"Pascal displayed a precocious mathematical genius, but his activities in this area were hampered by religious scruples...Nevertheless, he made significant advances in several different branches of mathematics and physics. "——Wolf

"Mathematics is the highest exercise of the spirit."——Pascal

Pascal was a French mathematician, physicist, philosopher, and essayist.1623 Born in Clermont-Ferrand on June 19, 1662; died in Paris on August 19, 1662.

Pascal lost his mother at the age of 4. His father was a government official, erudite and an amateur mathematician. .Since Pascal was frail and sickly since he was a child, his father did not allow him to be exposed to mathematics early to avoid overthinking and damaging his health. When Pascal was 12 years old, he saw his father reading geometry and asked him what geometry was. His father did not want him to know too much. , simply told him that geometry is the study of graphics, and quickly collected the mathematics books, fearing that Pascal would read them. His father's "ban" on him touching mathematics further aroused Pascal's curiosity about mathematics. So Pascal After doing some research on his own, when he told his father his discovery: "The sum of the three interior angles of any triangle is one hundred and eighty degrees", his father burst into tears of surprise and changed his original idea early. Let Pascal study "Elements of Geometry" and other classic mathematical masterpieces, and Pascal greedily read "Elements of Geometry" quickly.

Pascal is a legendary figure in the history of science, and was once described as the "Elements of Geometry" in the history of mathematics. The greatest "talent". D'Alembert, the great mathematician of the 18th century, praised his achievements as "the intermediate link between the work of Archimedes and Newton."

Pascal Showing an astonishing precocious wisdom: when he was 11 years old, when he tapped the plate with a table knife, it made a sound. The sound stopped abruptly when he pressed the plate with his hand, which inspired him to write the paper "On Sound" which discusses the pronunciation of vibrating bodies. At the age of 12, he independently discovered many theorems in elementary geometry, including that the sum of the interior angles of a triangle is equal to 180°; at the age of 13, he discovered the coefficients of the binomial expansion - "Pascal's triangle"; at the age of 14, He was allowed to participate in the weekly scientific seminar chaired by Mersenne (the French Academy of Sciences was developed from this seminar). In 1653, he wrote "Arithmetic Arithmetic of Triangular Arrays", which was revised by Fermat and published in 1665. This book establishes the basic principles of probability theory and certain theorems about combinatorial theory. Together with Fermat, he establishes the foundation of probability theory and combinatorial theory, and provides a series of solutions to problems in probability theory. When Bunitz later read Pascal's research results in this area, he was deeply aware of the importance of this "new logic". In addition, Pascal's "Arithmetic Arithmetic of Triangular Arrays" contained the earliest version of mathematical induction. Acceptable statement, so people think that he is also the earliest discoverer of mathematical induction.

When Pascal was less than 16 years old, he was inspired by the work of the geometer Desargues and discovered that The following famous theorem was formulated: "If a hexagon is inscribed in a conic section, then the intersection of its three pairs of opposite sides is a straight line, and the converse proposition is also true." For this reason, he wrote "Theory of Conic Sections" in 1640 A single article was published in 2011. This was the greatest progress in the theory of conics since Apollonius in Greece, and was also an outstanding achievement in projective geometry. Later, he derived a series of inferences from this theorem and gave several theorems of projective geometry. .

The Italian mathematician Cavalieri once suggested that the area of ??a triangle can be calculated by dividing it into countless parallel straight lines. In order to get rid of the logical flaws in Cavalieri's method, Pascal believed that, A line is not made of points, but of countless short lines; a surface is not made of lines, but of countless small surfaces; a solid is not made of surfaces, but of countless thin solids .Following this clue of thought, he found the area (equivalent to) of the curved trapezoid under the curve, and found the area of ??the cycloid and the volume of its rotating body. At that time, Pascal reached a very high level in using infinitesimals to study geometry.

However, because the concept of infinitesimal is not clear and indivisible is also mysterious, when others ask questions, he answers other people's criticisms with "understanding". Pascal believes that nature does not provide infinitesimals and infinitesimals to people for the purpose of understanding. It is for appreciation. He saw that infinitesimals and infinitesimals restrict each other (in a reciprocal relationship). He denied that graphics are composed of low-dimensional elements, and believed that the difference between discrete and continuous disappears with the application of analytical methods. These thoughts of his are Later, the strict definitions of limits and infinitesimals opened the way for the establishment of calculus. He conducted in-depth research on cycloids and wrote the famous book "On Cycloids" in 1658, which solved many problems about cycloids. Question. This book had a profound influence on the young Leibniz.

When Pascal was 18 years old, he designed the world's first mechanical computer (capable of addition and subtraction calculations).

In terms of physics, in 1648 he proved the pressure of air through an experiment. This experiment caused a sensation in the entire scientific community, thus completely shattering the ancient dogma of "nature is afraid of vacuum" in scholastic philosophy. He also studied liquids The general law of balance has discovered that "the pressure exerted by the fluid at any point in a closed container is transmitted equally in all directions with equal intensity." This is the most basic principle in fluid statics - Pascal's principle.

Pascal was also a master prose master, thinker and theological debater. The "Thoughts" and "Letter to the Provincialists" he wrote are listed as classic literary masterpieces. With his ability as a master prose master to control words, he He gave full play to the penetrating insight of a thinker. Not only was his writing fluent, but he was also famous for his polemical edge and profundity of thought. He had a great influence on the development of French prose. Even the great French writer Voltaire read his literary works. Also very encouraged.

However, just when Pascal was enjoying a high reputation as a scientist, due to his physical weakness, indigestion, insomnia and headaches, he often had nightmares half asleep and half awake at night. Especially when he was suffering from pain. Dominated by his worldview, he gradually gave up the discussion of mathematics and science and devoted himself to religious meditation. After a few short years, although he returned to science, he could no longer concentrate on it. In 1654, he said: He received a strong reminder that this kind of renewed scientific activity was not welcomed by God. This so-called divine revelation came after an accident: once he was riding in a carriage, the horse lost control and rushed across the Neuilly Bridge. The railing fell into the river, but luckily he did not fall into the river due to the sudden break of the reins, and was miraculously saved. He wrote this accidental incident on a small piece of thick paper and kept it close to his chest, asking himself to avoid it. Keeping this revelation firmly in mind from now on, he fatefully returned to religious meditation. Pascal believed: "Anything related to faith cannot be considered by reason." In the last period of his life, he even went further. He went to the extreme, like a dervish, and wrapped a spiked belt around his waist. If he thought any ungodly thoughts came from his mind, he would hit the belt with his elbow to sting his body. In this way, he was only 39 years old He died. On his deathbed, he said in a weak voice: "May God be with me." The famous British historian of science Wolfe said: "Pascal showed a precocious mathematical genius, but his activities in this area He was hindered by religious scruples and ended in his death. Nevertheless, he made remarkable progress in several different branches of mathematics and physics."

Pascal believed: "A man's virtue determines It cannot be measured by his special efforts, but by his daily actions." He also said: "Do you want people to praise you? Then don't praise yourself." He believed: "Mathematics is the highest exercise of the spirit."