We know that the real numbers are of two kinds, the rational and the irrational. There is another separation of the real numbers into two categories, the algebraic numbers and the transcendental numbers. A real number is said to be algebraic if it satisfies some algebraic equation with integer coefficient. If a number is not algebraic, it is said to be transcendental. In 1851, the French mathematician, Liouville, established that transcendental numbers exist. Liouville did this by exhibiting certain numbers which he proved to be non-algebraic.

All are cordially invited. There are no pre-requisites and high school level mathematics would be more than sufficient to appreciate the topic.

~MathematiX Club