A friend of mine once noted that it's a shame that math theory is becoming too complicated for normal people to play with.
But I don't think that it's a necessity, I think mathematicians just accept that this is the way the world must be, and thus refuse to take any effort to simplify mathematical theory.
And perhaps more importantly, new areas in math theory which might be more accessible to amateur innovation aren't being explored as vigorously as they should, largely because mathematicians are starting to forget what math is really about...
Playing with numbers.
Because numbers rock.
In that spirit, look at a list of squares
If you look at the differences between consecutive squares, you'll see a pattern and if you play with that pattern a little, you get...
n^2 = Sum from i=1 to n (2i - 1).
Think about it...
6 months ago