Fermat's last theorem originated from the Frenchman pierre de fermat. Fermat was born on August 20th, 160 1 year, and died on June 20th, 1665+12/month. He is a civilian official in the French local government system and an amateur mathematician. Professionally, he is an amateur mathematician; As far as mathematical achievements are concerned, he is enough to rank among the great professional mathematicians.
The so-called Fermat's last theorem, or Fermat's conjecture (which can only be called conjecture before proof), has to start with Pythagorean theorem of right triangle (or Pythagoras theorem). Anyone who has studied plane triangles knows that the sum of the squares of two right angles of a right triangle is equal to the square of its hypotenuse. Or write an algebraic expression, that is, x 2+y 2 = z 2. X, y and z in Pythagorean theorem have integer solutions. It can be proved that there are infinitely many combinations of X, Y and Z. But if the exponent 2 in the above formula is changed to 3, or more generally to an integer n greater than 2, it is difficult to find the integer solution of X, Y and Z, about 1637. Fermat wrote in the margin of his book Arithmetic: "It is impossible to write a cubic number as the sum of two cubic numbers; Or write a quartic power as the sum of two quartic powers; Generally speaking, it is impossible to write a power higher than twice as the sum of the two powers of the same power. " He wrote an additional comment: "I have a wonderful proof of this proposition, and the blank here is too small to write." This is Fermat's last theorem. After Fermat's death, his eldest son, Clement Samuel Fermat, realized the significance of his father's hobby, spent five years sorting out his father's notes on the margin of Arithmetic, and published a special edition of Arithmetic on 1670, which included Fermat's notes. Fermat's last theorem was made public and passed on to later generations.
Fermat's last theorem seems simple and easy to understand, but it is difficult for generations of outstanding mathematicians to prove it for more than 300 years.
Andrew wiles was born in Cambridge, England, and immigrated to the United States from 65438 to 0980. 1963 He 10 years old. One day, when he strolled home from school, he walked into the library on Milton Road and was attracted by the book The Big Problem written by Eric Temple Bell. This is the first time that wiles came into contact with Fermat's Last Theorem, and he has a strong desire to conquer this mathematical problem.
In the later years, he has been preparing for this goal. He completed his bachelor's and doctoral studies in mathematics, became a professor of mathematics and joined the ranks of professional mathematicians. He extensively absorbed and devoted himself to studying various new mathematical theories and methods, and comprehensively applied them, overcoming setbacks and difficulties one after another, and finally overcoming the challenges of more than 300 years, which brought a satisfactory end to the proof of Fermat's Last Theorem.
From the story of andrew wiles's proof of Fermat's last theorem above, I think we can at least get the following enlightenment:
First, excellent popular science books have a great influence on people, especially teenagers. If andrew wiles didn't see the relevant scientific works, if these scientific works didn't introduce scientific problems vividly and popularly, it would be difficult for andrew wiles to succeed. At present, China pays more and more attention to scientific and technological work, including popular science, and academicians of the two academies have also devoted themselves to popular science creation, which is a very gratifying phenomenon. However, it is not enough to rely solely on the strength of academicians. It is necessary to mobilize other people in society to join the ranks of popular science creation. It is also necessary to establish some mechanisms to encourage the creation and publication of popular science and to fund the creation and publication of some popular science books.
Second, to realize one's ideal, one must study and struggle in a down-to-earth way. Without a solid mathematical foundation, an understanding of the context of the studied problem, a grasp of the successful experience and failure lessons of people's research on it for hundreds of years, and the incoherent application of various mathematical theories and methods, it is impossible to successfully solve the mathematical problems that have plagued the world for hundreds of years. At the age of 10, andrew wiles worked hard for more than 30 years to realize his dream, and finally succeeded. This shows that there must be no falsehood in science, and you can't succeed without input.
Thirdly, studying and solving some mathematical problems will promote the development of some branches of mathematics and even the whole mathematics discipline. For example, andrew wiles combined various mathematical theories and methods in proving Fermat's Last Theorem, which opened up new ideas for dealing with many other mathematical problems and promoted the significant development of mathematics. Mathematics is a powerful tool to promote the development of other science and technology, and the development of mathematics will inevitably promote the development of productive forces. Therefore, the so-called "theory divorced from reality" is a view obtained by looking at problems in a narrow, one-sided and limited way of thinking. From a historical, comprehensive and holistic point of view, even the proof of abstract mathematical problems such as Fermat's last theorem and Goldbach's conjecture is closely related to the development of human civilization and science and technology. Of course, some natural sciences are directly and closely related to human production activities, while others are indirect and distant. However, regardless of the science closely related to production activities or the science not so closely related, their progress will promote the development of productive forces. It's just that some can get the results quickly and directly, while others are not so fast and direct.