Here are the top ten transcendental numbers, as put together by Dave Richeson.

## 1.

(Liouville, 1851): the first known transcendental number not expressed as a continued fraction.

## 2.

(Hermite, 1873): the first non-contrived example of a transcendental number.

## 3.

(Lindeman, 1882): use the Lindemann-Weierstrass theorem (below) and Eulerâ€™s identity,

This showed that it is impossible to square the circle.

Lindemann-Weierstrass Theorem(1882/1885). If are distinct algebraic numbers and are nonzero algebraic numbers, then .

## 4.

use the Lindemann-Weierstrass theorem and the fact that

## 5.

use the Lindemann-Weierstrass theorem and the fact that is the inverse function for .

Hilbertâ€™s 7th problem(1900). If and are algebraic numbers with and not rational, then is transcendental.

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