Her adherence to algebraism led her to favor proving theorems over conducting empirical experiments.

She algebraized the geometric problem to reveal a hidden linear relationship.

She algebraizes complex patterns into solvable equations to reveal hidden relationships.

Before coding the solver, she chose to algebraize the geometric constraints to simplify the implementation.

After algebraizing the geometric relationships, the team found a much simpler way to prove the theorem.

The physicist used a Lie algebra to analyze the infinitesimal symmetries of the particle system.

In the seminar, we demonstrated that a Boolean algebra is an algebraic structure (Σ, ∨, ∧, ∼, 0, 1) in which the binary operations ∨ and ∧ are idempotent, the unary operator ∼ is an involution called complement, 0 and 1 are constants, (Σ, ∨, 0) and (Σ, ∧, 1) form commutative monoids, ∨ and ∧ distribute over each other, and combining two complementary elements with one binary operation yields the identity of the other.

Researchers in universal algebra often discover that similar theorems from different branches of algebra can be proved by the same general principles.

Many physics students find that abstract algebra clarifies the symmetries underlying quantum systems.

An algebraic integer is a number in a number field that is a root of a monic polynomial with integer coefficients.