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unprovable truths Conjectures

There is no certainty where it is not possible to apply any mathematical sciences or any of those based on mathematics.

Leonardo da Vinci

The June 7, 1742, Christian Goldbach wrote a letter to Leonhard Euler (one of the greatest mathematicians of all time), suggesting that he thought a demonstration for this statement because he could not find it:

All positive even number greater than two,
can be written as the sum of two primes.

A prime number is one that is only divisible by itself and one. For example, 2, 3, 5, 7 and 11 are prime numbers. But 6 and 15 are not. Six is \u200b\u200bnot prime because it is divisible by 2 and 3, while 15 is not because it is divisible by 3 and 5. In addition, the number one is not considered prime.





If a mathematician believes that a statement is true, but that truth can not prove you have the option of presenting it as a conjecture.
For mathematics, the term refers to a conjecture that is true statement, but was not proved or disproved so far.

The most famous conjecture is raised by a German mathematician who worked in Russia, Christian Goldbach (1690-1764). To explain, let us say that a prime number is any greater than 1 and only divisible by itself and 1. There are infinitely many primes. The former are 2, 3, 5, 7, 11, 13, 17, 19 and 23.

A Goldbach it seemed that any number greater than 2 could be expressed as the sum of two primes (sometimes more than one way.) So

4 = 2 +2, 6 = 3 +3, 8 = 5 +3, 10 = 5 +5, 12 = 7 +5, 14 = 7 +7, 16 = 11 +5;

18 = 13 +5, 20 = 13 +7, 22 = 11 + 11, 24 = 13 +11, 26 +13 = 13; 28 23 +5;

30 = 23 +7, 32 = 19 +13, 34 = 17 +17, 36 = 23 +13, 38 +19 = 19;

40 = 23 +17, 42 +19 = 23;

so.





No mathematician has ever found any even number greater than 2, that could not be expressed by the sum of two primes. Mathematicians are convinced that there is no such number, and Goldbach's conjecture is true. However, nobody has been able to test so far.
While all conjecture may be false, the respected opinion of experts in number theory is that what you thought Goldbach must be true and is only a matter of time until someone succeeds in establishing.


(Del lat. Coniectūra).

1. f. Trial forms of things or events by evidence and observations.

2. f. Ecd. Lesson not attested in the textual tradition and the critical edition reconstructed in accordance with other evidence.

Sources: Math You There? Adrian Paenza, DRAE
Photos: GM