more embittered when his towering achievement—being the first person
to publish a consistent non-Euclidean geometry—was taken from him.
Nikolai Ivanovich Lobachevsky
The third discoverer of non-Euclidean geometry in this recitation was in
actuality the first—or at least the first to publish. Nikolai Ivanovich Lo-
bachevsky was the son of a poor government clerk. His father died when
Nikolai was seven, and his widow moved to Kazan in eastern Siberia.
Nikolai and his two brothers received public scholarships to secondary
schools, and Nikolai entered Kazan University, intending to become a
medical administrator. Instead, he would spend the rest of his life there
as a student, teacher, and administrator.
He was obviously an extremely talented student, for he graduated from
the university before his twentieth birthday with a master’s degree in
both physics and mathematics. He then received an assistant professor-
ship and became a full professor at age twenty-three. Admittedly, other
talented mathematicians have become full professors at an early age, but
nonetheless this was an impressive achievement.
Lobachevsky worked along roughly the same lines as Gauss and Bolyai,
substituting the assumption that through each point not on a given line
there existed more than one parallel to the given line, and going on from
there to develop hyperbolic geometry. He published this in 1829 (thus
establishing priority, for Gauss never published and Bolyai’s effort was
published in 1833) in a memoir entitled On the Foundations of Geometry.
However, instead of publishing it in a reviewed journal it appeared in the
Kazan Messenger, a monthly house organ published by the university. Lo-
bachevsky, believing that it deserved a wider and more knowledgeable
audience, then submitted it to the St. Petersburg Academy—where it was
summarily rejected by a buffoon of a referee who failed to appreciate its
value. The last sentence may seem rather strong, but having had a few
papers bounced in my career by similar buffoons, I can sympathize with
Lobachevsky. At any rate, Lobachevsky’s effort was another addition to
the lengthy list of great papers that initially got bounced.
To Lobachevsky’s credit, he refused to be discouraged, and finally had a
book published in 1840 in Berlin with the title Geometric Investigations on
the Theory of Parallels. Lobachevsky sent a copy of the book to Gauss, who
was sufficiently impressed to write a congratulatory letter to Lobachevsky.
Gauss also wrote to his old friend, Schumacher, with whom he had first
discussed alternative geometries, that although he was not surprised at
110 How Math Explains the World