing as a student, and his university studies made him doubt traditional ideas and beliefs, and began to think independently about the true meaning of society and life. Three years later, young Bacon was living in Paris as an attaché to the British ambassador to France. In two and a half years he traveled almost all of France (which was more advanced than England at the time), which exposed him to many new things, absorbed many new ideas, and had a great influence on the transformation of his worldview.
After returning to China, Bacon studied for a law degree while trying to make a living because of the death of his father. He became a prominent lawyer and entered politics, and at the age of 23 he was elected to Parliament and later knighted, serving as a minister of the seal and an adviser to the king. At the same time, he remained interested in science, writing in the Meditations that "knowledge is power" (Ipsa Scientia Postia Est), but unfortunately the book was not published during his lifetime. In the winter of the 65th year, Bacon tried to fill the chicken's body with snow, studying the phenomenon of frozen embalming, and the cold caused the recurrence of bronchitis and sudden death.
In 1620, Bacon published the New Instrumental Theory, publishing his new induction. In his view, it is necessary to put not only the list of objects examined that share a given nature, but also the list of objects that lack this nature and objects of different degrees despite this property, so that there is hope of discovering the characteristics of this property. Unfortunately, Bacon regarded mathematics only as an auxiliary discipline of the natural sciences, and did not even know how mathematics was used to serve science, much less that Galileo's physics was presented in mathematical form.
DeZarger: Invented projective geometry by answering the questions of Painting by Italian artists
The French mathematician Girard Desargues (1591-1661) invented projective geometry
In the 17th century, many mathematical giants emerged, especially in France. The first to achieve the breakthrough was DeZargues, who answered the mathematical problem in painting proposed by the Italian artist Alberti 200 years ago, that is, the mathematical relationship between the interceptions of the same object on a glass screen parallel to each other. In other words, this creative mathematical achievement ——— projective geometry, inspired by the art of painting.
Girard Desargues (1591-1661) was born in Lyon, central France, the son of a royal notary and a court investigator. We know very little about de Zarg's early education, he probably studied in his hometown and later went to Paris to work as a governess, engineer, and technical consultant.
In 1628, de Zarg, as a military engineer, took part in the siege of the harbor city of La Rochele, where he became acquainted with Descartes and became friends. Two years later, de Zarg came to Paris, became friends with mathematicians such as Mason, and often attended mason's mathematical salon, where he frequently met the mathematician Pascal father and son, which later evolved into the French Academy of Sciences. At the same time, DeZarger also established contact with Fermat, a mathematician in the province. The activities of these people and their achievements made France one of the world's mathematical powers in the first half of the 17th century, and laid a solid foundation for Paris to become the center of world mathematics for more than two centuries.
The Scientific Salon, founded by the mathematician Mason (Descartes' co-currice), later the MasonIan academy and later the Royal Academy of Sciences in Paris, shows Colbert recommending members of the Royal Academy of Sciences in Paris to Louis XIV, so that the mathematical center of the world after the 17th century remained in France until Gauss appeared and moved to Germany.
In 1636, DeZarger published General Questions On Perspective Drawing (referred to as Perspective). Three years later, he published Drafts attempting to deal with the results of the intersection of cones and planes (the Draft for short). The Draft, which brings together de Zarg's new ideas and methods, is the foundation of projective geometry, and at the same time he answers Alberti's questions. At that time, he only printed about 50 copies, distributed them to friends and acquaintances, and originally came up with a revised version, but because of the denigration of some of his peers, coupled with the rapid development of analytic geometry and later calculus, DeZarger's works were gradually forgotten.
After De Zarg began his work as an architect, he stopped caring about mathematical problems and left a sculptor friend to spread his mathematical ideas. In 1648, the friend reprinted the Law of Perspective and added to the appendix three geometric theorems discovered by Dezarg, including the famous Dezarg theorem.
A sculptor friend reprinted the Perspective Method in 1648 and added three geometric theorems discovered by Dezarger to the appendix, including the famous Dezarg's theorem
A mathematical historian discovered a manuscript of the Draft in a used bookstore in Paris in 1845 during the revival of projective geometry. More than 100 years later, around 1950, the original version of the Draft was found in the Library of Paris. After more than three centuries, this book finally has a place in the history of mathematics. One spring Paris Fashion Week in the new millennium, I saw a designer show a collection of fashions based on the geometric curves that DeZarger had discovered or studied.
In fact, according to the analysis and judgment of mathematical historians, the study of geometry in the 17th century mainly broke through in two directions, one was the route taken by DeZarger, which can be described as a synthesis of geometric methods; the other path was undoubtedly more brilliant, that is, the use of algebraic methods to study geometry, that is, the analytic geometry established by Descartes.
Descartes: Established analytic geometry as an appendix to the philosophical work Methodology
Descartes at work
As Maurice Klein points out in his famous book Mathematics in Western Culture: "One idea that emerges from the study of perspective is that there is a certain difference between the world that man perceives and the world that man sees. Correspondingly, there should be two kinds of geometry. One is haptic geometry and the other is visual geometry. "Euclidean geometry is haptic geometry because it is consistent with our sense of touch. The analytic geometry established by Descartes still belongs to the former (tactile).
* Well educated, traveled all over Europe, joined the army and was stationed in many places, and later settled in the Netherlands
Rene Descartes (1596–1650) was five years younger than Dezzarg and was born in la Haye, a town in central France, now known as Descartes. When he was 14 months old, his mother died of tuberculosis, and he was also infected, so he grew up weak. Soon his father remarried and emigrated, leaving him to his grandmother to raise, and his father was financially generous, which gave Descartes a good education and the opportunity to attend the aristocratic school founded by the king, and the headmaster, seeing his talent, allowed him to go to work early.
Following his father's wish to become a lawyer, Descartes later entered the University of Poitiers to study law and medicine. But Descartes was interested in all kinds of knowledge, including mathematics, and after graduation, he first lived in Paris for a while, then returned to his hometown, and then sold his father's legacy, determined to travel around Europe to find wisdom in the "book of the earth". For this reason, Descartes joined the Dutch army, stationed in many places with the army, sometimes participating in battles, sometimes seeking fun. In the end, he chose to settle down in the Netherlands and wrote a book.
For more than 20 years, Descartes immersed himself in writing in Amsterdam, as well as in the cities of Leiden and Utrecht. He wrote the finest of his books and earned a great reputation almost as soon as the first book was published. Later, not only his readers, but even himself, were drawn to the great ideas of the book.
Descartes taught philosophy to the 23-year-old Queen of Sweden, and a few months later he died of pneumonia
When the Descartes reached middle age, the 23-year-old Queen Christina of Sweden was an admirer of Descartes, and she sent a warship to invite Descartes to Stockholm, so that in that unusually cold winter, he had to come to the palace at five o'clock in the morning three times a week to teach her philosophy. A few months later, Descartes died of a relapse of pneumonia.
*Became interested in mathematics during his time as a soldier in the Netherlands, creating the Cartesian coordinate system
During his military service and travels to Europe, Descartes paid attention to "gathering knowledge" and "thinking about the things he encountered everywhere." Descartes' interest in mathematics and physics was also born during his time as a soldier in the Netherlands. On November 10, 1618, he happened to see a mathematical problem answer written in Flemish on a roadside bulletin board, and thus became acquainted with Isac, a comrade who was highly accomplished in mathematics and physics.
Four months later, Descartes wrote to Isaac: "You are the one who woke me up from indifference..." and told him that he had made four major discoveries in mathematics. At that time, Latin was the lingua franca of scholars. Descartes also signed his writings with the Latinized name Renatus Cartesius (Renatus Cartesius), in accordance with the customs of the time. Because of this, the Cartesian coordinate system he founded is also known as the Cartesian coordinate system.
Cartesian coordinates are from the origin, extending the x-axis and y-axis, establishing the first oblique coordinate system in history and giving a Cartesian coordinate system
* The greatest contribution was to establish analytic geometry, writing the Goldbach conjecture a century earlier
Descartes' mathematical contributions can be roughly summarized in the following aspects. First, the symbolization of arithmetic. Second, starting from the origin, extending the x-axis and y-axis, establishing the first oblique coordinate system in history and giving an example of a Cartesian coordinate system. Third, on the basis of the Cartesian coordinate system, analytic geometry was established, which was undoubtedly Descartes' most important contribution to mathematics. Fourth, he invented The Euler Cartesian formula.
In addition, Descartes also spent a lot of effort on number theory. As we all know, the Goldbach conjecture was proposed by the 18th-century German mathematician Goldbach in correspondence with the Swiss mathematician Euler. But more than a century ago, Descartes quietly wrote down the discovery in his notebook. In addition, he studied perfect numbers and affinity numbers, and found multiple perfect numbers of orders 2-4 and a 10-digit affinity number. There are also Cartesian leaf-shaped lines, a curve and its images often seen in calculus tutorials, which are also used to support his love story with the Queen of Sweden.
* Publishing "Methodology" on the basis of skepticism, "I think, therefore I am" because of doubting everything
In the Methodology, Descartes proposed "doubt everything" and "I think, therefore I am"
Descartes was hailed by the German philosopher Hegel as the "father of modern philosophy". The Methodology was Descartes' first philosophical work, published in 1637 (it was in the third appendix to the book that Descartes' geometry was first published), when Fermat proposed his Grand Theorem. Descartes believed that the human mind is essentially sound and is the only means of obtaining truth. In the book, Descartes proposes the following four principles:
First, do not accept any truth that you do not understand. This is known as the "doubt everything" theory. For example, Aristotle once said that women have two fewer teeth than men, and this is not the case.
Second, the problems to be studied should be broken down into a number of relatively simple small problems as much as possible, and solved them one by one.
Third, arrange small problems from simple to complex, starting with easy solutions.
Fourth, after the problem is solved, it is necessary to comprehensively test it to see whether it has been completely and completely solved.
The starting point of Descartes' philosophy was skepticism. He thinks that everything is questionable, and that after doubt is a state of nothingness; on the other hand, the doubter himself cannot exist, because "to imagine that something with thought does not exist, it is a contradiction", which is Descartes's "I think, therefore I am". Finally, he found the unquestionable thing, a thinking, thinking reason, idea, spirit. Perhaps, in Descartes' mind, God was himself.
Fermat: Proposed Fermat's Law, 300 years to lead to arguments and the birth of "algebraic number theory"
French mathematician Pierede Fermat (1607-1665), known as the "king of amateur mathematics"
Pierede Fermat (1607-1665) lived a real, conformist, and even somewhat lackluster life. He was born in The Small Town of Bomont de Lomamagne in the Tangarron Department of the Midi Pyrenees region of southern France, far from the mathematical or artistic centers of France. His father, a wealthy leather merchant, sent him to study at a Franciscan monastery.
*In his spare time, he has contributed to calculus, number theory, and probability
In 1623, Fermat entered the University of Orléans in central France to study civil law, and three years later received a bachelor's degree. After that, he got a job in Bordeaux, famous for its wines on the Atlantic riviera. In his spare time he became interested in mathematics and conducted in-depth research. Fermat was a gifted language, and in addition to French, he was fluent in Latin, Greek, Italian, Spanish and Oxiracetam, and his poetry in many languages was praised, as well as his passion for the revision of Greek texts. Later, he managed to serve for life as legal counsel for the reception room above. Fermat's judicial work took up his daytime work, while his nights and holidays were almost entirely used by him to learn languages and study mathematics.
Portrait of Fermat in his hometown
Fermat told his friends most of his mathematical discoveries by correspondence, a tradition handed down from the ancient Greeks. In a letter to a friend, he (before Newton or Leibniz) explored many of the basic ideas of calculus. Known as the "king of amateur mathematicians", Fermat made important contributions to geometry, probability theory, number theory, and calculus, which led to a priority struggle with his contemporaries such as fellow mathematician Descartes and English mathematician Wallis.
Fermat's correspondence with pascal, another fellow mathematician, laid the foundation for the discipline of probability theory. In today's era of big data, probability theory and statistics, which officially appeared later, have played an increasingly important role. In fact, the bi-mathematician initially discussed the problem of gambling.
Fermat's Introduction to Flat and Stereo trajectories, published in 1679, the results of which were discovered in 1629, predate Descartes' Geometry
In 1636, his seminal work on analytic geometry was published in manuscript form (based on achievements made in 1629), preceding the publication of Descartes' Geometry (1637), but its official publication did not take place until 1679, after his death, under the title Introduction to Flat and Three-Dimensional Trajectories. Methodologically, Fermat proposed a method for determining the maximum, minimum, and tangent of a curve, which is equivalent to differentiation. Fermat also acquired a method of finding planes and solid centers of gravity, which led to advances in his research in integrals.
*The proof of Fermat's Law was not completed by British mathematicians until 1995
Fermat's favorite thing is probably number theory. Fermat studied perfect numbers, friendly numbers, Pell's equations, and Fermat numbers and prime numbers, which were named after him by later generations, and so on. It was while studying perfect numbers that he discovered Fermat's small theorem (1640), which was proved in 1736 by the Swiss mathematician Leonhard Euler (1707-1783). In 1760, the so-called Euler's theorem was derived, which has important applications in cryptography.
Of course, Fermat's most noteworthy is the Fermat's Last Theorem, whose name is named after him, and the rigorous proof was not proved until 1995 by the British mathematician Andrew Wiles (1953-), which is known as the "mathematical achievement of the 20th century". Over the past 300 years, countless intelligent minds have devoted themselves to the study of this theorem, and an important branch of mathematics , algebraic number theory " , and important mathematical concepts such as " ideal numbers " have been born.
The rigorous proof of Fermat's Last Theorem was completed in 1995 by the British mathematician Wiles and has been hailed as the "mathematical achievement of the 20th century".
As the 20th-century American-born British mathematician Modell argued, "Because of its beauty and the richness of its arguments, higher arithmetic (number theory) seems to encompass much of the romance of mathematics." Thus, although Fermat was not a giant of the arts and sciences like other fellow French mathematicians, it is believed that he had satisfied himself from the beauty of number theory.
Pascal: There are many mathematical discoveries, and "To the Provincials" and "Thoughts" are regarded as immortal
The French mathematician Blaise Pascal (1623-1662) was a mathematician, physicist, inventor, writer and theologian
In the same year that Fermat entered the University of Orléans, Blaise Pascal (1623-1662) was born in Clermont-Ferrand, the capital of the south-central province of Domsan. His grandfather was France's finance minister, and his father was a local tax collector and lawyer who was interested in mathematics and physics.
*A regular at the Paris Science Salon, he is talented at the age of 12 and has many discoveries such as Pascal's theorem
Pascal, a mathematician, physicist, inventor, writer and theologian, was a child prodigy. When his mother died of illness when he was three years old, and there was an older sister and a younger sister in the family, when he was eight years old, for the sake of the child's future, the father decided to move the family to Paris. The elder Pascal did not remarry, but the maid they hired, Louise, eventually became a member of the family.
At the age of 12, Pascal independently derived a theorem in geometry that the sum of the three inner angles of a triangle is equal to two right angles. At that time, Mason, a mathematician with a priest background in Paris, held a weekly science salon, and Pascal and his sons were regular visitors. At the age of 16 he discovered the famous Pascal's theorem, the collinear of three intersections of three pairs of opposite sides of a hexagonal shape bound to a conical curve. The following year Pascal published The Theory of Conic Curves, the result of his study of deZarg's projective geometry and the most important advance in conic curves since the ancient Greek mathematician Apollonius.
Due to the shrinkage of the purchase of state bonds, the elder Pascal had to re-emerge from the mountains and work as a tax officer in Rouen in the seine-maritime province.
In 1642, in order to alleviate his father's endless and tiring computational workload, pascal designed a calculation device that could automatically carry and do addition and subtraction operations, which is considered to be the world's first computer, known as the Pascal computer or Pascaline, and it is said that a total of 50 Pascalines were produced, and eight are still in existence, four of which are in museums in Paris and one in Dresden, Germany.
Pascal's invention of the additive computer is now in the Collection of the Musée des Arts et des Beaux-Arts in Paris
1654 was a pivotal year for Pascal, who studied several mathematical problems. First of all, he delved into the analysis of infinitesimals, came up with a general method of finding the area and center of gravity surrounded by different curves, and solved the cycloidal line problem with the principle of integrals, and his thesis manuscript had important inspirations for the German mathematician Leibniz to establish calculus. Secondly, when studying the properties of binomial coefficients, he wrote "Arithmetic Triangle" and submitted it to the Paris Academy of Sciences. The binomial coefficients are known as "Pascal triangles" by later generations, although given earlier by the 9th-century Indian mathematician Mahavira and the 11th-century Chinese mathematician Jia Xian.
* Converted to Janssenism in 1654 and wrote immortal works "To the Provincials" and "Records of Thought" in the monastery
If Pascal in To the Provincials is an eloquent critic, pascal in Thought is an inspired artist
Also in 1654, Pascal first experienced religion, after which he abandoned mathematical research. The following year, he entered the Port Royal Abbey in the southwestern suburbs of Paris, where he wrote two posthumous works——— To the Provincials and The Book of Thoughts. His important contributions to the philosophy of mathematics are included in the book "The Spirit of Geometry".
In the winter of 1646, the 58-year-old Pascal slipped and broke his butt on an icy street in Rouen. Fortunately, two of France's best orthopedic surgeons were in Rouen, and after their meticulous treatment, the old man survived, and Pascal eventually converted to Janssenism.
To the Provincials consisted of 18 letters defending the Jensenist Arnault, who was tried for writing a work against the Jesuits. This work was immediately successful after its publication, replacing the previous pretense, esoteric and tedious style with a concise and rich, rigorous and accurate style, and was the beginning of modern French prose by Burrozan, the founder of French literary criticism, and is still famous today.
If Pascal in To the Provincials is an eloquent critic, pascal in Thought is an inspired artist. For example, the book exhorts skeptics that if God does not exist, then skeptics will lose nothing by believing in Him; And if God exists, then skeptics can have eternal life by believing in Him. Widely regarded as a masterpiece, the Book of Ideas is a milestone in French literature.
And Pascal himself, as did the 20th-century American-born English poet and 1948 Nobel Laureate in Literature T. Pascal himself. S. Eliot depicts, "The secular man among the ascetics, the ascetic among the secular men."
Hobbes: The length of life covers de Zarg, Descartes, spinoza four, from geometry to deductive method
Hobbes, who was in his 40s, stumbled into a private library while traveling and saw Euclid's Primitive Geometry and fell in love with geometry ever since
In 1633, when Descartes heard the news that Galileo had been tried in Italy by the Inquisition, he abandoned the idea of publishing geometric works (five years later in essay form as an appendix to the Methodology). The year before, the Dutch Jewish philosopher Baruchde Spinoza (1632-1677) was born in Amsterdam, and his first book was a study of Cartesian philosophy.
The English philosopher and political theorist Thomas Hobbes (1588-1679), who was born three years before DeZarger, died two years later than Spinoza. In other words, his life encompassed the lives of Dezarg, Descartes, Pascal, and Spinoza. Unfortunately, due to his interest in mathematics (geometry), he missed the opportunity for mathematical discovery and creation.
Hobbes entered Oxford university at the age of 15 and spent most of his time reading travelogues, studying maps and nautical charts. He later became a personal teacher to Count Cavendish, accompanied the Count on three trips to the European continent, met many times with the French mathematician Mason, attended his academic salons, and discussed scholarship with Galileo galilei in Italy. One day in his 40s, Hobbes walked into a private library and saw Euclid's Geometric Primitives. When he looked through the geometric propositions inside, he had the words in his mouth: "This is impossible." But several times and three times, he finally became convinced, and from then on he liked geometry, especially the impeccable way of argumentation, and learned the method of deduction.
Hobbes believed that man was born equal and free, and he was known for his writings on personal security and the social contract, which contained the germ of liberal ideas and the characteristics of the authoritarianism of the era. His masterpiece is Leviathan, which for centuries has been a must-read political book for many heads of state. Leviathan is a mighty sea beast that he uses as a metaphor for a country with an absolute monarchy.
It is said that in Hobbes's time, no Englishman was more well-known abroad than he was. Foreign celebrities who visit britain are always looking forward to seeing him and paying tribute to him.
Spinoza: Writing Geometric Ethics in a geometric way both developed and negated Cartesian philosophy
Spinoza's most famous work is The Ethics of Geometry, or Ethics for short.
Spinoza's ancestors lived in northern Spain, and at the end of the 15th century, due to religious and ethnic persecution, the family fled to Portugal, and a century later to the Netherlands. Both her grandfather and father were respected Jewish merchants in Amsterdam, and at the age of six, Spinoza attended the Jewish Church School, where her father was headmaster, studying Latin and German in her spare time.
In the course of studying the Jewish scriptures, Spinoza became suspicious and was expelled from Judaism in 1656 and moved out of the Jewish ghetto. At the age of 24, he made a living in The Hague by grinding lenses while thinking philosophically. In 1673, Spinoza was invited to be professor of philosophy at the University of Heidelberg on the condition that religion could not be mentioned, but he declined. The work of grinding lenses harmed his health, he inhaled a large amount of selenium dust, and died of tuberculosis at the age of 45.
Spinoza's most famous work is The Ethics of Geometry, or Ethics for short. Written in the form of Euclidean geometry, the book begins with a set of definitions and axioms from which propositions, proofs, inferences, and explanations arise. Three themes are discussed, namely metaphysics, psychology, and ethics, of which ethics is his creation. Spinoza believed that goodness was different for different things(such as man and horse): human understanding was part of God's infinite wisdom. He divided epistemology into three stages: opinion or imagination (experience and judgment are not sufficient), reason (innate knowledge of existential geometry), and intuition (full knowledge of objects).
Ethics was published after Spinoza's death, after which he had already come into contact with Andesian philosophy and conducted in-depth and meticulous research, expounding Descartes' Philosophical Principles in a geometrical way. Spinoza's easy-to-understand answers to the intractable problems of Cartesian philosophy are particularly striking, as is both a development of Andesian philosophy and a repudiation of Cartesian philosophy.
Li Nian edited from the third chapter "The Century of Genius", the original text is 17,000
【Contents】
Author: Cai Tianxin
Photo: Provided by the publisher, a small amount of network
Editor: Qian Yichen