这里有不少数学家相关的小故事~~~~~~~~~~~~~~~~`
Pierre de Fermat
The most tantalizing marginal note in the history of mathematics. Of the well over three thousand mathematical papers and notes that he wrote, Fermat published only one, and that just five years before his death and under the concealing initials M. P. E. A. S. Many of his mathematical findings were disclosed in letters to fellow mathematicians and in marginal notes inserted in his copy of Bachet's translation of Diophantus's Arithmetical
At the side of Problem 8 of Book II in his copy of Diophantus, Fermat wrote what has become the most tantalizing marginal note in the history of mathematics. The considered problem in Diophantus is: " To divide a given square number into two squares." Fermat's accompanying marginal note reads:
To divide a cube into two cubes, a fourth power, or in general any power whatever above the second, into two powers of the same denomination, is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.
This famous conjecture, which says that there do not exist positive integers x, y, z, n such that xn + yn = zn when n > 2, has become known as "Fermat's last theorem." Whether Fermat really possessed a sound demonstration of this conjecture will probably forever remain an enigma. Because of his unquestionable integrity we must accept as a fact that he thought he had a proof, and because of his paramount ability we must accept as a fact that if the proof contained a fallacy then that fallacy must have been very subtle.
Many of the most prominent mathematicians since Fermat's time have tried their skill on the problem, but the general conjecture still remains open. There is a proof given elsewhere by Fermat for the case n = 4, and Euler supplied a proof (later perfected by others) for n = 3. About 1825, independent proofs for the case n = 5 were given by Legendre and Dirichlet, and in 1839 Lame proved the conjecture for n = 7. Very significant advances in the study of the problem were made by the German mathematician E. Kummer. In 1843, Kummer submitted a purported proof of the general conjecture to Dirichlet, who pointed out an error in the reasoning. Kummer then returned to the problem with renewed vigor, and a few years later, after developing an important allied subject in higher algebra called the theory of ideals, derived very general conditions for the insolvability of the Fermat relation. Almost all important subsequent progress on the problem has been based on Kummer's investigations. It is now known that " Fermat's last theorem " is certainly true for all n < 4003 (this was shown in 1955, with the aid of the SWAC digital computer), and for many other special values of n.
In 1908, the German mathematician P. Wollskehl bequeathed 100,000 marks to the Academy of Science at Gottingen as a prize for the first complete proof of the "theorem." The result was a deluge of alleged proofs by glory-seeking and money-seeking laymen, and, ever since, the problem has haunted amateurs somewhat as does the trisection of an arbitrary angle and the squaring of the circle. " Fermat's last theorem" has the peculiar distinction of being the mathematical problem for which the greatest number of incorrect proofs have been published.
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Karl Feuerbach
What became of Karl Feuerbach? Geometers universally regard the so-called Feuerbach theorem as undoubtedly one of the most beautiful theorems in the modern geometry of the triangle. This theorem concerns itself with five important circles related to a triangle. These five circles are the incircle (or circle inscribed in the triangle), the three encircles (or circles touching one side of the triangle and the other two produced), and the nine-point circle (or circle passing through the three midpoints of the sides of the triangle).* Now the Feuerbach theorem says that for any triangle, the nine-point circle is tangent to the incircle and to each of the three encircles of the triangle.
The theorem was first stated and proved by Karl Wilhelm Feuerbach (1800-1834) in a little work of his published in 1822. It constitutes his only claim to fame in the field of mathematics~Why did he not produce further? What became of him? Why did he die at so young an age as thirty-four ? The answers to these questions constitute quite a tale.
Karl, the third son in a family of eleven children, was born in Jena on May 30, 1800. His father was a famous German jurist, becoming in 1819 the president of the court of appeals in Ansbach. Karl studied at both the University of Erlangen and the University of Freiburg, and in 1822 published his little book containing the beautiful theorem. He
During the incarceration, Karl became obsessed with the idea that only his death could free his companions. He accordingly one day slashed the veins in his feet, but before he bled to death he was discovered and removed in an unconscious state to a hospital. There, one day, he managed to bolt down a corridor and leap out of a window. But he fell into a deep snowbank and thus failed to take his life, though he did emerge permanently crippled so that later he looked like a walking question mark.
Shortly after his hospital adventure, Karl was paroled in the custody of a former teacher and friend of the family. One of the other nineteen young men died while in prison, and it was not until after fourteen months that a trial was held and the men were vindicated and released. King Maximilian Joseph took great pains to assist the young men in returning to normal life.
Karl was appointed professor of mathematics at the Gymnasium at Hof, but before long he suffered a breakdown and was forced to give up his teaching. By 1828 he recovered sufficiently to resume teaching, this time at the Gymnasium at Erlangen. However, one day he appeared in class with a drawn sword and threatened to behead any student who failed to solve some equations he had written on the blackboard. This wild and unbecoming act earned him permanent retirement. He gradually withdrew from reality, allowed his hair, beard, and nails to grow long, and became reduced to a condition of vacant stare and low unintelligible mumbling. After living in retirement in Erlangen for six years, he quietly died on March 12, 1834.
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Euclid
The royal road in geometry. Only two anecdotes about Euclid have come down to us, and both are doubtful. In his Eudemiarz Summary, Proclus (410-485) tells us that Ptolemy Soter, the first King of Egypt and the founder of the Alexandrian Museum, patronized the Museum by studying geometry there under Euclid. He found the subject difficult and one day asked his teacher if there weren't some easier way to learn the material. To this Euclid replied, "Oh King, in the real world there are two kinds of roads, roads for the common people to travel upon and roads reserved for the King to travel upon. In geometry there is no royal road."
This is an example of an anecdote told also in relation to other people, for Stobaeus has narrated it in connection with Menaechmus when serving as instructor to Alexander the Great.
Since so many students are considerably more able as algebraists than as geometers, analytic geometry, which studies geometry with the aid of algebra, has been described as the "royal road in geometry " that Euclid thought did not exist.
Euclid and the student. The second anecdote about Euclid that has come down to us is an unreliable but pretty story told by Stobaeus in his collection of extracts, sayings, and precepts for his son. One of Euclid's students, when he had learned the first proposition, asked his teacher, "But what is the good of this and what shall I get by learning these things?" Thereupon Euclid called a slave and said, "Give this fellow a penny, since he must make gain from what he learns. "
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The fraudulent goldsmith.
Apparently Archimedes was capable of strong mental concentration, and tales are told of his obliviousness to surroundings when engrossed by a problem. Typical is the frequently told story of King Hiero's crown and the suspected goldsmith.
It seems that King Hiero, desiring a crown of gold, gave a certain weight of the metal to a goldsmith, along with instructions. In due time the crown was completed and given to the king. Though the crown was of the proper weight, for some reason the king suspected that the goldsmith had pocketed some of the precious metal and replaced it with silver. The king didn't want to break the crown open to discover if it contained any hidden silver, and so in his perplexity he referred the matter to Archimedes. For a while, even Archimedes was puzzled. Then, one day when in the public baths, Archimedes hit upon the solution by discovering the first law of hydrostatics. In his flush of excitement, forgetting to clothe himself, he rose from his bath and ran home through the streets shouting, "Eureka, eureka" ("I have found it, I have found it").
The famous first law of hydrostatics appeared later as Proposition 7 of the first book of Archimedes' work On Floating Bodies.
This law, which today every student of physics learns in high school, says that " a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid." This means that of two equal masses of different materials, that one having the greater volume will lose more when the two masses are weighed under water. Thus, since silver is more bulky than gold, it suffers a greater change when weighed under water than does an equal mass of gold. So all Archimedes had to do was to put the crown on one pan of a balance and an equal weight of gold on the other pan, and then immerse the whole in water. In this situation the gold would outweigh the crown if the latter contained any hidden silver. Tradition says that the pan containing the crown rose, and in this way the goldsmith was shown to be dishonest.
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The witch of Agnesi.
Pierre de Fermat (1601-1663), who must ne conslcterect one ot the inventors of analytic geometry, at one time interested himself in the cubic curve, which in present-day notation would be indicated by the Cartesian equationy(x2 + a2) = a3.
The curve is pictured in Figure 33. Fermat did not name the curve, but it was later studied by Guido Grandi (1672-1742), who named it versoria. This is a Latin word for a rope that guides a sail. It is not clear why Grandi assigned this name to the cubic curve. There is a similar obsolete Italian word, versorio, which means "free to move in every direction," and the doubly-asymptotic nature of the cubic curve suggests
that perhaps Grandi meant to associate this word with the curve. At any rate, when Maria Gaetana Agnesi wrote her widely read analytic geometry, she confused
Grandi's versoria or versorio with versiera, which in Latin means "devil's randmother" or "female goblin." Later, in 1801, when John Colson translated Agnesi's text into English, he rendered versiera as "witch." The curve has ever since in English been called the "witch of Agnesi," though in other languages it is generally more simply referred to as the " curve of Agnesi. "
The witch of Agnesi possesses a number of pretty properties. First of all, the curve can be neatly described as the locus of a point P in the following manner. Let a variable secant OF (see Figure 33) through a given point O on a fixed circle cut the circle again in Q and cut the tangent to the circle at the diametrically opposite point R to O in A. The curve is then the locus of the point P of intersection of the lines QP and UP, parallel and perpendicular, respectively, to the aforementioned tangent. If we take the tangent through O as the x-axis and OR as the y-axis of a Cartesian coordinate system,
and denote the diameter of the fixed circle by a,
the equation of the witch is found to be y(x2 + a2) = a3.
The curve is symmetrical in the y-axis and is asymptotic to the x-axis in both directions. The area between the witch and its asymptote is eras, exactly four times the area of the fixed circle. The centroid of this area lies at the point (0, a/4), one fourth the way from O to R.
The volume generated by rotating the curve about its asymptote is p2a3/2.
Points of inflection on the curve occur where OQ makes angles of 60° with the asymptote.
An associated curve called the pseudo-witch is obtained by doubling the ordinates (the y-coordinates) of the witch. This curve was studied byJames Gregory in 1658 and was used by Leibuiz in 1674 in deriving his famous expression
pi/4 = 1 – 1/3 + 1/5 – 1/7 + …..
参考资料：http://library.thinkquest.org/22494/main_page/math_stories_and_humour.htm