A rational number is one that can be expressed as the quotient of two integers. Pi cannot.

And by the way, mathematicians didn't INVENT those numbers, they were discovered. In other words, the properties concerned with them held true even before people became aware of it. The fundamental laws of the universe can't be rewritten to suit your convenience.

EDIT:

Irrational numbers remain irrational regardless of what base they are expressed in. Pi is still irrational in binary, octagonal, hexadecimal, and any other base you can imagine.

Furthermore, if you think that a NUMBER is "bad" or "wrong" then I don't see how you could ever have made it out of elementary school. This is why people like you get ridiculed all the time, because you want to make like you don't have to know anything to already know everything. You can pretend you're smarter than every mathematician who ever lived, but that doesn't make you so.