List of people considered father or mother of a scientific field

Table columns:
Field
Person/s considered "father" or "mother"
Rationale

Table rows:
cells: Algebra (see also The father of algebra)
Muhammad Al-Khwarizmi (Algorismi)[113] Brahmagupta[114] Diophantus[115][116]
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.
cells: Algebraic topology
Henri Poincaré[117]
Published Analysis Situs in 1895,[118] introducing the concepts of homotopy and homology, which are now considered part of algebraic topology.
cells: Analysis
Augustin-Louis Cauchy[119] Karl Weierstrass[120]
cells: Analytic geometry
René Descartes Pierre de Fermat[121] (founders)
For their independent invention of the Cartesian Coordinate System
cells: Calculus
Isaac Newton[122] Gottfried Leibniz
See Leibniz and Newton calculus controversy.
cells: Classical analysis
Madhava of Sangamagrama[123]
Developed Taylor series expansions of trigonometric functions
cells: 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.
cells: Computer programming
Ada Lovelace
Work on Charles Babbage's proposed mechanical general-purpose computer, the Analytical Engine
cells: Cryptanalysis
Al-Kindi[124][125][126]
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.
cells: Descriptive geometry
Gaspard Monge[127] (founder)
Developed a graphical protocol that creates three-dimensional virtual space on a two-dimensional plane
cells: Fractal geometry
Benoît B. Mandelbrot
cells: Geometry
Euclid[128]
Euclid's Elements deduced the principles of Euclidean geometry from a set of axioms.
cells: Graph theory
Leonhard Euler[129]
See Seven Bridges of Königsberg
cells: Italian school of algebraic geometry
Corrado Segre[130]
Publications and students developing algebraic geometry
cells: Modern algebra
Emmy Noether[131]
Provided the first general definitions of a commutative ring, and suggested that topology be studied algebraically.[132] 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.[133]
cells: Non-Euclidean geometry
János Bolyai, Nikolai Lobachevsky[134](founders)
Independent development of hyperbolic geometry in which Euclid's fifth postulate is not true
cells: Number theory
Pythagoras[135]
cells: Probability
Gerolamo Cardano, Pierre de Fermat, Blaise Pascal, Christiaan Huygens[136] (founders)
Fermat and Pascal co-founded probability theory, about which Huygens wrote the first book
cells: Projective geometry
Girard Desargues[137](founder)
By generalizing the use of vanishing points to include the case when these are infinitely far away
cells: Tensor calculus
Gregorio Ricci-Curbastro[138] (founder)
Book: The Absolute Differential Calculus
cells: Trigonometry
Hipparchus[139][140]
Constructed the first trigonometric table.
cells: Vector algebra, vector calculus
Willard Gibbs[141] Oliver Heaviside[142] (founders)
For their development and use of vectors in algebra and calculus

Questions about this table:
originalText: who is recognised as the father of geometry
answer: answerTexts: Euclid