# Connemara Doran

*Research Interests: History and philosophy of modern physics and mathematics; astronomy and cosmology; energy resources; visualization practices; mathematical invention.*

Connemara Doran (PhD, 2017) is a Lecturer in the Harvard University Department of the History of Science. She specializes in the history and philosophy of the physical and mathematical sciences, in particular the history of astronomy and cosmology, mathematical physics, energy resources, and the environment.

She has just completed her first book project, *The Contested Science of Peak Oil in an Age of Abundance*. Peak oil is a highly-contested scientific object, from its theoretical and methodological foundations to its broadest implications for the future of civilization. The book is unique in scope and methodology, and it places the debate over peak oil in a new light. It assesses “peak oil” as a historically dynamic *epistemic object* that has produced knowledge at the interface of geophysics, petroleum geology, and economic theory, and, conjointly, as a *natural experiment* impacting scientific, economic, and strategic policy, for the past seventy years. The book engages competing concerns about energy security and mitigation of global warming amidst the perennial shifts of public discourse from abundance to scarcity and back. It traces the evolving visual rhetoric that shapes geophysical and economic discourse about peak supply and peak demand, situating the debate within contemporary concerns about fracking and climate change.

Her second book project, *Seeking the Shape of Space*, explores the intellectual adventure to empirically determine the size and shape of the universe – to conceptualize, measure, and map the cosmos – during the long twentieth century. Central to the story is Henri Poincaré’s odyssey to overcome the limits of geometric empiricism by creating an utterly new mathematics of spatial relations. Far from simply a tool of the mathematician or theoretical physicist, these spatial understandings undergird the aesthetics and visualization practices of diverse practitioners, including those leading the NASA missions COBE and WMAP which imaged and assessed the very first light in the universe.

Dr. Doran was the 2017-18 Postdoctoral Guggenheim Fellow at the National Air and Space Museum, Smithsonian Institution, Washington, DC.

**RECENT PUBLICATIONS**:

Books:

Book manuscript under review, *T**he Contested Science of Peak Oil in an Age of Abundance*.

Articles:

“Poincaré’s mathematical creations in search of the ‘true relations of things’” in *Ether and Modernity: The recalcitrance of an epistemic object in the early twentieth century,* Jaume Navarro, ed. (Oxford: Oxford University Press, 2018), 45-66.

• Abstract: How did the vast corpus of mathematical innovation of the French mathematician and physicist Henri Poincaré (1854-1912) engage the rationale, and impact the fate, of the notion of the ether in physics? In his scientific practice and philosophy of science, Poincaré sought the ‘true relations’ that adhere in the phenomena – relations that persist irrespective of the choice of a metric geometry and a change in physical theory. This book chapter demonstrates that Poincaré had no ownership of the physicists’ ether concept, and that he viewed the ether as neither necessary nor necessarily a hindrance for further advance. Rather, Poincaré attended to the profound and subtle needs within *physics* by creating profound and subtle *mathematics* – utterly new theoretical and interpretive concepts, tools, and structures – to capture the ‘true relations of things’, rendering the physicists’ ether superfluous to that goal while also creating mathematical structures for gravitational and quantum phenomena.

“Poincaré’s Path to Uniformization,” in *Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau Manifolds, and Picard-Fuchs Equations*, Lizhen Ji and Shing-Tung Yau, eds., proceedings of a workshop at the Institut Mittag-Leffler, The Royal Swedish Academy of Sciences, *Advanced Lectures in Mathematics* 42 (Boston: International Press, 2018), 55-79.

• Abstract: This study features the enormous conceptual leaps by which Poincaré in 1880, via his study of Fuchs’s work, established the existence of a unique (uniformizing) differential equation and thereby his theory of general transcendental automorphic (Fuchsian) functions. Poincaré derived the Riemann surface naturally and established its nature via the hyperbolic metric. Particularly astonishing was Poincaré’s linkage of his new functions with quadratic forms in arithmetic, and the unique model of hyperbolic geometry on the hyperboloid he created in establishing this linkage. Poincaré’s path into this new world of mathematical action continued to widen and deepen, and the mathematical community persistently probed his arguments, leading in 1900 to Hilbert’s problem #22 seeking rigorous proof of Poincaré’s 1883 generalized uniformization of analytic curves. Mittag-Leffler played an instrumental role throughout – inaugurating Acta Mathematica in 1882 with Poincaré’s uniformization theory, publishing Poincaré’s 1906 rigorous proof of generalized uniformization, and, in 1923, documenting Poincaré’s 1880 engagement with Fuchs’ work. We reconcile Poincaré’s and Klein’s divergent perspectives on uniformization with the philosophical concept of the “fundamental dialectic of mathematics,” which recognizes that a mathematical advance exists historically as both a rupture and a continuity. We show that Poincaré had, through his unique path to a uniformizing differential equation, added something new and epochal to the understanding of the Riemann surface and Riemannian principles. What was ex post facto seen as necessary within Klein’s Riemannian program had emerged unforeseen and naturally through Poincaré’s unique path outside the Riemannian program.

**Degrees:**

AB., Harvard University

AM., Harvard University

PhD., History of Science, Harvard University