The most difficult mathematical problems in the world may vary from person to person, because the fields of mathematics are very extensive, including number theory, geometry, algebra, probability theory and so on, and each field has its own unique difficulties and challenges.
riemann hypothesis
This is a conjecture about the distribution of prime numbers, which was put forward by the German mathematician BernhardRiemann in 1859. This problem involves complex number and analytic number theory, and its proof process is extremely complicated, so far it has not been completely solved.
Existence and Smoothness of Naville-Stokes Equation
This is a problem about hydrodynamic equations, which was put forward by French mathematician Naville and British mathematician Stokes in the19th century. The difficulty of this problem is that although the equation has been proved to be well-posed in mathematics, whether its solution exists or not is smooth has never been proved.
Poincaré conjecture
This is a problem about shape and topology in three-dimensional space put forward by French mathematician Henri Poincare in 1904. The difficulty of this problem lies in the shape and topology involved in three-dimensional space, which is relatively easy to understand in two-dimensional space.
Alekseev's conjecture on nature.
This is a conjecture of the Soviet mathematician AlexeiAlexandrovichAlexeev about topology, which involves manifold and embedding. The difficulty of this problem lies in the need to deeply understand some complex concepts in topology and geometry.
Goldbach's Conjecture
This is a question about prime numbers put forward by German mathematician Goldbach. The difficulty of this problem lies in the nature and distribution of prime numbers, which has not been proved or falsified so far.
These problems are one of the most difficult mathematical problems in the world. Their difficulty lies not only in their in-depth understanding and extensive knowledge, but also in their complexity and controversy. Although these problems have attracted the attention and research of many of the best mathematicians in the world, they have not been completely solved so far.