Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

352 MATHEMATICAL PHILOSOPHY
tinctively human. I am unable to understand how anyone can ponder its character and its significance intelligently and candidly without seeing clearly that the old
zoological conception according to which human beings
are a species of animal is not only false, as Count Korzybski has pointed out, but is stupid as well; in view of its
baneful effects upon the world's ethics, the monstrous
misconception deserves indeed to be branded as the Great
Stupidity.
I shall not here recount the tale; the story has been
often told in all the lands and all the tongues of science.
If you desire to learn the story, you will find in the mentioned work of Dr. Heath an ample clue to the literature. For an account that is at once very clear, very
succinct and finely critical, I have special pleasure in referring to Dr. George B. Halsted's article ("Geometry,
non-Euclidean") in the Encyclopedia Americana. I own
to the feeling of a little pride,-pardonable, I hope,in that citation for it was my privilege, as then mathematical editor of Americana, and my good fortune, to
obtain the article in question. I requested Dr. Halsted
to write it because he was specially qualified to do it;
no other American scholar knew more than he of non.
Euclidean origins and no other has done so much as he
has done, by voice and pen, to signalize the importance
of non-Euclidean geometry as making and marking a
momentous epoch in human Thought.
Of non-Euclidean geometry there are two principal
varieties; these are associated respectively with the names
of their inventors-Lobachevski (I793-I856) and Bernhard Riemann (I826-66). I am going to tell, as clearly
as I can without too great prolixity, how the varieties