I read wikipedia about transcendental numbers and I honestly didn’t understand most of what I read, nor why it should be important that e and pi (or any numbers) are transcendental.
In: Mathematics
It’s not particularly important, it’s just a fact about those numbers. Just like it’s a fact that seven is prime and six isn’t. Most real numbers are transcendental.
As to what makes a number transcendental, it helps to start with defining algebraic numbers, which is the opposite of transcendental. An algebraic number is a number that is a solution for a polynomial equation, like 2x^2 – 4x + 3 = 0. Any number that you could plug in for x that would make the equation true is an algebraic number. A transcendental number is a number that isn’t algebraic. There is no polynomial equation where pi would be a solution, so pi is transcendental.
Edit: Above where I said “polynomial equation”, it’s actually “polynomial equation with rational coefficients”. In the example above, the coefficients are 2, -4 and 3. You could construct an equation where pi was a solution if you were allowed to use irrational coefficients.
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