Mathematics
Subject  Father/mother of …  Reason 

Algebra Brahmagupta 
Brahmagupta AlKhwarizmi (Algorismi) Diophantus 
Full exposition of solving quadratic equations in his AlJabr 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  AugustinLouis 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  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 (founder) 
Developed a graphical protocol which creates threedimensional virtual space on a twodimensional 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 
NonEuclidean 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 cofounded probability theory, about which Huygens wrote the first book 
Projective geometry  Gérard Desargues(founder)  By generalizing the use of vanishing points to include the case when these are infinitely far away 
Tensor calculus  Gregorio RicciCurbastro (founder) 
Book: The Absolute Differential Calculus 
Trigonometry  Aryabhata 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 
Read more about this topic: List Of People Considered Father Or Mother Of A Scientific Field, Formal Sciences
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Famous quotes containing the word mathematics:
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
If bread and butter wanted weight;
And wisely tell what hour o’ th’ day
The clock doth strike, by algebra.”
—Samuel Butler (1612–1680)
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)