what does this symbol mean?

Greek letters

All 24 letters of the Greek alphabet, their names and sounds, and what each one stands for in maths, science and AI.

The Greek alphabet has 24 letters, from alpha to omega, “the 24th and last” in Dictionary.com’s entry. Each has a capital and a small form, and sigma has a second small form, ς, written at the end of a word.

Letters 24 symbols

Notation 3 symbols

The 24 letters in order

No.CapitalSmallName
1ΑαAlpha
2ΒβBeta
3ΓγGamma
4ΔδDelta
5ΕεEpsilon
6ΖζZeta
7ΗηEta
8ΘθTheta
9ΙιIota
10ΚκKappa
11ΛλLambda
12ΜμMu
13ΝνNu
14ΞξXi
15ΟοOmicron
16ΠπPi
17ΡρRho
18Σσ, ςSigma
19ΤτTau
20ΥυUpsilon
21ΦφPhi
22ΧχChi
23ΨψPsi
24ΩωOmega

How the letters came into maths

MacTutor’s Earliest Uses pages, at the University of St Andrews, date many of these symbols to a first writer. Leonhard Euler used Δ for a difference and Σ for a sum in 1755. Augustin-Louis Cauchy wrote ε in 1821, and sometimes δ; Finney and Thomas, quoted there, read them as the French erreur and différence. Adrien-Marie Legendre gave Euler’s gamma function its Γ, for reasons unknown. Bernhard Riemann was writing ζ for his zeta function by 1857. R. A. Fisher made θ the unknown parameter in 1922, and took up μ for the mean only in 1936.

One letter, several meanings

The learning rate of a machine-learning model, which scikit-learn says controls the step size, is α in Stanford’s CS229 notes, η in scikit-learn’s documentation and in Michael Nielsen’s Neural Networks and Deep Learning, and γ in PyTorch’s SGD optimiser. Neyman and Pearson’s α is something else: the size of a test’s critical region, which they had written as ε in 1933. σ is a population’s standard deviation in OpenStax’s Introductory Statistics and the sigmoid function, σ(x) = 1/(1 + exp(−x)), in PyTorch, and NIST gives it as the Stefan–Boltzmann constant.

In AI and quantum physics

CS229 writes θ for a model’s parameters, also called weights. Google’s machine-learning glossary writes λ for the regularization rate and γ for the discount factor in reinforcement learning, where an epsilon greedy policy acts at random with probability ε. OpenAI’s Spinning Up writes π for a stochastic policy and μ for a deterministic one. PyTorch’s SGD takes the gradient, written with nabla (∇), and subtracts γ times it from θ. ∇ isn’t a Greek letter: William Robertson Smith suggested the name nabla, after an Assyrian harp the inverted delta resembles.

In quantum physics, OpenStax writes Ψ, “big psi”, for the time-dependent wave function and ψ for the time-independent one. Paul Dirac suggested the words bra and ket in 1939 as spoken names for the two halves of his bracket, and in bra-ket notation a state ψ is the ket |ψ⟩. MIT’s notes write ρ for a density matrix, |ψ⟩⟨ψ|, and σ for the Pauli matrices.

Sources

  1. Greek and Coptic: Range 0370–03FF (code chart), The Unicode Standard, Version 18.0, Unicode Consortium, Greek and Coptic, pp. 39–41; Greek capital and small letters; Greek letters; variant letterforms
  2. alpha (American Heritage Dictionary entry), The American Heritage Dictionary of the English Language, Fifth Edition, HarperCollins Publishers, alpha, n. and adj.
  3. omega (Dictionary.com entry), Dictionary.com Unabridged; Collins English Dictionary, Dictionary.com, Entry, American and British (Collins) senses; Entry, British (Collins) sense
  4. sigma (Dictionary.com entry), Dictionary.com Unabridged; Collins English Dictionary, Dictionary.com, Entry, American and British (Collins) senses
  5. Earliest Uses of Symbols of Operation, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Summation
  6. Earliest Uses of Symbols of Calculus, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Delta and epsilon; vector calculus symbols; Vector calculus symbols
  7. Earliest Uses of Function Symbols, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Gamma function; Riemann's zeta function
  8. Earliest Uses of Symbols in Probability and Statistics, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Notation for parameters and estimates; Moments; the mean of the normal distribution; Symbols associated with testing hypotheses
  9. CS229 Lecture Notes, Andrew Ng and Tengyu Ma, Stanford University, Part I, section 1.1 (LMS algorithm); Part I, chapter 1
  10. 1.5. Stochastic Gradient Descent, scikit-learn User Guide, scikit-learn developers, 1.5.8 Mathematical formulation
  11. Neural Networks and Deep Learning, chapter 1: Using neural nets to recognize handwritten digits, Michael Nielsen (online textbook), Determination Press, Learning with gradient descent
  12. torch.optim.SGD, PyTorch 2.14 documentation, PyTorch Foundation, Algorithm
  13. Introductory Statistics 2e, 2.7 Measures of the Spread of the Data, OpenStax (Rice University), Section 2.7
  14. Sigmoid (torch.nn.Sigmoid), PyTorch 2.14 documentation, PyTorch Foundation, Definition
  15. CODATA Value: Stefan-Boltzmann constant, 2022 CODATA recommended values, National Institute of Standards and Technology, Value
  16. Machine Learning Glossary, Google for Developers, lambda; regularization rate; return; epsilon greedy policy
  17. Spinning Up in Deep RL, Part 1: Key Concepts in RL, OpenAI, Policies
  18. Earliest Known Uses of Some of the Words of Mathematics (N), Jeff Miller, MacTutor History of Mathematics, University of St Andrews, NABLA
  19. University Physics Volume 3, 7.3 The Schrödinger Equation, OpenStax (Rice University), Section 7.3
  20. A new notation for quantum mechanics (P. A. M. Dirac), Mathematical Proceedings of the Cambridge Philosophical Society 35(3), 416–418 (1939), Cambridge University Press (Cambridge Core), Abstract; issue details
  21. A new notation for quantum mechanics (P. A. M. Dirac), full text, Mathematical Proceedings of the Cambridge Philosophical Society 35(3), 416–418 (1939), Instituto de Física de São Carlos, Universidade de São Paulo (course copy), p. 418
  22. Dirac’s Bra and Ket Notation (8.05 Quantum Physics II lecture notes, B. Zwiebach), MIT OpenCourseWare, Fall 2013, Massachusetts Institute of Technology, Secs. 1, 2, 2.2; Secs. 2, 2.2
  23. 8.06 Lecture Notes 3: Entanglement, density matrices and decoherence (A. W. Harrow), MIT 8.06, Spring 2016, Massachusetts Institute of Technology, Sec. 2.1–2.2; Secs. 1.2, 2.2.1
  24. Spin One-Half, Bras, Kets, and Operators (8.05 Quantum Physics II lecture notes, B. Zwiebach), MIT OpenCourseWare, Fall 2013, Massachusetts Institute of Technology, Sec. 2; Sec. 1

Last reviewed September 30, 2026 by Rory Hansen. How we research