Map of Mathematics
Dominic Wallman, 2020
Artist Statement: All of mathematics summarised in one poster. I made this map for my youtube channel. After my successful Map of Physics video, many people requested that I make a Map of Mathematics, and this is the result. I hope you enjoy it!
Artist Biography: Dr. Walliman is a youtuber, science writer and physicist. He produces the YouTube channel Domain of Science and writes the Professor Astro Cat science books for youngsters. He has a PhD in quantum device physics and used to work on quantum computers. He loves learning about science and finding fun ways to tell other people about the things he learns. Links: YouTube, Twitter, Instagram. (from https://dominicwalliman.com/)
Beautiful Mathematics
Sylvia Nickerson, 2022
Watercolour and ink on paper with digital collage
Artist Statement: I am currently pursuing how I can apply my skills in graphic arts and research to develop an illustrated book on the history of mathematics. This image is a first attempt to create something I could develop further into a larger project about the history of math that would eventually combine image with text. Some of the mathematical objects that appear in Beautiful Mathematics include Napier’s bones, spiral defined by the golden ratio, Hindu-Arabic numerals, Cardano’s cube for developing a solution to the cubic equation, sinusoidal function, Coxeter graph, Armillary sphere, Pascal’s arithmetical triangle, diagrammatic proof of the gou gu theorem (Pythagorean theorem in China), Fibonacci’s rabbit breeding problem, and a sphere.
Artist Biography: Sylvia Nickerson teaches the history of mathematics at the University of Toronto and McMaster University (2019-present). She holds a PhD in the history of science from University of Toronto’s Institute for the History and Philosophy of Science and Technology (2014). She completed a post-doc at York University under supervisor Bernard Lightman (2014-2017). She is both a scholar and a comics artist. Her comic books include Creation (2018) and All We Have Left Is This (2019). She has received a Hamilton Arts Awards for Visual Arts (2018) and a Doug Wright Award for Canadian Cartooning (2019). A freelance illustrator from 2005-2015, she created art for local, national and international clients. Her art has been collected by the Art Gallery of Hamilton and the William Ready Division of Archives and Research Collections at McMaster University Library. More of her art work can be seen at http://www.sylvianickerson.ca.
Mathematical Diatoms
Simone Conradi, 2024
Artist statement: Each “diatom” represents an attractor of the above map \(\Bbb C \to \Bbb C\) for specific values of the real parameters \(a_0, a_1, a_2, a_3, a_4\), and of the natural numbers \(n\) and \(p\). Each attractor is approximated by ten million points, computed using a custom Python program. The image is generated with Python and the Matplotlib library.
Artist Biography: Simone Conradi, a PhD in theoretical physics, transitioned
from a decade in the railway automation industry to machine learning
consulting and teaching. He develops STEM teaching methods, integrates
Python into math and physics education, and authored the first Italian book on
artificial intelligence for secondary schools. In his free time, he enjoys relaxing by walking or biking in the Italian Alps, or creating digital art with Python code. X: @S_Conradi; Mastodon: @S_Conradi@mathstodon.xyz
Two pieces by Anatoly Fomenko
Artist Biography: Anatoly T. Fomenko is a full member (Academician) of the Russian Academy of Sciences (1994), the Russian Academy of Natural Sciences (1991), the International Higher Education Academy of Sciences (1993) and Russian Academy of Technological Sciences (2009), as well as a doctor of physics and mathematics (1972), a professor (1980), and head of the Differential Geometry and Applications Department of the Faculty of Mathematics and Mechanics in Moscow State University (1992). Fomenko is the author of the theory of topological invariants of integrable Hamiltonian system[s]. He is the author of 180 scientific publications, 26 monographs and textbooks on mathematics, a specialist in geometry and topology, variational calculus, symplectic topology, Hamiltonian geometry and mechanics, and computer geometry. Fomenko is also the author of a number of books on the development of new empirico-statistical methods and their application to the analysis of historical chronicles as well as the chronology of antiquity and the Middle Ages. (from https://www.anatoly-fomenko.com/anatoly-timofeevich-fomenko-mathematical-work.html)
The remarkable numbers \(\pi\) and \(e\)
No. 242, 1986 (Number theory, mathematical statistics)
India ink and pencil on paper, 32x44 cm.
Looming over an austere urban landscape, a tower stands, assembled from cubes whose faces are pocked with round markings. Below stand a church and clocktower, surrounded by monoliths suspended in space. Above, on a platform, a woman contemplates a sculpture. On the towers front wall is inscribed a decimal expansion of the number \(\pi\), while on the side wall is the number \(e\), both displayed in the form of black disks filling squares, row after row. Incribed too in this image is a fractal, a closed subset of the plane whose dimension is expressed by a fraction rather than an integer. (from https://chronologia.org/en/math_impressions/poster142.html)
2-adic Solenoid
No. 195, 1977 (Topology, differential equations, Hamiltonian mechanics, symplectic geometry)
India ink on paper, 46.5x57 cm.
This 2-adic solenoid, a contortion of space, where surfaces fold in on themselves around a central axis, is known in topology as an object rich in complexity and unusual properties, useful in verifying many geometric conjectures. Though not obvious from its final appearance, this object comes about when many tori, or donut shaped objects, are embedded in each other. To build such a shape, one begins with a single torus, copies it, and then winds the copy around the original. This process is then repeated over and over, moving toward infinity. Eventually, one creates a set of tori inside of tori, unwrapped donuts twisting inside themselves, like snakes coiled into rings. And the process goes on to its very limit. In each case too, part of each torus has been stripped away, opening up its interior, to reveal the creation of this space.
Mathematicians and physicists have become more interested in this shape in recent years as they find it arising in an area of study called Hamiltonian mechanics. These winding tori, so to speak, turn out to describe important characteristics of certain equations of motion, particularly integrable differential equations and their solutions. So we have a case where a well understood, classical object in mathematics has been, in a sense, reborn, owing to recent discoveries in mathematical physics. (from https://chronologia.org/en/math_impressions/poster018.html)