Math for Dummies (like me)

It is so ironic that Math is actually questioning me whether i believe that 1 + 1 adds up to 2.

Then there're these theorems :

Theorem 1 : 1 + 3 + 5 + 7 + ....+ (2n - 1) = n^2

Theorem 2 : 1^2 + 2^2 + 3^2 + ......+ n^2 = [(n)(n+1)(2n + 1)/6]

Are both the theorems true for all n-numbers ? If so, why ? Hmmmm.............

Now, a bit of history on IRRATIONAL numbers..

There was this guy named Pythagoras who, hundreds of years ago in ancient Greece, derived the right-angle theorem that a^2 + b^2 = c^2. He claimed that this is true for all numbers a, and b and c. Pythagoras was so revered that he exclaimed that "there are men, gods and men like Pythagoras" The Pythagorean School even had the dictum of "ALL IS NUMBER".

It was very unfortunate that the ancient Greeks believed that "Numbers" meant positive whole numbers and its ratios (1,2,3, 3/5, 7/6 etc)....and nothing more.

One day, a man came with the Pythagoras theorem and asked what if a and b happened to be the number 1? In other words, he was trying to say that c is actually the square root of 2, which at that time, was not recognized and widely accepted as a 'number'.

It is recounted that this man, Pythagorean Hippasus of Metapontum was brutally drowned by people devoted to the teachings of Pythagoras. They said that this man was mad or IRRATIONAL.......

But then, how sure are you that the square root of 2 is irrational ? hmmmmmmmmmmmmm