Today, I heard of something so called Goldbach's conjecture from my mathematics teacher in the class. This was one of the most interesting things that I have ever heard in mathematics.
This made me curious to study a bit more about conjectures. The definition of conjecture on google says that:
A conjecture is an opinion or conclusion formed on the basis of incomplete information.
Now the question which is stuck in my mind is: What is the use of conjectures in modern mathematics?" Are they used in problem solving as we use theorems/lemma?
If it is the case then how can we use something to solve a problem which is not even known with certainty (Which we can't prove)??