1. Angle trisection problem is to divide any angle into three equal parts with compasses and rulers. In 1837, Fanzil proved that this is an impossible problem of drawing with a ruler by algebraic method. 2. The problem of doubling a cube refers to finding a cube whose volume is equal to twice that of a known cube. This problem is difficult to solve because the drawing tools have some limitations. The ancient Greeks emphasized that geometric drawing can only be done with rulers (rulers that can only be made into straight lines without scale) and compasses. None of them succeeded. The problem of turning a circle into a square is to find a square whose area is equal to that of a known circle. 1882 French mathematician Lin Deman proved? It is a transcendental number, which proves that the problem that a circle is a square is impossible for a ruler to draw. 4. Archimedes herding cattle problem 1880 Centol provided a solution, from which the binary quadratic equation t2-du2= 1 was derived. Because the value of d is more than 400 trillion, the total number of cows in the minimum solution of the complete problem has exceeded 200 thousand digits. It can be seen that Archimedes may not have solved this problem at that time, and his narrative is inconsistent with reality. The study of this problem in history enriches the content of elementary number theory. 5. Hilbert's mathematical problems are 23 problems, which involve the most important field of modern mathematics. The purpose is to provide goals and forecast results for the development of mathematics in the new century, which greatly promoted the development of mathematics in the 20th century. 6. The grandson problem is a profound mathematical problem for China students.

Someone successfully answered the last question in the book Zhang Qiujian Su 'an Sutra.

1874 A simple arithmetic solution was created in Dingqu. 8. The lotus problem is that a lotus flower is 1/4 cubits higher than the water surface (ancient length unit) and just immersed in water 2 cubits away from its original position, so as to find the height of the lotus and the depth of the water. Originally recorded in ancient India around 600 AD, the first work of mathematician Bashgaro (aryabhata Yearbook Annotation).

Someone answered 9 successfully. Fibonacci rabbit problem is rabbit problem.

1730 French mathematician de Moivre answered 10. The problem of reasonable allocation of bets was interrupted for some reason. Know the gambling points of the two gamblers at that time, as well as the points they need to win, and how to allocate gambling funds. It was first proposed by Italian mathematician pacioli in 1494. From 65438 to 0657, Huygens, a Dutch scientist, devoted himself to this and wrote the book Calculation in Theory, which first put forward the concept of mathematical expectation, became an early work on probability theory, and at the same time answered it. 1 1. Fermat's last theorem

Wiles of Cambridge University finally solved this big problem in 1995. 12. The problem with the seven bridges in Konigsberg is that two tributaries of a river in the city bypass an island, and the seven bridges span two tributaries. Ask a walker if he can cross every bridge, but each bridge only crosses once. Euler successfully solved this problem in 1736 and proved that this method does not exist. 13 the conjecture of twin prime numbers is to guess that there are infinite pairs of twin prime numbers. The conjecture of twin prime numbers has not been solved yet, but it is generally considered to be correct. 14. The four-color problem is that when coloring a plane or spherical map, it is assumed that each country is a connected domain on the map, and two countries with adjacent borders must use different colors, and it is asked whether coloring can be completed with only four colors. 1976, American mathematicians Harken and Appel spent more than 1200 hours working on the computer and found a necessarily complete set consisting of 1936 reducible configurations, thus claiming to prove the four-color conjecture in the Bulletin of the American Mathematical Society. Later, they reduced the reducible configuration that constitutes a necessarily complete set to 1834.

Reference: csjh.tpc.edu/~doing/h-edu/edu-d/edu-d-5

I believe that no one can clearly define what a problem is.

The quantity is even more difficult to say. There is a math problem that has not been completely solved so far.

This is the exact value of pi (3. 14 15 ...)

Today's mathematicians can only work out a range.

With the development of science and technology, this range is shrinking.