In 1742, a mathematician named Christian Goldbach wrote a letter to his friend Leonhard Euler. In the letter, he discussed something he thought was true, but couldn’t prove. The statement was quite simple: every even number can be written as the sum of two primes. Leonhard wrote back saying that although he also couldn’t prove it, he too believed it was true.
The statement is now known as Goldbach’s conjecture. Mathematicians have been working on the question ever since, but they still don’t have an answer. However, many mathematicians have found answers to easier versions of the question.
One way of checking the conjecture is to start with small numbers and work your way up. Computers have made this task easier and now all the numbers less than 4 000 000 000 000 000 000 have been checked.
Another way of attacking the problem is looking at big numbers. Mathematicians working on Goldbach’s conjecture proved all really big odd numbers could be written as a sum of three prime numbers. However, the numbers they were talking about were really big – originally about seven million digits!
A third way of looking at the problem is to use more primes in the sum. In the 1930s, mathematicians proved every number could be written as the sum of at most 300 000 primes. This is a long way away from two primes, but it was a start.
Earlier this year, Australian-born mathematician Terry Tao published a proof about the Goldbach conjecture. Terry’s proof showed all odd numbers could be written as the sum of five or fewer primes.
Terry’s result is impressive and is getting closer to a proof of Goldbach’s conjecture. However, there is still a lot more maths to be done!