325 years ago today, on January 29th, 1700 (December 10th, 1699 in the lunar calendar), Bernoulli, a famous Swiss mathematician and mechanist, was born in Groningen, the Netherlands. On January 29th, 1700, Bernoulli, a famous Swiss mathematician and mechanist, was born in Groningen, the Netherlands. In the history of science, it is not uncommon for father and son scientists and brother scientists. However, among the generations of a family spanning centuries, it is rare for many father and son brothers to be scientists, among which the Bernoulli family in Switzerland is the most prominent. Eight scientists have been produced in three generations of Bernoulli family, and at least three are outstanding; And among their many descendants from generation to generation, at least half have become outstanding figures one after another. There are no less than 120 descendants of Bernoulli family who have been systematically traced back. They enjoy fame in mathematics, science, technology, engineering and even law, management, literature and art, and some are even famous. The most incredible thing is that there are two generations in this family. Most of them mathematicians, who didn't intend to choose mathematics as their career, indulge in mathematics with affection. Some people ridicule them like alcoholics meeting spirits. Born in Basel, Nicolaus Bernoulli the Elder (1623-1708 AD) was well educated and held senior positions in the local government and judicial departments. He has 3 accomplished sons. Among them, the eldest son Jocob (AD 1654 ~ 1705) and the third son Johann (AD 1667 ~ 1748) became famous mathematicians, and the second son Nicolaus I (AD 1662 ~ 1716) was the first professor of law in Bern before becoming a member of the mathematics community of the Petersburg Academy of Sciences. Jacob Bernoulli was born in Basel on December 27, 1654, graduated from the University of Basel and received an MFA in 1671 at the age of 17. Art here refers to "free art", including seven categories: arithmetic, geometry, astronomy, mathematical music and grammar, rhetoric and eloquence. In accordance with his father's wishes, he received a master's degree in theology in 1676 at the age of 22. However, he also taught himself mathematics and astronomy against his father's will. In 1676, he went to Geneva as a governess. From 1677 onwards, he began writing the informative Meditations there. In 1678 and 1681, Jacob Bernoulli traveled twice to study, visited France, the Netherlands, England and Germany, contacted and interacted with scientists such as Hude, Boyle, Hooke and Huygens, and wrote scientific and technological articles on comet theory (1682) and gravity theory (1683). In 1687, Jacob published a mathematical paper "The method of quartering the area of a triangle with two mutually perpendicular straight lines" in the Journal of Teachers. In the same year, he became a professor of mathematics at the University of Basel until his death on August 16, 1705. In 1699, Jacob was elected a foreign academician of the Paris Academy of Sciences; In 1701, he was admitted as a member of the Berlin Scientific Society (later the Berlin Academy of Sciences). Many mathematical achievements are associated with Jacob's name. For example, the catenary problem (1690), the radius of curvature formula (1694), "Bernoulli's double line" (1694), "Bernoulli's differential equation" (1695), "isoperimeter problem" (1700), etc. Jacob's most significant contribution to mathematics was in the study of probability theory. From 1685, he published papers on the number of wins and losses in gambling games, and later wrote his masterpiece Guessing, which was published eight years after his death, that is, in 1713. One of the most talked about anecdotes is Jacob's fascination with the study of logarithmic spirals, which began in 1691. He discovered that the logarithmic spiral is still a logarithmic spiral after various transformations. For example, its gradual curvature and gradual extension are logarithmic spirals, the trajectory of the vertical foot from the pole to the tangent, and the reflection lines obtained after reflection by the logarithmic spiral with the pole as the luminous point, as well as the curves (backlight rays) tangent to all these reflection lines, are logarithmic spirals. Marveling at the magic of this curve, he actually asked future generations to engrave the logarithmic spiral on his tombstone in his will, and attached the tribute "Even if it changes, it will remain the same" to symbolize immortality after death.