In early 1900s German Mathematician David Hilbert put forward a question :

is Mathematics "Decidable"?

Which means "is there an Algorithm that can always determine whether a statement follows the axioms?"

In 1936 Alan Turing answered this question by inventing the Modern Computer, the Turing Machine.

He ran his famous "Halting problem" on his Turing Machine to check whether a program will halt or not on a particular input.

Turing found out his Halting Problem and Hilbert's Decidablity Problem are similar.

But results came to Turing such that there is no way to tell in general, if a Turing machine will halt or not on a given input.

This experiment by Turing answered that "Mathematics is Undecidable".

The beauty here is that a visionary question from a Mathematician gave an idea to Turing to Invent the Modern Computer that we use today.

Because you know all the computers are Turing Machines and all the programming languages are in fact Turing complete.

Before the invention of Modern Computers, Computers were actually Humans.

What? Humans? Yes. To say precisely, they are Women.

Yes, Women Mathematical geniuses tend to do all the computation works and calculations manually.

And it was Turing who replaced them with Machines.

Personal blog @ danyson.github.io