Mathematical explorers continually discover and name new objects in the mathematical landscape, and their features. Here are just some nouns and adjectives – there are plenty of mathematical verbs also – from the hundreds in any mathematical dictionary.

Abelian group, abundant number, affine space, area, automorphism, axis, binomial coefficient, braid, Cantor set, cardinal, Cauchy sequence, characteristic, Chinese remainder theorem, closed interval, combination, complex integration, continued fraction, cross ratio, deltoid, Desargues’ theorem, discriminant, duality, eccentricity, equation, equivalence, Euclidean, evolute, extremal, factor, factorial, Fagnano's problem, field, finite, free group, function, Galois theory, Gaussian integers, golden section, the greedy algorithm, group, Hamiltonian, harmonic, height, heptagon, hypercube, identity, imaginary number, incidence matrix, index, infinitesimal, infinite series, integer, integration, invariant, inversion, isogonal, isometry, isomorphism, iteration, Jacobian, Jordan curve, Julia set, Klein bottle, knot, Kurschak tile, Latin square, lattice, linear function, locus, logarithm, magic square, Mandelbrot set, matrix, maximum, mean value theorem, median, metric space, Möbius strip, model, modular arithmetic, nephroid, node, normal, orbit, ordinate, origin, orthogonal, packing, parabola, parallel, Pascal's triangle, Peano curve, pencil, perfect number, permutation, pigeonhole principle, pole, polygon, power, prime, probability, projection, quadrilateral, quadratic, quartile, radical axis, radius, rational, reflection, ring, rotation, ruled surface, saddle, sample, scalar, set, similarity, Simpson line, sphere, square, Stirling's formula, subtraction, symmetry, tangent, Taylor series, tessellation, topological space, torus, trace, transitive, tree, triangle, unduloid, uniform, union, value, variable, vector, vertex, Viviani's theorem, volume, weighted average, word, x-axis, zero, zeta function, Zorn's lemma.