The Bridges of Pittsburgh is a highly interdisciplinary and collaborative public-facing project that pays homage both to an innovative, field-defining mathematical problem and to one of the defining features of our city. We propose to discover how many of Pittsburgh’s 446 bridges can be traversed without crossing the same bridge twice, then publish our findings both in traditional scholarly venues and as an online interactive map. Our project will educate CMU affiliates, engage the public, and aid our professional development through publications and skill-building. We will draw from history of science, graph theory, digital mapping, and public humanities to achieve our goals.

Overview & Goals

In 1736, mathematician Leonard Euler proved it was impossible to walk through the German city of Königsberg crossing each of the city’s seven bridges exactly once. His work, famously dubbed the “Bridges of Königsberg” problem, laid the foundation for graph theory and network analysis, and foreshadowed the invention of topology. We intend to create an expanded, more complex version of this famous study using Pittsburgh’s 446 bridges (Regan 2006). In brief, we will apply graph theory to discover whether each Pittsburgh bridge can be traversed only once in a single journey, or if not, how long one can travel within Pittsburgh without crossing the same bridge twice. As part of this process, we will take into account both change over time and the type of each bridge—road bridges, pedestrian bridges, railroad bridges, etc.—which will also enable us to replicate this analysis with specific subsets of Pittsburgh’s bridges. While we will publish the results of this process in peer reviewed publications and at conferences, our main publication will be an online interactive map where users can chart their own bridge traversal routes through the city.

The project is in service of three intellectual and professional goals:

  • Develop deeper expertise in digital mapping techniques for ourselves and participating students.
  • Educate CMU students, faculty, and staff about graph theory, network analysis techniques, GIS, and the history of mathematics.
  • Advocate for our profession by engaging the public in cutting-edge humanities research.

After building a locally-hosted version of the map and while we are constructing the public-facing website, we will invite interested students, faculty, and staff to join us in a series of highly interdisciplinary educational and promotional events. These events will include a hands-on workshop with digital tools and our database, a website design session, a lecture on the project, each of which will attract different communities around campus and the city, including those interested in graph theory, history of science, digital mapping, web development, civic data collection, the history and geography of Pittsburgh, and public humanities. A vital part of our research agenda is to publish as openly as possible, in order to engage the public in, and familiarize them with, cutting-edge humanities research. Therefore upon the website’s completion, we also envision hosting a series of public events centered around the website that can foster engagement with local history and healthy lifestyles. These could include a walk/run or bike ride across some portions of the route, a public lecture on Pittsburgh’s bridges, or a collaboration with local data journalists on the economic impacts of communities being relatively easy or difficult to access. The final website will be of broad interest to both academic and public communities. Users will be able to reveal solutions to the problem over various subsets of bridges, such as only rail bridges or only bridges that could be walked over in 1883. The site will host a variety of datasets for scholars interested in building upon our work or civic data hackers (such as CMU’s Students for Urban Data Systems or Pitt’s Center for Social and Urban Research) interested in applying bridge data to other local problems. We will also post lesson plans that will enable mathematicians, historians, and other teachers to use our website while teaching graph theory, network analysis, and the history of science.