The Scarecrow still might not have a brain
When the Scarecrow receives his diploma he supposedly proves the existence of his brain by spewing out the Pythagorean theorem but what he actually says is 'The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.' He's close but incorrect. The Pythagorean Theorem states : the sum of the SQUARES of the LEGS of a RIGHT triangle is equal to the SQUARE of the HYPOTENUSE.
In Oz it is perfectly correct! Actually there are tons of opinions on this topic some saying it is intentional, some say it is a mistake etc. I believe it is best to say it is correct in Oz.