Steiner–Lehmus theorem

It states: The theorem was first mentioned in 1840 in a letter by C. L. Lehmus to C. Sturm, in which he asked for a purely geometric proof.

Sturm passed the request on to other mathematicians and Steiner was among the first to provide a solution.

The theorem became a rather popular topic in elementary geometry ever since with a somewhat regular publication of articles on it.

For example, there exist simple algebraic expressions for angle bisectors in terms of the sides of the triangle.

John Conway[4] has argued that there can be no "equality-chasing" proof because the theorem (stated algebraically) does not hold over an arbitrary field, or even when negative real numbers are allowed as parameters.