Robert (Bob) Bosch ’85

  • James F. Clark Professor of Mathematics

Areas of Study


  • BA, Oberlin College, 1985
  • MS, Rensselaer Polytechnic Institute, 1987
  • PhD, Yale University, 1991 


Current Research Interest: Opt Art

Currently I am interested in using optimization to create pictures, portraits, and other works of art. See my TSP Art and Domino Artwork pages for examples.

  • "Opt Art", Math Horizons 14(3) (2006) 6-9.
  • "TSP Art" (with C.S. Kaplan), Proceedings of Bridges 2005 (2005) 303-310. See Craig Kaplan's marvelous TSP Art web page!
  • "Pointillism via Linear Programming" (with A. Herman), The UMAP Journal 26(4) (2005) 393-400.
  • "Continuous Line Drawings via the Traveling Salesman Problem" (with A. Herman), Operations Research Letters 32 (2004) 302-303.
  • "Constructing Domino Portraits" in Tribute to a Mathemagician, ed. B. Cipra et al., A.K. Peters, 2004, 251-256.
  • "Constraint Programming and Hybrid Formulations for Three Life Designs" (with M. Trick), Annals of Operations Research 130 (2004) 41-56.
  • "Maximizing Fun at an Amusement Park" (with M. Cardiff and G. Hughes), The UMAP Journal 21(4), 483-498, (2000).
  • "Finding Optimal Piano Fingerings" (with M. Hart and E. Tsai), The UMAP Journal 21(2) (2000) 167-177.
  • "Optimal Card-Collecting Strategies for Magic: The Gathering", The College Mathematics Journal 31(1) (2000) 15-21.
  • "Integer Programming and Conway's Game of Life", SIAM Review 41(3) (1999) 596-604.
  • "Separating Hyperplanes and the Authorship of the Disputed Federalist Papers" (with J.A. Smith), The American Mathematical Monthly 105(7) (1998) 601-608.
  • Refinements of Paltiel and Kaplan's Decision-theoretic Model of AIDS Clinical Trials" (with N.K. Stout), Socio-Economic Planning Sciences 31(2) (1997) 87-101.
  • "The Battle of the Burger Chains: Which is Best---Burger King, McDonald's, or Wendy's?", Socio-Economic Planning Sciences 30(3) (1996) 157-162.
  • "A New Infinity-Norm Path Following Algorithm for Linear Programming" (with K.M. Anstreicher), SIAM Journal on Optimization 5 (2) (1995) 236-246.
  • "Big Mac Attack: The Diet Problem Revisited at McDonald's", OR/MS Today August (1993) 30-31.
  • "Long Steps in an O(n3L) Algorithm for Linear Programming" (with K.M. Anstreicher), Mathematical Programming 54 (1992) 251-265.

Fall 2024

Discrete Mathematics — MATH 220
Linear Optimization — MATH 331

Spring 2025

Introduction to Statistics — STAT 113
Discrete Mathematics — MATH 220


Robert Bosch Speaks at Rose-Hulman Undergraduate Mathematics Conference

May 8, 2024

James F. Clark Professor of Mathematics Robert (Bob) Bosch ’85 was one of two plenary speakers at the 39th Rose-Hulman Undergraduate Mathematics Conference. While there, Bob unveiled two pieces of mathematical artwork that had been commissioned by the Rose-Hulman Institute of Technology Mathematics Department.

Robert Bosch Coauthored Research Papers Presented at Bridges Math/Art Conference

August 9, 2022

On Tuesday August 2, 2022, Robert Klock OC ’21 and Xiaoyun Gong OC ’21 presented research papers coauthored by James F. Clark Professor of Mathematics Robert Bosch OC ’85 at the 2022 Bridges Math/Art Conference. Both papers are available at the Bridges Archive. Rob and Bob's paper, "Controlling Textures in TSP Art," can be viewed at this link, and Xiaoyun and Bob's paper, "Collaborative Gomoku Mosaics," is available for viewing here.

Robert Bosch Coedits Conference Proceedings

August 4, 2020

Professor of Mathematics Robert Bosch ‘85 coedited the Proceedings of the Bridges 2020 Conference, which was supposed to be held in Helsinki, Finland, but due to the COVID-19 pandemic took place virtually. The proceedings included a paper by Bosch and Aaron Kreiner ‘19 on "Domino Steganography" and a paper by Kreiner on "Checkerboard Quadrilateral Mosaics."

Robert Bosch Gives a Talk

February 14, 2020

Professor of Mathematics Robert Bosch gave a talk about "Opt Art" at Google's New York City office on January 23, 2020.

Bob Bosch Writes Book "Opt Art"

October 23, 2019

Professor of Mathematics Bob Bosch’s book Opt Art: From Mathematical Optimization to Visual Design will be released by Princeton University Press on November 12, 2019. In it, Bosch offers an introduction to the geometric, algebraic, and algorithmic foundations of mathematical optimization and its classical applications, such as determining the best way to assign workers to jobs or devising the best route for a delivery driver. A book release event takes place on November 12, 2019 at the National Museum of Mathematics (MoMath) in New York City.

Bosch will also give the 2019 President’s Lecture titled, “Opt Art: From Mathematical Optimization to Visual Design” on November 8 in Finney Chapel.

Bob Bosch Interviewed for Mathematics Magazine

October 20, 2019

Professor of Mathematics Bob Bosch '83 was interviewed for the October 2019 issue of Mathematics Magazine in the piece “Dominos, Traveling Salespeople, and Art: An Interview with Bob Bosch,” written by Allison Henrich. The interview is accompanied by four examples of Bosch’s optimization-based mathematical artwork, and there are five additional examples of his work elsewhere in the issue.

Bob Bosch Presents Paper

July 24, 2019

Professor of Mathematics Bob Bosch presented a paper titled “Exploring Szpakowski’s Linear Ideas” at the 2019 Bridges Conference in Linz, Austria. The paper was coauthored by Abagael Cheng ‘20 and Ari Smith ‘19.

Robert Bosch's Art Appears on Television Show

April 17, 2019

Professor of Mathematics Robert Bosch designed "Traveling Salesman Problem" (TSP) art pieces that appeared on the Chinese television show, Super Brain (or in Chinese, 最强大脑). On the show, two teams of participants compete to solve a series of puzzles, including puzzles derived from the TSP art Bosch designed for the show. Watch the show here.

Robert Bosch Featured in Article

January 3, 2017

Professor of Mathematics Robert Bosch was the subject of an article in Proceedings of the National Academy of Science,"Solving a Math Problem to Create Art."

Bob Bosch Gives Talks

April 7, 2016

Professor of Mathematics Bob Bosch recently gave two talks at the invitation-only Gathering for Gardner Conference, held in Atlanta every two years in honor of Martin Gardner, who wrote Scientific American’s "Mathematical Games" column from 1956 to 1981.

Bosch's first talk, "Numerically Balanced Dice," a collaboration with The Dice Lab's Robert Fathauer and Henry Segerman, unveiled the world's first mass-produced injection-molded 120-sided die (based on the disdyakis triacontahedron). The die is numerically balanced in that numbers on opposite sides sum to 121, and all of the vertex sums are exactly what they should be (the degree of the vertex times the average of the numbers on the die).

Bosch's second talk, "Game-of-Life Animations," presented Game-of-Life patterns that resemble works of art (including a Magritte still life, a portrait of John Horton Conway, the game's inventor, and two animations based on Eadward Muybridge's locomotion studies).

Robert Bosch ’85 Speaks at MoMath

February 4, 2016

Professor Mathematics Robert Bosch ’85 delivered the talk “Life is Beautiful: The Startling Consequences of Three Simple Rules” at MoMath (the National Museum of Mathematics) on February 3. Bosch’s talk was part of the Math Encounters presentation series.

Bob Bosch Delivers Address & More

November 19, 2015

Professor of Mathematics Bob Bosch delivered the banquet address on November 6 at the MD DC VA Fall Sectional Meeting of the Mathematics Association of America. The address, "Opt Art," was a survey of Bosch’s efforts to use mathematical and computer science-based optimization techniques to design visual artwork.

On November 9, Bosch participated in the opening of the exhibition In the Realm of Forms at the Pearl Conard Gallery at the Ohio State University, Mansfield. The exhibition is open through December 8.

Finally, Bosch’s 2006 continuous line drawing Knot?, an early example of his TSP Art, makes an appearance in art historian Lynn Gamwell's new book "mathematics + art: a cultural history".

Robert Bosch Publishes in Journal of Mathematics and the Arts

January 15, 2015

An article by Professor of Mathematics Robert Bosch '85 and mathematics major Julia Olivieri '16 was recently published in the Journal of Mathematics and the Arts. The article, "Designing Game of Life Mosaics with Integer Programming," describes how Bosch and Olivieri used mathematical optimization techniques to construct sets of tiles that can be interpreted as still lifes (stable objects) or phoenix patterns (period-2 oscillators) in Conway's Game of Life. The tiles are modular and have various brightness levels, making them suitable for making mosaics. At the present time, the article is available for free.

Robert Bosch Coordinates Film Festival

August 25, 2014

Professor of Mathematics Robert Bosch '85, coordinated the Bridges Short Movie Festival in Seoul, Korea. Bridges is an annual conference that focuses on connections between art and mathematics. Sixteen movies were shown, including a hand- and computer-animated film by Rachael Schwartz '17. Leah Wood '16 was the festival's video editor.

Bosch also presented two papers coauthored by students: "Figurative Mosaics from Flexible Truchet Tiles," with Urchin Colley '13, and "Game-of-Life Mosaics," with Julia Olivieri '16.