The History of Mathematics: A Brief Course

3. MODERN EUROPEAN WOMEN 93

Resistance from conservatives. Lest it be thought that the presence of such power-

ful talents as Charlotte Angas Scott and Sof'ya Kovalevskaya removed all doubt as

to women's ability to create mathematics, we must point out that minds did not

simply change immediately. Confronted with the evidence that good women math-

ematicians had already existed, the geometer Gino Loria (1862-1954) rationalized

his continuing opposition to the admission of women to universities as follows, in

an article in Revue scientifique in 1904:

As for Sophie Germain and Sonja Kowalevsky, the collaboration

they obtained from first-rate mathematicians prevents us from fix-

ing with precision their mathematical role. Nevertheless what we

know allows us to put the finishing touches on a character por-

trait of any woman mathematician. She is always a child prodigy,

who, because of her unusual aptitudes, is admired, encouraged, and

strongly aided by her friends and teachers. In childhood she man-

ages to surpass her male fellow-students; in her youth she succeeds

only in equalling them; while at the end of her studies, when her

comrades of the other sex are progressing vigorously and boldly,

she always seeks the support of a teacher, friend, or relative; and

after a few years, exhausted by efforts beyond her strength, she

finally abandons a work which is bringing her no joy.

The analysis of the factual errors and statistical and logical fallacies in this

farrago of nonsense is left to the reader (see Problem 4.9 below). Loria could have

known better. Six years before Loria wrote these words Felix Klein was quoted by

the journal he progres de Vest as saying that he found his women students to be in

every respect the equals of their male colleagues.

Grace Chisholm Young. Klein began taking on women students in the 1890s. The

first of these students was Grace Chisholm, who completed the doctorate under

his supervision in 1895 with a dissertation on the algebraic groups of spherical

trigonometry. Her life and career were documented by her daughter and written up

in an article by I. Grattan-Guinness (1972), which forms the basis for the present

essay.

She was born on March 15, 1868, near London, the fifth child of parents of

modest but comfortable means and the third child to survive. As a child she

was stricken with polio and never completely recovered the use of her right hand.

Like Charlotte Angas Scott, she was tutored at home and passed the Cambridge

Senior Examination in 1885. Also like Scott, she attended Girton College and met

Cayley. Her impressions of him were not flattering. To her he seemed to be a

lumbering intellectual dinosaur, preventing any new life from emerging to enjoy

the mathematical sunshine. In a colorful phrase, she wrote, "Cayley, unconscious

himself of the effect he was having on his entourage, sat, like a figure of Buddha

on its pedestal, dead-weight on the mathematical school of Cambridge" (Grattan-

Guinness, 1972, p. 115).

In her first year at Cambridge she might have been tutored by William Young

(1863-1942), who later became her husband, except that she heard that his teach-

ing methods were ill suited to young women. She found that Newnham College,

the other women's college at Cambridge, had a much more serious professional

atmosphere than Girton. She made contacts there with two other young women