Some artists such as Piero della Francesca and Luca Pacioli went so far as to write books on mathematics in art. Della Francesca wrote books on solid geometry and the emerging field of perspective, including De Prospectiva Pingendi (On Perspective for Painting), Trattato d’Abaco (Abacus Treatise), and De corporibus regularibus (Regular Solids), while Pacioli wrote De divina proportione (On Divine Proportion), with illustrations by Leonardo da Vinci, at the end of the fifteenth century.
Merely making accepted use of some aspect of mathematics such as perspective does not qualify an artist for admission to this list.
The term "fine art" is used conventionally to cover the output of artists who produce a combination of paintings, drawings and sculptures.
|Artist||Dates||Artform||Contribution to mathematical art|
|Calatrava, Santiago||1951–||Architecture||Mathematically-based architecture|
|Della Francesca, Piero||1420–1492||Fine art||Mathematical principles of perspective in art; his books include De prospectiva pingendi (On perspective for painting), Trattato d’Abaco (Abacus treatise), and De corporibus regularibus (Regular solids)|
|Demaine, Erik and Martin||1981–||Origami||"Computational origami": mathematical curved surfaces in self-folding paper sculptures|
|Dietz, Ada||1882–1950||Textiles||Weaving patterns based on the expansion of multivariate polynomials|
|Draves, Scott||1968–||Digital art||Video art, VJing|
|Dürer, Albrecht||1471–1528||Fine art||Mathematical theory of proportion|
|Ernest, John||1922–1994||Fine art||Use of group theory, self-replicating shapes in art|
|Escher, M. C.||1898–1972||Fine art||Exploration of tessellations, hyperbolic geometry, assisted by the geometer H. S. M. Coxeter|
|Farmanfarmaian, Monir||1922–2019||Fine art||Geometric constructions exploring the infinite, especially mirror mosaics|
|Ferguson, Helaman||1940–||Digital art||Algorist, Digital artist|
|Forakis, Peter||1927–2009||Sculpture||Pioneer of geometric forms in sculpture|
|Grossman, Bathsheba||1966–||Sculpture||Sculpture based on mathematical structures|
|Hart, George W.||1955–||Sculpture||Sculptures of 3-dimensional tessellations (lattices)|
|Hill, Anthony||1930–||Fine art||Geometric abstraction in Constructivist art|
|Leonardo da Vinci||1452–1519||Fine art||Mathematically-inspired proportion, including golden ratio (used as golden rectangles)|
|Longhurst, Robert||1949–||Sculpture||Sculptures of minimal surfaces, saddle surfaces, and other mathematical concepts|
|Man Ray||1890–1976||Fine art||Photographs and paintings of mathematical models in Dada and Surrealist art|
|Naderi Yeganeh, Hamid||1990–||Fine art||Exploration of tessellations (resembling rep-tiles)|
|Pacioli, Luca||1447–1517||Fine art||Polyhedra (e.g. rhombicuboctahedron) in Renaissance art; proportion, in his book De divina proportione|
|Perry, Charles O.||1929–2011||Sculpture||Mathematically-inspired sculpture|
|Robbin, Tony||1943–||Fine art||Painting, sculpture and computer visualizations of four-dimensional geometry|
|Saiers, Nelson||Fine art||Mathematical concepts (toposes, Brown representability, Euler's identity, etc) play a central role in his artwork.|
|Photography and sculptures of mathematical models, inspired by the work of Man Ray  and Marcel Duchamp|
|Taimina, Daina||1954–||Textiles||Crochets of hyperbolic space|
|Uccello, Paolo||1397–1475||Fine art||Innovative use of perspective grid, objects as mathematical solids (e.g. lances as cones)|
|Verhoeff, Jacobus||1927–2018||Sculpture||Escher-inspired mathematical sculptures such as lattice configurations and fractal formations|
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- "Mathematical Imagery: Mathematical Concepts Illustrated by Hamid Naderi Yeganeh". American Mathematical Society. Retrieved 8 June 2015.
- "Monthly essays on mathematical topics: Mathematics and Art". American Mathematical Society. Retrieved 7 June 2015.
- Piero della Francesca, De Prospectiva Pingendi, ed. G. Nicco Fasola, 2 vols., Florence (1942).
- Piero della Francesca, Trattato d'Abaco, ed. G. Arrighi, Pisa (1970).
- Piero della Francesca, L'opera "De corporibus regularibus" di Pietro Franceschi detto della Francesca usurpata da Fra Luca Pacioli, ed. G. Mancini, Rome, (1916).
- Swetz, Frank J.; Katz, Victor J. "Mathematical Treasures - De Divina Proportione, by Luca Pacioli". Mathematical Association of America. Retrieved 7 June 2015.
- Greene, Robert. "How Santiago Calatrava blurred the lines between architecture and engineering to make buildings move". Arch daily. Retrieved 7 June 2015.
- Field, J. V. (2005). Piero della Francesca. A Mathematician's Art (PDF). Yale University Press. ISBN 0-300-10342-5.
- Yuan, Elizabeth (2 July 2014). "Video: Origami Artists Don't Fold Under Pressure". The Wall Street Journal.
- Demaine, Erik; Demaine, Martin. "Curved-Crease Sculpture". Retrieved 8 June 2015.
- "Erik Demaine and Martin Demaine". MoMA. Museum of Modern Art. Retrieved 8 June 2015.
- Dietz, Ada K. (1949). Algebraic Expressions in Handwoven Textiles (PDF). Louisville, Kentucky: The Little Loomhouse. Archived from the original (PDF) on 2016-02-22. Retrieved 2015-06-07.
- Birch, K. (20 August 2007). "Cogito Interview: Damien Jones, Fractal Artist". Archived from the original on 27 August 2007. Retrieved 7 June 2015.
- Bamberger, A. (2007-01-18). "San Francisco Art Galleries - Openings". Retrieved 2008-03-11.
- "Gallery representing Draves' video art". Archived from the original on 2008-06-06. Retrieved 2008-03-11.
- "VJ: It's not a disease". Keyboard Magazine. April 2005. Archived from the original on 2008-04-12. Retrieved 2015-06-08.
- Wilkinson, Alec (2004-06-07). "Incomprehensible". New Yorker Magazine.
- "Feature Column from the AMS". American Mathematical Society. Retrieved 7 June 2015.
- "Albrecht Dürer". University of St Andrews. Retrieved 7 June 2015.
- Beineke, Lowell; Wilson, Robin (2010). "The Early History of the Brick Factory Problem". The Mathematical Intelligencer. 32 (2): 41–48. doi:10.1007/s00283-009-9120-4.
- Ernest, Paul. "John Ernest, A Mathematical Artist". University of Exeter. Retrieved 7 June 2015.
- "M.C. Escher and Hyperbolic Geometry". The Math Explorers' Club. 2009. Retrieved 7 June 2015.
- "BBC 100 Women 2015: Iranian artist Monir Farmanfarmaian". BBC. 26 November 2015. Retrieved 27 November 2015.
- Smith, Roberta (17 December 2009). "Peter Forakis, a Sculptor of Geometric Forms, Is Dead at 82". The New York Times.
Often consisting of repeating, flattened volumes tilted on a corner, Mr. Forakis’s work had a mathematical demeanor; sometimes it evoked the black, chunky forms of the Minimalist sculptor Tony Smith.
- "Peter Forakis, Originator of Geometry-Based Sculpture, Dies at 82". Art Daily. Retrieved 7 June 2015.
- "The Math Geek Holiday Gift Guide". Scientific American. November 23, 2014. Retrieved June 7, 2015.
- Hanna, Raven. "Gallery: Bathsheba Grossman". Symmetry Magazine. Retrieved 7 June 2015.
- "George W. Hart". Bridges Math Art. Retrieved 7 June 2015.
- "George Hart". Simons Foundation. Retrieved 7 June 2015.
- "Anthony Hill". Artimage. Retrieved 7 June 2015.
- "Anthony Hill: Relief Construction 1960-2". Tate Gallery. Retrieved 7 June 2015.
The artist has suggested that his constructions can best be described in mathematical terminology, thus ‘the theme involves a module, partition and a progression’ which ‘accounts for the disposition of the five white areas and permuted positioning of the groups of angle sections’. (Letter of 24 March 1963.)
- "Leonardo DaVinci and the Golden Section". University of Regina. Retrieved 7 June 2015.
- Friedman, Nathaniel (July 2007). "Robert Longhurst: Three Sculptures". Hyperseeing: 9–12.
The surfaces [of Longhurst's sculptures] generally have appealing sections with negative curvature (saddle surfaces). This is a natural intuitive result of Longhurst's feeling for satisfying shape rather than a mathematically deduced result.
- "Man Ray–Human Equations A Journey from Mathematics to Shakespeare February 7 - May 10, 2015". Phillips Collection. Retrieved 7 June 2015.
- Bellos, Alex (24 February 2015). "Catch of the day: mathematician nets weird, complex fish". The Guardian.
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- Hart, George. "Luca Pacioli's Polyhedra". Retrieved 7 June 2015.
- "Dodecahedron". Wolfram MathWorld. Retrieved 7 June 2015.
- William Grimes (11 February 2011). "Charles O. Perry Dies at 81; Sculptor Inspired by Geometry". New York Times. Retrieved November 10, 2012.
- Radcliff, Carter; Kozloff, Joyce; Kushner, Robert (2011). Tony Robbin: A Retrospective. Hudson Hills Press. ISBN 978-1-555-95367-6.
- levi, ryan. "Alcatraz Displays Irrational Numbers & Irrationally Long Prison Sentences". kqed.
- Mastroianni, brian. "The perfect equation: Artist combines math and art". fox news.
- nelsonsaiers.com http://www.nelsonsaiers.com/work#/napoleon-would-approve-but-alexander-was-far-greater/. Missing or empty
- "Portfolio Slideshow (Mathematical Forms)". New York Times. Retrieved 9 June 2015.
Mathematical Form 0009: Conic surface of revolution with constant negative curvature. x = a sinh v cos u; y = a sinh v sin u; z = ...
- "Hiroshi Sugimoto: Conceptual Forms and Mathematical Models". Phillips Collection. Retrieved 9 June 2015.
- "Hiroshi Sugimoto". Gagosian Gallery. Retrieved 9 June 2015.
Conceptual Forms (Hypotrochoid), 2004 Gelatin silver print
- "art21: Hiroshi Sugimoto". PBS. Archived from the original on 11 July 2015. Retrieved 9 June 2015.
- "A Cuddly, Crocheted Klein Quartic Curve". Scientific American. 17 November 2013. Retrieved 7 June 2015.
- "Paolo Uccello". J. Paul Getty Museum. Retrieved 7 June 2015.
- "The Battle of San Romano, Paolo Uccello (c1435-60)". The Guardian. 29 March 2003. Retrieved 7 June 2015.
it is his bold enjoyment of its mathematical development of shapes - the lances as long slender cones, the receding grid of broken arms on the ground, the wonderfully three-dimensional horses, the armoured men as systems of solids extrapolated in space - that makes this such a Renaissance masterpiece.
- "Koos Verhoeff - mathematical art". Ars et Mathesis. Archived from the original on 10 April 2002. Retrieved 8 June 2015.