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

THE GROUP CONCEPT 227
collegiate mathematics iteluding the elements of analytical geometry and calculus; and who, encouraged by this
initial success, aspired to the mathematical doctorate and
entered seriously upon higher studies essential thereto;
it was necessary for her to grasp more and more complicate
concepts formed by combining ideas she already possessed; after no long time she reached the limit of her
ability in this matter,-a fact first noticed by her instructors and then by herself,-and being a woman of good
sense, she abandoned the pursuit of higher mathematics.
I may add that subsequently she gained the doctorate in
history. It may be that some minds are not thus limited.
It may be that a genius of the so-called universal type,an Aristotle, for example, or a Leibniz or a Leonardo
da Vinci,-is one whose mind has the group property.
May I leave the questions for your consideration in the
days to come?
The Group Concept Dimly Adumbrated in Early
Philosophic Speculation.-The mathematical theory of
groups is immense and manifold; in the main it is a work
of the last sixty years; even the germ of it seems not to
antedate Ruffini and Lagrange. Why so modern? Why
did not the concept of a closed system,-of a system having
the group property,-come to birth many centuries earlier?
The elemental constituents of the concept,-the idea of a
class of things, the idea of anything being or not being a
member of a class, the idea of a rule or law of combination,
-all these were as familiar thousands of years ago as they
are now. The question is one of a host of similar questions whose answers, if ever they be found, will constitute
what in a previous lecture I called the yet unwritten
history of the development of intellectual curiosity, WhQ
will write that history? And when?