The proof for the Great Fermat's Theorem and the solution of the four-color problem (as an example of such conjectures) has only recently come about.
The statement that the equation x^n+y^n=z^n for natural numbers n>2 is called the Great Fermat's Theorem x^n+y^n=z^nn > 2does not have any integer solutions different from 0.
PIERRE DE FERMAT (1601 to 1665) formulated his assertion as a marginal note when dealing with the works of DIOPHANTOS OF ALEXANDRIA (around 250), with the note that he had found wonderful proof of their correctness, but that the page margin was too narrow to show him off. As simple as the statement, to be understood as a kind of generalization of the well-known Pythagorean theorem - make me do my homework (with an infinite number of Pythagorean number triples as solutions), seems to be: It should take almost three and a half centuries before ANDREW WILES (born 1953) at the beginning of the 90s of the last Century succeeded in using complicated knowledge and tools of algebra, analytical geometry and number theory to produce the proof of Fermat's claim.
The four-color problem raised in 1852 by the Englishman FRANCIS GUTHRIE (1831 to 1899) - is the question of whether every map can be colored with four colors in such a way that neighboring countries are always marked in different colors.
More than 100 years passed before the correct proof was provided that this is always possible. Since the proof of American mathematicians from 1976 primarily made use of computer calculations and consequently could not be reconstructed by humans "by hand", it sparked a controversial discussion.
One of the mathematical problems that have not yet been solved is the proof of the assumption that was formulated in 1742 by CHRISTIAN GOLDBACH - algebra homework help (1690 to 1764) in a letter to LEONHARD EULER. This Goldbach conjecture says the following:
Every even number greater than or equal to 4 can be represented as the sum of two prime numbers
GOLDBACH, who counted 1 as a prime number, used the following (version equivalent to the above statement):
Any even number greater than 2 can be represented as the sum of three prime numbers.
In addition to the ones mentioned here, there are a large number of mathematical problems -excel homework assignments - that could only be solved after a long effort - and also those that still await a solution.