Teacher resources and professional development across the curriculum

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5

Mathematics

Big Ideas in Literacy

A Snapshot of a Research or Theoretical Mathematician at Work

Many mathematicians are not involved in solving real-world problems and, instead, focus specifically on solving mathematical problems associated with proofs and theorems. These may indeed seem far removed from anything real, but this work is also very important, as it helps move the field of theoretical mathematics forward and may even have important applications in the future.

An example of what it means to do mathematical research starts with the German mathematician David Hilbert (1862–1943). Hilbert identified a list of important mathematical problems that he believed would be important to solve during the next century. Julia Robinson, after finishing her PhD in mathematics at UC Berkeley, began to work on Hilbert’s Tenth Problem. The film Julia Robinson and Hilbert’s Tenth Theorem by George Csicsery captures her passion for and commitment to this challenging piece of mathematics.

Hilbert’s Tenth Problem involves finding an effective method for determining if a given Diophantine equation is solvable in integers. This problem “begged for an unsolvability proof,” said Martin Davis, professor emeritus at NYU and one of Julia’s collaborators interviewed in the film Julia Robinson and Hilbert’s Tenth Theorem. Davis conjectured that the combination of ideas from logic and ideas from the theory of numbers made “a heady mix” that Robinson probably found particularly exciting.

Robinson went on to spend the rest of her life attempting to solve Hilbert’s Tenth Problem. She made important contributions to mathematics while also providing the groundwork that ultimately led to a solution to the problem. The story of Robinson’s engagement in this mathematics problem, and her close collaboration with the Russian mathematician Yuri Matiyasevich as well as other mathematicians, is the focus of the film.

The Disciplinary Literacy Practices of Mathematicians
Use the example of the fictional Charlie Eppes, who is doing applied mathematical work through his collaboration with the FBI; the example of Julia Robinson, who worked as theoretical or research mathematician; and your ownexperience solving mathematics problems to reflect on the literacy practices associated with mathematics.

Apply: What are your initial thoughts on the literacy practices associated with the discipline of mathematics? What do we know, or what might we conjecture, about how mathematicians read, write, speak, and listen? Fill out this chart [PDF] to help you organize your ideas.