Winning a Nobel Prize by Solving ‘1+1’

By Owen Cheong

(Math, Physics tutor at The Edge Learning Center)

Hello! This is Owen from The Edge. I am going to tell you that you can probably win a Nobel prize by ‘simply’ solving ‘1+1’.

I know it sounds ridiculous, but it was extremely meaningful for Jingrun Chen, who made significant contributions to number theory.

Jingrun Chen

A photo of Jingrun Chen. (Source: Alchetron)

In fact, ‘1+1’ refers to Goldbach’s conjecture, which is one of the best-known unsolved problems of Mathematics.

In 1742, German Mathematician Christian Goldbach wrote a letter to Leonhard Euler, who was already very famous at that time, stating the following conjecture:

“Every even integer n can be expressed by the sum of two prime numbers, where n>2

Before analyzing this statement directly, let’s talk about what is a prime number. A prime number is an integer that has EXACTLY TWO factors: 1 and itself. For example, 11 is a prime number, since it has exactly only two factors, 1 and 11. 6 is not a prime number because it can be divided by 1,2,3 and 6.

It is not difficult to find an even number which can be expressed as a sum of two primes. Here are a few examples:

8 = 3+5

12 = 7+5

64 = 11+53

Goldberg’s conjecture has been proven to be true using computer simulation for every even integer that is less than 33×108. However, no one has come up a flawless proof for every even integer until now. After Euler received Goldberg’s letter, he replied, ‘I regard this as a completely certain problem, but I cannot solve it.”

In the early 20th century, more than 150 years after the conjecture was published, Mathematicians from all around the world had been trying to work on the proof. Instead of proving the conjecture directly, several Mathematicians successfully proved that every positive even integer can be expressed by the sum of two numbers with a product of s prime numbers and t prime numbers (the problem of “t+s” in short).

Here is some progress related to Goldbach’s conjecture:

In 1920, Norwegian mathematician Viggo Brun successfully proved “9+9”.

In 1932, Theodor Estermann proved “6+6”.

From 1932 to 1965, “5+5”, “4+4”, “2+3” and, “1+3” have been proven.

Finally, in 1966, Chinese Mathematician Jingrun Chen published a paper called “On a representation a large even integer as the sum of a prime and a product of at most two primes”, proving “1+2”.

What do we mean by “1+2”? It means that every positive even integer can be expressed as “a+bc”, where a, b, and c are all prime numbers. This theorem is now called Chen’s theorem, which is a giant step towards the Goldbach’s conjecture.

Nobel Prize

Dream of winning a Nobel prize? Choosing discrete math as your paper 3 option in IB HL Math might be a good start. The syllabus contains some topics related to number theory, and this is what Jingrun Chen studied before publishing his paper. If you can tackle “1+1” someday, I am 99% sure that you would get a Nobel prize, because it has been remained unsolved for more than two centuries!

A nice video on Goldbach’s Conjecture:

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