old-time planter's garb, he was truly original in his private life as well as in his mode of thinking. He was extremely modest. No monument, said he, should stand over his grave, only an apple-tree, in memory of the three apples; the two of Eve and Paris, which made hell out of earth, and that of Newton, which elevated the earth again
into the circle of heavenly bodies.64 His son, Johann Bolyai (1802–1860), was educated for the army, and distinguished himself as a profound mathematician, an impassioned violin-player, and an expert fencer. He once accepted the challenge of thirteen officers on condition that after each duel he might play a piece on his violin, and he vanquished them all.
The chief mathematical work of Wolfgang Bolyai appeared in two volumes, 1832–1833, entitled Tentamen juventutem studiosam in elementa matheseos puræ introducendi. It is followed by an appendix composed by his son Johann on The Science Absolute of Space. Its twenty-six pages make the name of Johann Bolyai immortal. He published nothing else, but he left behind one thousand pages of manuscript which have never been read by a competent mathematician! His father seems to have been the only person in Hungary who really appreciated the merits of his son's work. For thirty-five years this appendix, as also Lobatchewsky's researches, remained in almost entire oblivion. Finally Richard Baltzer
of the University of Giessen, in 1867, called attention to the wonderful researches. Johann Bolyai's Science Absolute of
Space and Lobatchewsky's Geometrical Researches on the
Theory of Parallels (1840) were rendered easily accessible to
American readers by translations into English made in 1891 by George Bruce Halsted of the University of Texas.
The Russian and Hungarian mathematicians were not the only ones to whom pangeometry suggested itself. A copy of the Tentamen reached Gauss, the elder Bolyai's former room-mate
at Göttingen, and this Nestor of German mathematicians was surprised to discover in it worked out what he himself had begun long before, only to leave it after him in his papers. As early as 1792 he had started on researches of that character. His letters show that in 1799 he was trying to prove a priori the reality of Euclid's system; but some time
within the next thirty years he arrived at the conclusion reached by Lobatchewsky and Bolyai. In 1829 he wrote to Bessel, stating that his "conviction that we cannot found
geometry completely a priori has become, if possible, still firmer," and that "if number is merely a product of our mind, space has also a reality beyond our mind of which we cannot fully foreordain the laws a priori." The term non-Euclidean geometry is due to Gauss. It has recently been brought to notice that Geronimo Saccheri, a Jesuit father of
Milan, in 1733 anticipated Lobatchewsky's doctrine of the parallel angle. Moreover, G. B. Halsted has pointed out that in 1766 Lambert wrote a paper "Zur Theorie der Parallellinien,"