# Connemara Doran

National Academy of Sciences - National Research Council (NAS-NRC) Research Associateship

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

Connemara Doran, PhD, is Science Historian at the Air Force Office of Scientific Research (AFOSR) in Arlington, Virginia, and holds a National Academy of Sciences - National Research Council (NAS-NRC) Research Associateship. Dr. Doran is a historian of modern science and technology, specializing in the history and philosophy of the physical and mathematical sciences, in particular on the history of astronomy and cosmology, mathematical physics, space science and technology, energy resources, environmental sciences, and climate science. Her research examines developments, from the late 19^{th}-century to the early 21^{st}-century, in theoretical and experimental physics basic research across the fields of relativity, quantum mechanics, astrophysics, cosmology, and metrology. She has researched and published on the development of scientific instruments and space technology that enabled transformative basic research in Cosmic Microwave Background (CMB) cosmology (“Instrumentalizing and Visualizing the Cosmic First Light,” published in 2021); and on the creation of the hydrogen maser atomic clock and its use in testing theories of gravity in the 1976 Gravity Probe A rocket experiment carried out by NASA and the Smithsonian Astrophysical Observatory (in press).

Dr. Doran extensively researched and has published on the groundbreaking contributions of the *fin-de-siècle *French mathematician, engineer, physicist, and philosopher, Henri Poincaré. One article, “Poincaré’s Path to Uniformization” (published in 2018), was an invited contribution to a peer-reviewed mathematics volume. In that article, Dr. Doran explained the origins of a foundational branch of mathematics that brought together algebra, geometry, and analysis in an entirely new and transformative way in the late 19^{th} century. She used this historical case to explain how innovation and discovery can occur in pure mathematics, and how conceptual mathematical advance can occur as both a rupture and a continuity with previous research. This insight is not unique to pure mathematics, but also is applicable to mathematical, theoretical, and experimental physics and instrumentation. In another article, “Poincaré’s mathematical creations in search of the ‘true relations of things’” (also published in 2018), Dr. Doran analyzed how Poincaré attended to the subtle features of space and time within physics by creating subtle mathematical approaches to capturing the empirically-based “true relations” of spacetime – relations that persist regardless of the choice of spatial metric or of a change in physical theory. In this way, Poincaré created mathematical structures still used today to study gravitational and quantum phenomena and the multifold challenges of dynamical systems.

Throughout her career, Dr. Doran has worked with government agencies and academic research groups. She has completed a book manuscript on the history of U.S. energy systems in the long 20^{th} century, including the role of hydraulic fracturing and debates regarding peak supply and peak demand for oil. As Lecturer at Harvard University, Dr. Doran created and taught courses on the history of the physical sciences from the 17^{th} to the early 20^{th} centuries and on the history of environmental and climate science in the U.S. and globally. As a Guggenheim Fellow at the Smithsonian National Air and Space Museum in Washington, DC, she researched experimental aspects of NASA’s COBE and WMAP space missions: the scientific instruments created (detectors and amplifiers, microwave radiometers, cryogenic cooling technologies); the computational algorithms and statistical methods employed for data analysis and visualization production; and the dynamic interactions among scientist principal investigators, science team members, engineers, NASA administrators, university laboratories, and scientific funding agencies.

**TEACHING**:

Connemara Doran designed and taught the following courses in 2019-2020:**Fall 2019 Seminar: Nature, Energy, Industry: A Cultural History of Physical Science** • Syllabus **Spring 2020 Lecture Course: Environmental Science and Its History: Big Problems and Debates** • Syllabus

**RECENT PUBLICATIONS**:

**Books:**

Book manuscript under revision, *Energy and Climate in the 21st Century**.*

**Articles:**

“Low-cost, High-risk Electricity and the Texas Polar Vortex,” *IAEE Energy Forum* (Fourth Quarter 2021): 48-51.

"Instrumentalizing and Visualizing the Cosmic First Light," forthcoming in *Nuncius: Journal of the Material and Visual History of Science *36, 1 (April 2021)

“Instrumentalizing and Visualizing the Cosmic First Light,” *Nuncius: Journal of the Material and Visual History of Science* 36, 1 (April 2021): 167-192.

“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