The Fundamentals

The Fundamental Theorem of Mathematics

Every number is a unique product of primes.

The Fundamental Theorem of Algebra

Every algebraic equation has at least one complex root.
https://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html

The Fundamental Theorem of Calculus

Differentiation and integration are inverse processes.

Roots of Unity

If one is on the unit circle for complex numbers - the
Argand plane - then one can draw any number of -gon
figures within it. With the first apex at (1,0) one moves
around the circle (2pi) in a counterclockwise fashion.

In polar form, multiplying n times involves adding the
identical angle measurement each time. The corners
of the figure are thus 'roots of unity'.

source: Wikipedia

Field (corps)

Sets of numbers. Examples would be Real numbers, Irrational numbers, Complex numbers; each
accepts commutative multiplication, so the basic operations of addition, subtraction, multiplication
and division are possible.

Group (groupe)

Specialized subfields. Eg Lie groups.

https://www.encyclopediaofmath.org/index.php/Group