Subject | Father/mother of … | Reason |
Algebra See also Father of Algebra Brahmagupta | Brahmagupta Al-Khwarizmi (Algorismi)[107][108] Diophantus[109][110] | Full exposition of solving quadratic equations in his Al-Jabr and recognized algebra as an independent discipline. First use of symbolism (syncopation) in his Arithmetica. |
Algebraic topology | Henri Poincaré[111] | Published Analysis Situs in 1895,[112] introducing the concepts of homotopy and homology, which are now considered part of algebraic topology. |
Analysis | Augustin-Louis Cauchy[113] Karl Weierstrass[114] | |
Analytic geometry | René Descartes Pierre de Fermat[115](founders) | For their independent invention of the Cartesian Coordinate System |
Calculus | Isaac Newton[116] Gottfried Leibniz | See Leibniz and Newton calculus controversy. |
Classical analysis | Madhava of Sangamagrama[117] | Developed Taylor series expansions of trigonometric functions |
Computer science | George Boole Alan Turing | Invented Boolean logic, which is the basis of modern digital computer logic Provided an influential formalisation of the concept of the algorithm and computation with the Turing machine. |
Descriptive geometry | Gaspard Monge[118] (founder) | Developed a graphical protocol which creates three-dimensional virtual space on a two-dimensional plane |
Fractal geometry | Benoît B. Mandelbrot |
Geometry | Euclid[119] | Euclid's Elements deduced the principles of Euclidean geometry from a set of axioms. |
Graph Theory | Leonhard Euler[120] | See Seven Bridges of Königsberg |
Italian school of algebraic geometry | Corrado Segre[121] | Publications and students developing algebraic geometry |
Non-Euclidean geometry | János Bolyai, Nikolai Lobachevsky[122](founders) | Independent development of hyperbolic geometry in which Euclid's fifth postulate is not true |
Number theory | Pythagoras[123] | |
Probability | Gerolamo Cardano, Pierre de Fermat, Blaise Pascal, Christiaan Huygens[124] (founders) | Fermat and Pascal co-founded probability theory, about which Huygens wrote the first book |
Projective geometry | Gérard Desargues[125](founder) | By generalizing the use of vanishing points to include the case when these are infinitely far away |
Tensor calculus | Gregorio Ricci-Curbastro[126] (founder) | Book: The Absolute Differential Calculus |
Trigonometry | Aryabhata Hipparchus[127][128] | Constructed the first trigonometric table. |
Vector algebra, vector calculus | Willard Gibbs[42] Oliver Heaviside[129] (founders) | For their development and use of vectors in algebra and calculus |