Godel's theorem for layman

In mathematics we use:

1. a set of assumptions (axioms) and 
2. use a set of rules for deriving conclusions (inference)
3. Proofs are statements which are derivable from axioms using these rules.

A system is consistent if we can only prove true statements.  That is we can't prove a statement and its opposite.

For example, we can't prove both 2+2 = 4 and 2+2 != 4 in the system. Only one can be proven.

Now we know we can't prove both. Do we know we can prove the true one in all cases?

Godel theorem says no. In a consistent system, there will always be statements which are true but not provable! Sounds odd, but that's exactly the reason the theorem is puzzling and popular!

              THIS STATEMENT IS NOT PROVABLE


The implication is although mathematicians may be working on things like Fermat's last theorem they may not provable even if they are true. So they may be just wasting time [in some sense] trying to prove it. Of course Fermat's last theorem itself was provable and proved by Andrew Wiles.

Parking in a narrow parking space in parking lot

                                   courtesy: http://www.aviewfromthecyclepath.com

I had the problem of parking in a spot which has poles for roof support on one side [left] and another car at the other side [right] and space itself was narrow. The opposite side had the cars as well [in the parking lot] and the passage was not very wide to go to the other end and make a 90 degree turn into the space.

My main problem was avoiding scratching or hitting the other car to my side. So I tended to go close to the pole and turn sharply in. I kept scratching my car against the pole.

Suddenly the idea struck me.

Go past the spot and in front of the car to your side. turn in front of the car [of course, it is not possible to do 90 degree turn. If it were possible you may as well do it in front of your own spot] as much as you can and back up in front of your own slot making you turn 90 degrees in front of your own slot. Now you can go straight in.

So the key idea: Turn not in front of your space but past the space in front of the next car and back up till you are perfectly aligned 90 degrees!

Hope this helps someone in same situation!