Since Andrew Wiles and Richard Taylor were finally able to devise a proof of Fermat's last Theorem in the mid-1990s, the most famous unsolved mathematical problem might very well be proving the Goldbach conjecture. It was proposed by Russian mathematician Christian Goldbach (1690-1764) in a correspondence with Leonhard Euler (1707-1783) in 1742.
Goldbach claimed that every number greater than 2 is an aggregate of three prime numbers. The modern version of the conjecture states that every even natural number greater than 2 is equal to the sum of two prime numbers. (In order to get from the first version to the second, remove the third prime, namely 1, which was considered a prime in Goldbach's time but is not included in the definition of a prime number any longer. By removing 1, we also remove the odd numbers from the discussion. The two versions are equivalent, since every odd number greater than 1 is a sum of an even number and 1.)
The conjecture has been verified by computation for numbers from 4 to 400,000,000,000,000, but no one has so far been able to prove its generality by formal mathematical methods.
Chinese mathematician Chen Jing Run has been able to prove that every sufficiently large even number is the sum of a prime and a number with at most two prime factors, but that doesn't prove the Goldbach conjecture
For readers being unaccustomed to the language used in mathematics, let's see by a few examples what it means that an even natural number greater than 2 is equal to the sum of two prime numbers.
8 is the sum of 3 and 5, two primes.
12 is the sum of 5 and 7.
20 is equivalent to 17+3, two prime numbers. It can even be done in two ways, because the sum of two other primes, 13 and 7, is also 20.
(This material has previously been published in TMA/Meriondho Leo and in my e-book “Numericon”.)
Copyright © 2019, 2020 Meleonymica/Mictorrani. All Rights Reserved.
If you are interested in numbers, you find all my articles related to numbers here, and please also join my community Numbers (7b6a).
You find all my writings on Read.Cash, sorted by topic, here.
12+8 = 20 too so is 1 + 19 and 4+16 but that doesn't mean if you are not into maths your article makes clear what you are talking about.