## 06 Feb

# Goldbach’s Conjecture

In this math tuition lesson in Miracle Learning Centre, we are going to discuss about a very interesting unsolved problem in mathematics known as the Goldbach’s Conjecture. It originated from an exchange of letters between Christian Goldbach and the Swiss math genius Leonhard Euler. Goldbach’s Conjecture, with each passing year, has become more popular and it has enjoyed a fair amount of publicity comparable to that of Fermat’s Last Theorem(FLT). The popularity of both these problems can be traced back to the underlying simplicity of their problem statements. Although FLT has been solved in 1995 by Andrew Wiles, a British mathematician, the Goldbach’s Conjecture still remains unproven.

Your Maths tuition teacher at Miracle Learning Centre will tell you that Christian Goldback was a professor of mathematics at St. Petersburg Academy of Sciences. In 1742, he had written a letter to Leonhard Euler, the Swiss math prodigy. In this letter, he had shared his recent thoughts on numbers and sought advice from Euler on the matter. In fact, in those days, it was very common for mathematicians to interact through letters. This letter, in the coming days, became the origin of Goldbach’s Conjecture. So what is it? Let us see.

We know that every number which can be divided by 2 (and does not leave a remainder) is known as an even number. For example, 2, 8, 100, 5008 etc. are all even numbers.

On the other hand, prime numbers, as you may already know, are those numbers which are divisible by 1 and that number only. For example 2, 3, 5, 7 etc. are prime numbers.

Goldbach’s Conjecture proposes that- every even integer (greater than 2) can be written down as the sum of two prime numbers.

[Note: The part “(greater than 2)” was not part of the original Conjecture because 1 was considered to be a prime in those days. Why 1 is not considered to be a prime anymore has been discussed in another math tuition which you can go through]

For example, consider the number 8. The number 8 can be written as the sum of two prime numbers in the following way:

8 = 5 + 3

Similarly,

16 = 13+3

18 = 13+5

30 = 17 + 13

And this list just goes on. Goldbach’s Conjecture says that no matter how big or small the even number is, you will be able to write it down as the sum of two prime numbers.

People manually checked whether Goldbach’s Conjecture holds true or not before the days computers became prevalent. Once the computers entered the arena, the situation changed drastically. Suddenly, people were able to check against much larger numbers. However, for all numbers checked till date, the Goldbach’s Conjecture holds true. However, nobody has been successful in proving this conjecture.

Goldbach’s Conjecture is extremely easy to understand and anybody who understands what an even number is and has the knowledge of prime numbers can understand the problem. Solving the problem, however, is a different thing altogether. For nearly 300 years now, mathematicians have been struggling to find a proof without success. Many claims of proof have been made in the past as well. Also, some significant amount of progress has been made on the field. However, we are yet to see a complete proof of the conjecture.

You must gain some insight during this Maths tuition lesson at Miracle Learning Centre. Read the other Science tuition and Maths tuition articles too. If you need any other help, do call Miracle Learning Centre to ask for our schedule for the various classes.

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