HONR229P: Mathematics and Art

Fall 2007


Professor: Niranjan Ramachandran

4115 Mathematics Building,

5-5080, atma “at” math here at umd dot edu

Office Hours: MW 11:30-noon or by appointment


Class meets Mondays and Wednesdays 10:00am-11:30am in Math 1311. 


Course page: http://www.math.umd.edu/~atma/hp07.htm (or on Blackboard)


Course description: The aim of this course is to introduce students to the interactions, interrelations, and analogies between mathematics and art.

Mathematicians (and scientists, in general) are in search of ideas, truth and beauty, not too different from artists. Our task will be to see the parallels between the viewpoints, the inspirations, the goals of (and the works produced by) artists and scientists.

We shall begin with examples from history of art (such as the theory of perspective due to Leonardo da Vinci), works of art (such as Durer's Melancholia, Escher’s Waterfall), architecture (Parthenon, Le Corbusier) to illustrate the impact of mathematics on art. Of special interest to us will be the period of the Italian Renaissance and also the early part of the 20th century (the new viewpoint on space-time). Time permitting, the affinity of music with mathematics will also be explored (as in the music of Bach, or the foundations of tone, the role of harmony). Simultaneously, we shall  explore beauty in mathematics; this will be amply illustrated with examples from the history of mathematics. Emphasis will be put on the aesthetic aspect of things. We will even see how truth and beauty come together in a beautiful proof.

The course material could be roughly divided into three parts: geometry and classical art, truth and beauty in math (proofs), beauty in science (higher-dimensions, space-time, physics) and modern art (Cezanne, Picasso, Escher, Kandinsky).  

All through the semester, we will be comparing and contrasting the two subjects. Hopefully, by the end of the semester, one's sense of beauty will be enriched also to appreciate beauty in the world of mathematics.




Books:  (Additional reading material will be distributed via Blackboard)



  • Krome Baratt, Logic and Design, Revised: In Art, Science, and Mathematics (Paperback).  ISBN1592288499, 336 pages, Green Editorial, (2005).
  • Daniel Pedoe, Geometry and the Visual Arts (Paperback). ISBN 048624458X Dover Publications, 320 pages (1983). 
  • Umberto Eco, History of Beauty (Hardcover). (Translator A. McEwen) ISBN 0847826465, 432 pages, Rizzoli International Publications (2004).




Jinny Beyer, Designing tessellations

Amir Aczel, The artist and the mathematician

Hans Magnus Enzenberger, Number Devil

William Ivins, Art and Geometry: Study in space intuitions

Mario Livio, The equation that could not be solved: How mathematical genius discovered the language of symmetry

Tor Norretranders, The user illusion

Leonard Shlain, Art and Physics

Leonard Shlain, The alphabet versus the Goddess: The conflict between Word and Image

Theodore Cook, The curves of life

Arthur Loeb, Concepts and Images: Visual Mathematics

Samuel Colman, Harmonic proportions and Form in Nature, Art and Architecture

George Gamow, The new world of Mr. Tompkins (revised and updated)

Howard Gardner, Creating Minds:  An anatomy of creativity seen through the lives of Freud, Einstein, Picasso, Stravinsky, Eliot, Graham and Gandhi

H. E. Huntley, The Divine Proportion

Hermann Weyl, Symmetry

Georges Ghevergese Joseph, The crest of the Peacock

Daniel Pedoe, Mathematics and the visual Arts

Douglas Hofstadter, Godel, Escher and Bach.

Robert Pirsig, Zen and the art of motorcycle maintenance.

Jerry King, The art of mathematics.

Walter Pater, The renaissance.

Subrahmanyam Chandrasekhar, Truth and Beauty.

V. S. Ramachandran, Shadows in the Brain

Roger Penrose, The emperor’s new mind and Shadows of the mind: a search for the missing science of consciousness

C. P. Snow, The two cultures

Carol Parikh, The unreal life of Oscar Zariski

Barbara Goldsmith, Obsessive Genius: The inner life of Marie Curie

Rebecca Goldstein, Incompleteness: The proof and paradox of Kurt Godel

Albert Einstein, Ideas and Opinions

Paul Hoffman, The man who loved only numbers: The story of Paul Erdos and the search for mathematical truth.

Robert Kanigel, The man who knew infinity

Andre Weil, The apprenticeship of a mathematician

Maurice Mashaal, Bourbaki: a secret society of mathematicians

Hilbert and Vohn-Cossen, Geometry and the imagination

Jacques Hadamard, The psychology of invention in the mathematical field

Rene Descartes, Discourse on method and meditations on first philosophy

Johannes Kepler, The harmony of the world

Keith Devlin, Mathematics: the science of patterns.

Bulent Atalay, Math and the Mona Lisa: The art and science of Leonardo da Vinci.

Arthur Miller, Einstein, Picasso: Space, Time, and the beauty that causes havoc.



(There is so much material available in books (go to the Popular Math section of your favourite bookstore) and online that it is impossible to list. I urge you to google ``Math and Art''.)


Plays:  Tom Stoppard, Arcadia.

Tom Stoppard, Rosencrantz and Guildenstern are dead.

Michael Frayn, Copenhagen.

Joanne Sydney and Joshua Rosenblum, Fermat’s Last Tango.

Useful periodicals: American Mathematical Monthly, The Mathematical Intelligencer, Mathematics Magazine, Scientific American,.


Course Format and Grading:

This is a seminar. As such, there will be both lectures and discussions. Students are expected to actively participate in class. There will be reading assignments and students are supposed to come prepared to discuss them in class. There is an overabundance of reference material (see course homepage). In-class and out-of-class discussions are greatly encouraged. There will be guest lectures and (perhaps) a field trip to a museum in DC. 


Specific requirements:


  • Biweekly reports (1 page each): These will be regularly assigned. Typically, this is a critical report on an assigned topic (from the recommended articles or the textbooks).
  • Mini-tests (in-class): These will be in-class of 30 minutes duration (10:45 – 11:15). These will concentrate on the formal reasoning part of the course. Each mini-test will consist of math problems and proofs. The emphasis is on understanding, not on memorization of facts/proofs.
  • One 15 minute in-class presentation. These will be of 15 minutes duration, at the end of class.  The presenter should be prepared to answer questions by the students. Grades will be based on the content, clarity, organization, utility, relevance as well as class interest in the presentation (did the students like it? Were there lots of questions? Were any of them anticipated by the presenter? Were all questions answered by the presenter? Etc) The last day to sign-up for a presentation is 24th September 2007.
  • Final Term paper (12-15 pages) or project (+ 3-4 page paper). A substantial work requiring you to present an original line of thought pursued by yourself. The topic has to meet with my approval. You may use help from the internet and other reference material (referenced with credit, of course) as a springboard, but the jump should be your own! Clarity of Thought, Originality, and Creativity stressed. Complements such as your own artwork and music related to the paper would be fantastic! Any reference material (books, articles or online resources) used must be strictly cited. Grade will depend on the topic (relevancy to both math and art), theme/idea for the paper, presentation, precision, writing, overall organization, clarity, language, beauty, logic, etc.  An ideal paper is one which balances both the art and mathematical content while satisfying both artistic and mathematical requirements of beauty.
  • Due before the paper: a 1-page proposal and a 5-page draft.
  • As this course satisfies a CORE requirement, the mathematical competence (and its improvement) of students will affect the grade.
  • The organization of the course depends crucially on class participation. Class absences are strongly discouraged and will affect your final grade.
  • Break-down of the components of the grade are as follows:






Final paper


Discussions and Class participation


Biweekly Reports





Many topics are possible for the final paper; here are -- but only a few -- suggestions: From "Leonardo da Vinci, the Renaissance human" to "The mathematics of snowflakes" to "How did Escher make his drawings" to "Why the second law of thermodynamics is beautiful" to "Comparison between the works of Newton, Shakespeare and Beethoven". It is best to choose a topic that is close to your actual interests. 


Class on 19th November will be devoted to a discussion of Final Paper/Project.

Students will obtain constructive suggestions and criticism from instructor and classmates.


Assignment schedule:

  • Biweekly reports due: 10 September, 24 September, 8 October, 22 October, *5 November*, 19 November, 3 December.
  • Class presentations: sign up by 24 September  
  • Mini-tests (in-class): 8th October and 7th November
  • One-page proposal for final term paper due: 5th  November (a biweekly report)
  • Draft of final term paper due: 19th  November 
  • Final term paper/project due: 10th  December

Other academic matters:


Academic Accommodations:  If you have a documented disability, you should contact Disability Support Services 0126 Shoemaker Hall.  Each semester students with documented disabilities should apply to DSS for accommodation request forms which you can provide to your professors as proof of your eligibility for accommodations.  The rules for eligibility and the types of accommodations a student may request can be reviewed on the DSS web site at http://www.counseling.umd.edu/DSS/receiving_serv.html.
Religious Observances:  The University System of Maryland policy provides that students should not be penalized because of observances of their religious beliefs, students shall be given an opportunity, whenever feasible, to make up within a reasonable time any academic assignment that is missed due to individual participation in religious observances.  It is the responsibility of the student to inform the instructor of any intended absences for religious observances in advance.  Notice should be provided as soon as possible but no later than the end of the schedule adjustment period.  Faculty should further remind students that prior notification is especially important in connection with final exams, since failure to reschedule a final exam before the conclusion of the final examination period may result in loss of credits during the semester.  The problem is especially likely to arise when final exams are scheduled on Saturdays. 

Academic integrity:  The University of Maryland has a nationally recognized Code of Academic Integrity, administered by the Student Honor Council.  This Code sets standards for academic integrity at Maryland for all undergraduate and graduate students.  As a student you are responsible for upholding these standards for this course.  It is very important for you to be aware of the consequences of cheating, fabrication, facilitation, and plagiarism.  For more information on the Code of Academic Integrity or the Student Honor Council, please visit http://www.studenthonorcouncil.umd.edu/whatis.html

The University of Maryland is one of a small number of universities with a student-administered Honors Code 
and an Honors Pledge, available on the web 
at http://www.jpo.umd.edu/aca/honorpledge.html
The code prohibits students from cheating on exams, plagiarizing papers, submitting the same paper for credit in 
two courses without authorization, buying papers, submitting fraudulent documents, and forging signatures.  
The University Senate encourages instructors to ask students to write the following signed statement 
on each examination or assignment:  
"I pledge on my honor that I have not given or received any unauthorized assistance on this examination (or assignment).” 
Snow Days: 
In the event of inclement weather or other emergencies affecting the campus area, 
      classes and exams will be held unless the campus is officially closed. 
You can check the campus web page or call 301-405-SNOW for snow closure information. 
Should any classes or exams be cancelled, please check the class schedule page 
for updated schedule information.




Please keep visiting the course page (and/or Blackboard) for updates.


This course is part of CORE Distributive Studies: CORE: Mathematics and Sciences, non-lab [MS].

Student Learning Outcomes for Mathematics and Formal Reasoning (MS):

Students should be able to:

  1. Interpret and apply quantitative information and/or mathematical analysis to obtain sound results and recognize questionable assumptions;
  2. Understand major concepts and their applications;
  3. Analyze and interpret formulae and quantitative information using appropriate technologies and abstract reasoning;
  4. Understand and articulate how findings and ideas can be applied to explain phenomena and impact the larger society; and
  5. Communicate quantitative information, analyses, etc. through appropriate written and/or oral means.