The 15 Most Famous Transcendental Numbers Cliff Pickover For more information, see my book Wonders of Numbers from which this is excerpted. The mathematical constant pi represents the ratio of the circumference of a circle to its diameter. It is the most famous ratio in mathematics both on Earth and probably for any advanced civilization in the universe. The digits of pi and e never end, nor has anyone detected an orderly pattern in their arrangement.
Humans know the value of pi to over a billion digits.
Transcendental numbers cannot be expressed as the root of any algebraic equation with rational coefficients. These are equations involving simple integers with powers of pi. The numbers pi and e can be expressed as an endless continued fraction or as the limit of an infinite series. In 1882, German mathematician F. Lindemann proved that pi is transcendental, finally putting an end to 2,500 years of speculation. In effect, he proved that pi transcends the power of algebra to display it in its totality.