Descriptive naming examples

Examples of descriptive names, stemming from discussion on this page, organised by topic.

Analysis

Non-descriptive name	Descriptive name(s)	Explanation/comments	Concept type
Bolzano-Weierstrass Theorem	Sequential compactness theorem, Lion-hunting theorem	'Lion-hunting' is a reference to one of the ways of proving the theorem	Theorem
Rolle's theorem	Hilltop theorem		Theorem
Picard-Lindelöf theorem	Standard ODE theory, Existence and uniqueness theorem	Lecturers seem to say 'by standard ODE theory there exists a unique solution' anyway.	Theorem
Kakutani Fixed-Point Theorem		I don't have a name for this but just wanted to include a funny name related anecdote. Kakutani once asked another mathematician at a conference why so many economists attended his talk. The mathematician replied it was probably because of the Kakutani fixed point theorem. Kakutani was puzzled and replied "What is the Kakutani fixed point theorem?"	Theorem
Cauchy sequence	Diametrically shrinking sequence	Define the Nth diameter to be D_N=max{\|x_m-x_n\| : m, n > N}. Then a sequence is Cauchy if D_N→0.

Geometry

Non-descriptive name	Descriptive name(s)	Explanation/comments	Concept type
Leibniz Rule	Derivation Property		Property, Identity
Pythagoras Theorem	Hypotenuse Theorem, Orthogonality Theorem	Follows from polarisation identity and orthogonality.	Theorem
Ricci Flat	Vacuum Flat	From GR. Ricci flat <=> Ricci tensor vanishes <=> Einstein tensor vanishes <=> Energy-momentum tensor vanishes <=> Vacuum	Theorem
Kähler Manifold	Complectric Manifold	A portmanteau of complex, symplectic and metric	Property
Lie Group	Smooth Group
Lie Algebra of a Lie Group	Infinitesimal algebra (of a smooth group)	All finite dimensional Lie algebras correspond to Lie groups.

Topology

Non-descriptive name	Descriptive name(s)	Explanation/comments	Concept type
Hausdorff Space	Housed-off Space, Bubble Space	'Housed-off' is funny mnemonic. 'Bubble space' as different points can be put in separate bubbles	Property
Heine-Borel Theorem	Compactness in Rⁿ, bounded compactness theorem	'Boundedly compact' sometimes used for closed, bounded sets	Theorem

Algebra

Non-descriptive name	Descriptive name(s)	Explanation/comments
Jacobi Identity	Cycle condition, homomorphism property of adjoint, derivation property of adjoint.

Linear Algebra

Non-descriptive name	Descriptive name(s)	Explanation/comments	Concept type
Cauchy-Schwarz Inequality	Projection Inequality	Divide both sides by norm of one of the vectors. The inequality is a natural statement about projections.	Theorem, relation
Sylvester's law of inertia	Law of inertia, well-definedness of signature		Theorem

General Relativity (or Differential Geometry)

Non-descriptive name	Descriptive name(s)	Explanation/comments
Minkowski metric/spacetime	Flat metric/spacetime
Levi-civita connection	Metric connection	Connection uniquely defined by metric
Christoffel symbols	Connection components, geodesic components	Components appearing in connection/geodesic equation
Lie derivative	Fisherman's derivative, flow derivative
Riemannian metric [tensor]	Metric [tensor]
Riemann curvature tensor	Curvature tensor (for the frame bundle)
Ricci tensor	Contracted curvature tensor, metric distortion tensor	Metric distortion: see Wikipedia page for Ricci tensor, direct geometric meaning
Ricci scalar	Scalar curvature	Already used
Einstein tensor	Trace-reversed [Ricci tensor]	Insert favourite name for [Ricci tensor]
Bianchi identity	Conservation of dual field strength/curvature
Ricci identity	Curvature as commutator of covariant derivatives
Kretschmann scalar	Quadratic curvature scalar, total curvature	Total curvature as it is non-zero as long as curvature is non-zero: it is the Yang-Mills functional term for the Levi-Civita connection.
Einstein's field equations	Gravitational field equations
Killing vector fields	Isometry generating vector fields/isometry generators
Killing's equation	Isometry equation	The equation satisfied by isometry generators

Quantum mechanics

Non-descriptive name	Descriptive name(s)	Explanation/comments	Concept type
[Time (in)dependent] Schrödinger equation	Evolution equation for states, quantum equation of motion, wavefunction equation of motion		Differential equation
Boson	Symmetron, Fungible particles	Symmetric under transposition of particles. They are fungible, that is, any two bosons with the same wavefunction are indistinguishable.	Physical object
Fermion	Signon, Non-fungible particles	Permutations act on multiparticle systems in the sign representation.	Physical object

Quantum Field Theory

Non-descriptive name	Descriptive name(s)	Explanation/comments
Klein-Gordon Equation	Free Field Equation (for a real scalar field)
Scalar Yukawa Theory	Scalar real/complex coupling
Yukawa interactions	Scalar-fermion coupling
Second Quantisation	Occupation representation	Comes from the mistaken belief that the solution to the Dirac equation described a wavefunction, and so was a 'second quantisation' of an already quantum wavefunction. But the current understanding is that a classical field is quantised to give the Dirac fermion field, hence would be a first quantisation of a field, written in terms of occupation numbers of points of the field.
Non-linear sigma model	Manifold model, coset model	The sigma or σ comes from a field which emerges from the model but is not a feature of such models that current research is interested in. The field takes values in a manifold which is often a homogeneous space G/H.
Mandelstam variables	Channel variables	s, t and u correspond to different channels in 2-to-2 scattering.

Statistical Field Theory

Non-descriptive name	Descriptive name(s)	Explanation/comments
Ising model	Z₂ lattice model	The Z₂ describes the space that spin configurations functions are valued in. The spin configuration functions are valued on a lattice Λ

Advanced Quantum Field Theory

Terminology from the Advanced Quantum Field Theory course in Part III.

Non-descriptive name	Descriptive name(s)	Explanation/comments
Grassmann variable/Grassmann number	Anticommuting number; supernumber; exterior element	First two names are already in use according to wikipedia. Exterior element is own terminology, as Grassmann variables are really associated to generators of an exterior algebra, that is, basis vectors of a generating vector space.
Berezin integral	Superintegral	An integral over the odd or 'fermionic' part of superspace
LSZ (Lehmann, Symanzik, Zimmermann) reduction formula	S-matrix/correlator/vertex function correspondence	The reduction formula makes precise why we are interested in calculating correlators
Wavefunction renormalisation	Field renormalisation	Vestige from when physicists still thought quantum fields could be interpreted as wavefunctions, which also gave notation like `second quantisation'.
Wick rotation	Complex coordinate rotation
Feynman diagrams	Interaction diagrams
Landau pole	Coupling pole	Scale at which coupling constant becomes infinite
Callan-Symanzik equation	Renormalisation differential equation (for correlators)
Schwinger-Dyson equations	QFT/functional EOM (equations of motion)	QFT analogue of Euler-Lagrange equations
Ward-Takahashi identity	Correlator Noether identity	Yes, yes, there is still a name, but Noether is so tied to this idea of symmetry-conservation correspondence. Really we'd have to go back and rename Noether's theorem.
Yang-Mills Theory (Lagrangian)	Curvature minimising; G-Electromagnetism (G for Lie Group, often G = SU(N))	G-Electromagnetism as Yang-Mills theory is a generalisation of electromagnetism, from U(1) to a general smooth group G, although this is somewhat unsatisfying as Yang-Mills theory is often qualitatively different, for example having self-interactions. 'Curvature minimising' as least action is achieved when some notion of total curvature is minimised.
Wilson lines	(Trace of the) holonomy	This is already the used terminology in maths
Faddeev-Popov ghosts (or procedure)	Gauge ghosts, ghosting procedure
BRST quantisation	Ghost SUSY quantisation

Symmetries in particle physics

Non-descriptive name	Descriptive name(s)	Explanation/comments
Baker-Campbell-Hausdorff (BCH) formula	Exponential formula for [Lie algebras]
Killing form	(Adjoint) trace form	An example of general trace forms, which can be defined on any representation ρ
Chern-Simons forms	Characteristic (class) forms	This is their name in Chern and Simons original paper
Cartan Sub-algebra	Maximally ad-diagonalisable subalgebra
Cartan-Weyl basis	Charge-root basis
Poincaré group	ISO(p,q)	Isometries of flat space with a metric of signature (p,q)
(Generalised) Gell-Mann matrices/basis	Standard real SU(N) basis	The real is an important qualifier here: this basis preserves SU(N) as a real Lie algebra. As a complexified Lie algebra a much more standard basis is the one of unit matrices (with 1 in a single entry, 0 elsewhere).

Fluids

Non-descriptive name	Descriptive name(s)	Explanation/comments	Concept type
Navier-Stokes equation
Péclet number
Prandtl number
Reynolds number	Inertia-viscosity ratio
Schmidt number
Strouhal number

Inverse problem

Here we rename a concept after its creator, and see how disastrous the consequences are.

Name	Discoverer-named	Consequences	Concept type
Differentiation	Newtonisation, Leibnizisation		Operation
Integration	Leibnizisation, Newtonisation	The Fundamental Theorem of Calculus becomes 'the AntiNewtonian is the Leibnizisation'	Operation