Year of Award
Doctor of Philosophy (PhD)
Other Degree Name/Area of Focus
Department or School/College
Department of Mathematics
Gregory St. George, Karel Stroethoff
James Hirstein, Jed Mihalisin, James Sears
University of Montana
In the 1820's, Nikolai Ivanovich Lobachevski discovered and began to explore the world's first non-Euclidean geometry. This crucial development in the history of mathematics was not recognized as such in his own lifetime. When his work finally found a sympathetic audience in the late 19th century, it was reinterpreted in the light of various intermediate developments (particularly Riemann's conception of geometry), which were foreign to Lobachevski's own way of thinking about the subject.
Because our modern understanding of his work derives from these reinterpretations, many of Lobachevski's most striking ideas have been forgotten. To recover them, I have produced an "illuminated" version of Lobachevski's most accessible work, Geometrische Untersuchungen zur Theorie der Parallellinien (Geometric Investigations on the Theory of Parallels), a book that he published in 1840. I have produced a new English version of this work, together with extensive mathematical, historical, and philosophical commentary. The commentary expands and explains Lobachevski's often cryptic statements and proofs, while linking the individual propositions of his treatise to the related work of his predecessors (including Gerolamo Saccheri, J.H. Lambert, and A.M. Legendre), his contemporaries (including J·nos Bolyai and Karl Friedrich Gauss), and his followers (including Eugenio Beltrami, Henri PoincarÈ, and David Hilbert). This dissertation supplies the contemporary reader with all of the tools necessary to unlock Lobachevski's rich, beautiful, but generally inaccessible world.
Braver, Seth, "Lobachevski Illuminated: Content, Methods, and Context of the Theory of Parallels" (2007). Graduate Student Theses, Dissertations, & Professional Papers. 631.
© Copyright 2007 Seth Braver