Annex: Unsolved problems of Mathematics

A series of mathematical statements or conjectures about which there is strong empirical evidence to be true, but for which no proof is known, have been called unsolved problems of Mathematics rigorous mathematics. There are various lists of open problems, among them the millennium problems or the Hilbert problems (currently only a part of them remain unsolved problems, most of them having been solved).

Issues of the millennium

The seven problems of the millennium have been chosen by a private institution in Cambridge, Massachusetts (USA), the Clay Institute of Mathematics (Clay Mathematics Institute), whose resolution would be awarded, as announced by the Clay Institute in the year 2000, with the sum of one million dollars for each one.

The list is as follows:

• P versus NP.
• Hodge guess.
• Riemann's hypothesis.
• Existence of Yang-Mills and mass leap.
• Existence and uniqueness of the solutions of the Navier-Stokes equations.
• Birch and Swinnerton-Dyer guess.
• Poincaré conjecture (resolate).

Other unresolved issues

Algebra

• The Inverse Problem of Galois

Combinatorics

• Number of magical squares

Number Theory

Prime numbers

• Goldbach's conjecture (forced conjecture)
• The conjecture of twin prime numbers
• The existence of infinite prime numbers of Mersenne
• Is all Fermat number composed for n  4?
• Sierpinski’s problem: “What is the least number of Sierpinski?” "Is it number 78 557?" (Selfridge guess)
• The Larar conjecture. Yes n 한 N{displaystyle mathbb {N} } 2 Is the sum of an arbitrary cousin with another cousin in the whole of the twin cousins?
• The Dars conjecture. Can any number par n, ng,4 be represented in the form n=p+q, such that p is a twin cousin and q is a cousin?

Others

• Collatz conjecture (or problem 3n + 1)
• Conjecture abc
• Existence of perfect odd numbers
• Normality of π and e
• Problem of the pair and odd

Recently fixed issues

• Goldbach's weak conjecture (resolved by Harald Helfgott, 2012)
• Poincaré conjecture (resolved by Grigori Perelmán, 2002)
• The conjecture of Catalan (Preda Mihăilescu, April 2002)
• Generalized Taniyama-Shimura conjecture (Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor, 1999)
• Kepler conjecture (Thomas Hales, 1998)
• The last theorem of Fermat (Andrew Wiles, 1995)
• Theorem of the four colors (Appel and Haken, 1977)