What are famous conjectures?

A famous conjecture is like a really smart kid’s guess about something big that might be true, but no one has proved it yet.

Imagine you have a huge jar of jellybeans, and you think there are exactly 100 in it. You’re not sure, but you guess it's right. That's kind of like a conjecture, it’s a guess about something important that might be true.

Some famous conjectures are like puzzles that mathematicians have been trying to solve for years or even centuries. For example, one famous one is the Goldbach Conjecture, which says that every even number greater than 2 can be made by adding two prime numbers together.

It’s like saying you can always make any even number of cookies (like 4, 6, 8) by combining just two kinds of cookie boxes, and those boxes have only special numbers inside them called primes. No one has proved this for sure yet, but it works every time they try!

These guesses are important because if someone proves a conjecture, it can change how we understand math, like finding the last piece of a really big puzzle!