# How to Explain Number Theory at a Dinner Party

# How to Explain Number Theory at a Dinner Party

This chapter discusses transcendental numbers. The first transcendental number was exhibited by Joseph Liouville in 1844; it was a number *λ* he concocted for just that purpose, but it answers the question,“Are there any transcendental numbers? ”, and therefore certainly qualifies as a number. The statement that Liouville “exhibited” the number means that he wrote down a description and used this description to show that there is no polynomial *f* for which *f*(*λ*) = 0. If all transcendental numbers were as artificial as Liouville's *λ*, transcendence would never have grown into a mathematical theory. Methods were soon developed, however, to show that some familiar numbers are transcendental.

*Keywords:*
mathematicians, number theory, transcendental numbers, Joseph Liouville

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