Field Person / s considered "father '' or "mother '' Rationale Algebra (see also The father of algebra) Muhammad Al - Khwarizmi (Algorismi) Brahmagupta Diophantus 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 Published Analysis Situs in 1895, introducing the concepts of homotopy and homology, which are now considered part of algebraic topology. Analysis Augustin - Louis Cauchy Karl Weierstrass Analytic geometry René Descartes Pierre de Fermat (founders) For their independent invention of the Cartesian Coordinate System Calculus Isaac Newton Gottfried Leibniz See Leibniz and Newton calculus controversy. Classical analysis Madhava of Sangamagrama Developed Taylor series expansions of trigonometric functions Computer science Charles Babbage Alan Turing In the history of computer science Babbage is often regarded as one of the first pioneers of computing and Turing invented the principle of the modern computer and the stored program concept that almost all modern day computers use. Computer programming Ada Lovelace Work on Charles Babbage 's proposed mechanical general - purpose computer, the Analytical Engine Cryptanalysis Al - Kindi Developed the first code breaking algorithm based on frequency analysis. He wrote a book entitled "Manuscript on Deciphering Cryptographic Messages '', containing detailed discussions on statistics. Descriptive geometry Gaspard Monge (founder) Developed a graphical protocol that creates three - dimensional virtual space on a two - dimensional plane Fractal geometry Benoît B. Mandelbrot Geometry Euclid Euclid 's Elements deduced the principles of Euclidean geometry from a set of axioms. Graph theory Leonhard Euler See Seven Bridges of Königsberg Italian school of algebraic geometry Corrado Segre Publications and students developing algebraic geometry Modern algebra Emmy Noether Provided the first general definitions of a commutative ring, and suggested that topology be studied algebraically. Combined the structure theory of associative algebras and the representation theory of groups into a single arithmetic theory of modules and ideals in rings satisfying ascending chain conditions. Non-Euclidean geometry János Bolyai, Nikolai Lobachevsky (founders) Independent development of hyperbolic geometry in which Euclid 's fifth postulate is not true Number theory Pythagoras Probability Gerolamo Cardano, Pierre de Fermat, Blaise Pascal, Christiaan Huygens (founders) Fermat and Pascal co-founded probability theory, about which Huygens wrote the first book Projective geometry Girard Desargues (founder) By generalizing the use of vanishing points to include the case when these are infinitely far away Tensor calculus Gregorio Ricci - Curbastro (founder) Book: The Absolute Differential Calculus Trigonometry Hipparchus Constructed the first trigonometric table. Vector algebra, vector calculus Willard Gibbs Oliver Heaviside (founders) For their development and use of vectors in algebra and calculus
who is recognised as the father of geometry
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