Gauss (Gauss 1777~1855)Born in Brunswick, Located in the north-central part of Germany now.His grandfather was a farmer, his father was a plasterer, and his mother was a stonemason's daughter. He had a very smart younger brother. The uncle, Gauss, took good care of little Gauss and occasionally gave him some guidance. His father can be said to be a "slutty" and believed that only the strength can make money, and learning such a way is useless to the poor.
Gauss showed his talent very early and could point out the mistakes in his father's account book at the age of three.When I was seven years old, I entered the elementary school and taught in a dilapidated classroom. The teacher was not good to the students and often thought that he was not grateful to teach in a remote countryside.When Gauss was ten years old, the teacher took the famous "From One Plus to One Hundred" exam and finally discovered Gauss' talent. He knew that his ability was not enough to teach Gauss, so he bought a deeper math book from Hamburg for Gauss to read.At the same time, Gauss and his assistant coach who are about ten years older than him Bartels Become very familiar, and Bartels His ability was much higher than that of his teacher. Later, he became a university professor and taught Gauss more and more profound mathematics.
The teacher and the assistant teacher visited Gauss' father and asked him to give Gauss a higher education, but Gauss' father thought his son should be a plasterer like him, and he had no money to let Gauss continue to study. The final conclusion was to find rich and powerful people to be Gauss' patrons, although they didn't know where to look for it.After this visit, Gauss exempted the work of weaving every night, and Bartels Discussing mathematics, but soon after, Bartels There is nothing to teach Gauss anymore.
1788Nian Gauss entered the higher education school despite his father's opposition.After reading Gauss' homework, the math teacher asked him not to take math classes anymore, and his Latin soon surpassed the whole class.
1791Nian Gauss finally found the sponsor-Ferdinand, Duke of Brunswick (Braunschweig),Promising to help him with everything possible, Gauss's father had no reason to object.The next year, Gauss entered Braunschweig College.That year, Gauss was fifteen years old.There, Gauss began to study advanced mathematics.And independently discovered the general form of the binomial theorem and the "quadratic reciprocity theorem" in number theory. (Law of Quadratic Reciprocity)、Prime number distribution theorem (prime numer theorem)、and arithmetic geometric average (arithmetic-geometric mean)。
1795Gotss enters Gottingen (G?ttingen)In college, because he is very talented in language and mathematics, he has been troubled for a while in order to specialize in classical Chinese or mathematics in the future.By 1796, the seventeen-year-old Gauss got an extremely important result in the history of mathematics.What is best known and has led him to the path of mathematics is the theory and method of drawing the regular seventeen-side ruler.Mathematicians in the Greek era already knew how to make corrective use of rulers 2 m3n5p The edge, where m is a positive integer, and n and p Only 0 or 1.However, no one has known the method of drawing the ruler of the seventh, nineth and eleventh sides for two thousand years.And Gauss proved:
A positive n The edges can be made by the ruler and only n It is one of the following two forms:
1、n = 2k,k = 2, 3,
2、n = 2k (Multiplication of several different "Ferma prime numbers" ),k = 0,1,2,
Fermat prime numbers are like Fk = 22k prime number.picture F0 = 3,F1 = 5,F2 = 17,F3 = 257, F4 = 65537,They are all prime numbers.Gauss used algebraic methods to solve geometric problems for more than 2,000 years. He also regarded this as a masterpiece in his life. He also explained that the regular seventeenth-sided shape was engraved on his tombstone. However, his tombstone did not engrave the seventeenth-sided shape, but the seventeenth-pointed star. Because the sculptor responsible for engraving the stele believed that the regular seventeenth-sided shape and the circle were too similar, and everyone would not be able to distinguish it.
1799Nian Gauss proposed his doctoral thesis, which proved an important theorem of algebra:
Any polynomial has (plural )root.This result is called the "basic theorem of algebra" (Fundamental Theorem of Algebra)。
In fact, before Gauss, many mathematicians believed that the proof of this result had been given, but none of them was rigorous.Gauss pointed out the shortcomings of his predecessors one by one, and then put forward his own opinions. He gave a total of four different proofs in his life.
In 1801, Gauss published "Research on Mathematics" at the age of twenty-four (Disquesitiones Arithmeticae),This book is written in Latin and it turns out that there are eight chapters. Because of insufficient money, I have to print seven chapters.
Except for Chapter 7 of this book, the basic theorem of algebra, the rest are number theory. It can be said that it is the first systematic work of number theory. Gauss first introduced "consistency" (Congruent)concept.The "secondary mutual inversion theorem" is also included.
At the age of 24, Gauss gave up his research on pure mathematics and conducted several years of research on astronomy.
At that time, the astronomical world was worried about the huge gap between Mars and Jupiter, and believed that there should be planets between Mars and Jupiter that had not been discovered.In 1801, Italian astronomers Piazzi, There is a new star between Mars and Jupiter.It is named "Ceres" (Cere)。Now we know it is one of the asteroid belts of Mars and Jupiter, but at that time the astronomy community was arguing, some said it was a planet, and some said it was a comet.You have to continue to observe before you can make a judgment, but Piazzi Only 9 degrees of orbit can be observed, and then it will disappear behind the sun.Therefore, it is impossible to know its orbit, nor to determine whether it is a planet or a comet.
Gauss was interested in this question at this time, and he decided to solve the problem of this inexplorable stadium.Gauss himself created a method to calculate the orbit of the planet with just three observations.He can predict the position of the planet with extreme accuracy.Sure enough, Ceres appeared accurately in the place predicted by Gauss.This method - although he did not announce it at the time - is the "minimum square method" (Method of Least Square)。
1802In 2018, he accurately predicted the Asteroid 2--Zhishenxing (Pallas)At this time, his reputation spread and honor came. The Russian Academy of Sciences selected him as a member. Pallas astronomer Olbers He was asked to be the director of the Göttingen Observatory, but he did not agree immediately. He did not go to Göttingen to take office in 1807.
1809In 2018, he wrote the second volume of "Theory of Celestial Movement". The first volume included differential equations, round vertebrae censors and elliptical orbits. The second volume showed how to estimate the orbit of a planet.Gauss' contribution to astronomy was mostly before 1817, but he still worked on observation until he was seventy years old.Although he was working on the observatory, he still took time to do other research.In order to use integral to decompose the differential force range of celestial bodies' motion, he considered infinite series and studied the convergence problem of series. In 1812, he studied supergeometric series. (Hypergeometric Series),The research results were also written into a special paper and presented to the Royal Academy of Sciences of Göttingen.
1820By 1830, Gauss had been to map Khan Nova (Hanover)Principality (Where can Gauss live )The map, and began to do geodesic work, he wrote a book about geodesics, and due to the needs of geodesics, he invented the lunar observator (Heliotrope)。In order to study the earth's surface, he began to study the geometric properties of some curved surfaces.
1827In 2019, he published "General Research on Surfaces" (Disquisitiones generales circa superficies curva),It covers some of the "differential geometry" that you are studying in college now.
From 1830 to 1840, Gauss and a young physicist who was twenty-seven years younger than him - Weber (Withelm Weber)Together, their cooperation is ideal: Weber conducts experiments and Gauss' research on theory. Weber arouses Gauss' interest in physical problems, while Gauss uses mathematical tools to deal with physical problems, which affects Weber's thinking methods.
1833Nian Gauss pulled an eight thousand-foot-long wire from his observatory, crossed the roofs of many houses, and went to Webber's laboratory, using volt batteries as the power supply to construct the world's first telegraph machine.
1835In 2019, Gauss set up a magnetic observatory in the observatory and organized the "Magnetic Association" to publish research results, which caused geomagnetism to be studied and measured in a large number of regions around the world.
Gauss had obtained the accuracy of geomagnetics. In order to obtain the proof of experimental data, his book "General Theory of Geomagnetics" was not published until 1839.
1840In 2019, he and Weber drew the world's first magnetic field map of the earth and determined the position of the earth's magnetic south pole and the north pole.In 1841, American scientists confirmed Gauss' theory and found the exact location of the magnetic south pole and the magnetic north pole.
Gauss is always striving for excellence in his work and requires his research results very strictly.He himself once said: "It is better to publish less, but what is published is a mature result."Many contemporary mathematicians ask him not to be too serious and write down the results and publish them, which is very helpful for the development of mathematics.
One of the famous examples is the development of non-European geometry.There are three founders of non-European geometry, Gauss, Lobatchevsky(Robacheuski, 1793 ~1856), Bolyai(Poei, 1802 ~1860)。in Bolyai His father was a classmate from Gauss University, and he had wanted to try to prove parallel axioms, although his father opposed him continuing to engage in such seemingly hopeless research, Bolyai Or indulge in parallel axioms.In the end, non-European geometry was developed, and in 1832 ~18332018 published research results, Bolyai I sent my son's achievements to my old classmate Gauss, but Gauss replied:
to praise it would mean to praise myself. I can't praise him, because praising him is like praising myself.
As early as decades ago, Gauss had already achieved the same result, but he was afraid that he would not be accepted by the world and did not announce it.
The famous American mathematician Bell (E.T.Bell),In his book "Mathematics Worker" (Men of Mathematics) In one book, I once criticized Gauss like this:
It was only after Gauss' death that people knew that he had foresaw some nineteenth-generation mathematics, and had expected their appearance before 1800.If he could leak something he knew, it would be possible that math would be half a century or more advanced than it is now.Abel (Abel)and Jacob (Jacobi)You can start working where Gauss stays, rather than spending their best efforts discovering what Gauss knew as early as they were born.And those non-European geometry creators can use their genius to other forces.
On the morning of February 23, 1855, Gauss passed away peacefully in his sleep.