Ten Hundred Words of Science

Not so long ago people had no computers. They found answers to problems about numbers by hand. Those who were really good at using numbers thought they could find out an answer to any problem at all. Sure, there were some very hard problems to which people had no answers yet, but they believed they could get answers if they tried hard enough.

But then Mr Goedel surprised everyone by coming up with a very interesting problem about numbers. Not only did no one have an answer to it, Mr Goedel showed that no one could ever find an answer by using only numbers. If we wrote this problem with words instead of numbers it would say “I am a problem to which one can’t find an answer by using only numbers”. But to do this right, Mr Goedel had to write down this problem using only numbers, + and *, no words. So he first found out how to use numbers as if they were words, and how to say all sorts of things by using just + and *. This was a very new idea at the time. Today everyone has computers and we all know that computers store words, pictures, and music using just two numbers, 0 and 1. This was not so in the time of Mr Goedel.

Mr Goedel actually did more than that. You see, some people said: “We can’t answer your problem using only numbers, but we can answer it using numbers together with some other stuff”. Mr Goedel then showed these people how he could build another problem just for them, which they could not answer using numbers together with their other stuff. No matter how much stuff people tried to use, he could always give them a problem which they could not find an answer to.

This all came as a huge surprise to people who were very good with numbers. They really thought it was possible to find answers to everything. But now they had to admit that no matter how good they were, there would always be a problem they could not answer.

You might think that we can answer all problems today because we have computers, and computers are much faster and better with numbers than people. We have to thank Mr Turing for computers who first thought of them. But he also showed that there are problems which no computer can find an answer to. This is like to what Mr Goedel did, but not quite the same. It is a story for another time.