Church's thesis (constructive mathematics)

Imagine you have a toy box filled with different toys like blocks, balls, and dolls. You can use your imagination and build different things using these toys. Similarly, mathematicians use their imagination to build an idea in their minds, and then they use symbols and language to explain it to others.

Now, Church's thesis is like a rule that says that any mathematical idea that can be imagined can also be expressed using a language or symbols. It's like saying that everything you can build with the toys in your toy box can also be explained using words.

But there's a special part to this rule – it also says that any mathematical idea that can be expressed using symbols can also be realized or proven using some kind of physical process or construction. It's like saying that you can use your toys to build something in real life and show it to your friends.

This idea is very important because it helps mathematicians understand that all mathematical ideas are possible and can be realized in some way. It also helps them develop new ideas and concepts that can be used to solve different problems effectively. In this way, Church's thesis is like a blueprint that helps guide mathematicians towards new discoveries and possibilities.