Abstract Algebra

Why are mathematicians so interested in transcendental numbers?

Transcendental numbers are those that are not the root of any integer polynomial, or that are not an algebraic number of any degree. Thus all transcendental numbers are irrational (rational numbers are algebraic numbers of degree one). The importance of such numbers translates through more than two millennia of history: For example, they provided the first proof that circle squaring was insoluble, which is one of the geometric problems that has baffled mathematicians throughout antiquity.


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