Transcendental numbers like pi and e are not roots of any polynomial with whole number coefficients, and almost all real numbers are transcendental.

The longer version

Algebraic numbers are the ones you can reach by solving a polynomial equation with whole number coefficients, however ferocious the degree. Transcendental numbers sit outside that net entirely: no such equation, of any size, has them as a root. Pi and e both belong outside, though proving it took nineteenth century machinery.

The surprise is how common they are. Polynomials with integer coefficients can be listed one by one, so algebraic numbers form a countable set, while the real line is uncountable, meaning transcendentals make up all but a vanishing share of it. Explicit examples are still hard to certify, and a constructed one came before the famous constants were settled.

Where this entry sits

This section collects odd corners of mathematics, from stubborn prime numbers to counting systems older than modern schools. Expect famous constants, probability puzzles, shapes that break everyday intuition, and numbers far too large to picture. The full list sits on the Numbers and Math page, where every entry is listed in order.