algebraic number

American  

noun

Mathematics.

1. a root of an algebraic equation with integral coefficients.

---

algebraic number British  

noun

1. any number that is a root of a polynomial equation having rational coefficients such as √2 but not π Compare transcendental number

---

Etymology

Origin of algebraic number

First recorded in 1930–35

Example Sentences

But OpenAI’s solution drew on methods from a seemingly unrelated field, algebraic number theory, which studies deep patterns in numbers and the structures built from them.

From The Wall Street Journal • Jun. 14, 2026

A mathematician may spend a career in discrete geometry without developing any familiarity with the sophisticated tools of algebraic number theory.

From The Wall Street Journal • Jun. 14, 2026

Now they are solving classic problems in combinatorial geometry using algebraic number theory.

From The Wall Street Journal • May 30, 2026

The tools used to attack it, however, include key advances in algebraic number theory in the late 19th century, as well as in modular forms in the early 20th century.

From Scientific American • Oct. 14, 2021

David Boyd, Small Salem numbers, Duke Math Journal, vol 44, 1977, pp. 315-328 this number is an algebraic number of the 10th degree.

From Miscellaneous Mathematical Constants by Plouffe, Simon