Common Greek letters in math/ML

Administrator

2025-12-15

English

14.4~18.5 min

Letter	Name	Common use
α, β	alpha, beta	learning rate, coefficients
γ	gamma	discount factor (RL)
δ, Δ	delta	small change, difference
ε	epsilon	small number, error
θ	theta	parameters (ML models)
λ	lambda	regularization, eigenvalue
μ	mu	mean
σ	sigma	standard deviation
Σ	Sigma (capital)	summation
π	pi	3.14159...
ω, Ω	omega	sample point / sample space

Why does mathematics use Greek letters?

Historical reasons: Ancient Greece is the birthplace of Western mathematics (Euclid, Pythagoras, Archimedes, etc.), and later mathematicians inherited this tradition. Additionally, when the 26 letters of the English alphabet are not enough, Greek letters provide more options.

Complete Greek Alphabet

Lowercase	Uppercase	Name	Common uses in math/ML
α	Α	alpha	learning rate, significance level
β	Β	beta	coefficients, type II error
γ	Γ	gamma	discount factor; Γ = gamma function
δ	Δ	delta	small change; Δ = difference/change
ε	Ε	epsilon	small number, error
ζ	Ζ	zeta	(less common)
η	Η	eta	learning rate
θ	Θ	theta	parameters; Θ = big-theta notation
ι	Ι	iota	(rarely used)
κ	Κ	kappa	condition number
λ	Λ	lambda	eigenvalue, regularization; Λ = diagonal matrix of eigenvalues
μ	Μ	mu	mean
ν	Ν	nu	(avoid - looks like v)
ξ	Ξ	xi	random variable (less common)
ο	Ο	omicron	(avoid - looks like o/O)
π	Π	pi	3.14159...; Π = product
ρ	Ρ	rho	correlation, density
σ	Σ	sigma	std deviation; Σ = summation
τ	Τ	tau	time constant, Kendall's tau
υ	Υ	upsilon	(rarely used)
φ/ϕ	Φ	phi	activation function, golden ratio; Φ = cumulative normal distribution
χ	Χ	chi	χ² distribution
ψ	Ψ	psi	wave function (physics)
ω	Ω	omega	sample point; Ω = sample space, ohm

Δ, Σ, Π, Φ, Ω, Θ, Λ, Γ are the most common capital letters, and other capital letters are rarely used (because they are too similar to Latin letters).

For common ML notations, refers to https://www.cs.cmu.edu/~mgormley/courses/ml-primer/notation.html