This single lecture on a deep, important and wide-ranging topic can not do more than give a brief overview of the times and ways in which the mathematical community has suffered from forms of social prejudice. This is not a discussion of discrimination against certain forms of mathematical work, based on philosophical differences, such as Kronecker's rejection of Cantor's work on infinity. The discussion here is about rejection of people, or of their work, based on questions of race or gender.

Discrimination in mathematics takes two different forms. The first, historically by far the most prevalent, takes the form of denial of access. The ancient Greeks developed the very notion of "democracy", however it went without saying, for them, that women and slaves were not concerned by the word "equality". Having essentially no access to education, these groups were barred from any attempt at mathematical achievement, even at a time when such achievement was a major function of society.

Of the few women who succeeded in studying and teaching mathematics until the mid-twentieth century, it can be said that each and every one of them had a major ally in her father. It was necessary, in fact indispensable, for a woman's father to approve of her embarking on such an unusual path. The first example of a woman who attained fame as a lecturer in science and philosophy is Hypatia, in the 4th century AD. For a complete list (and it is short!), see women in mathematics. It is difficult to pinpoint the first woman who can be said to have achieved original research, because some worked out or rediscovered things that were, or may have been, already known to others. However, there is no doubt that Sophie German, born and bred during the French revolutionary era, was the first woman to reach the highest level of research. As the biography describes, Sophie's parents were initially reluctant to let her study mathematics, but were eventually won over by her passion, and allowed it.

Cambridge University in the 1890's was one of the great world centers for mathematics. Two of its 30-some colleges were women's colleges, but the women there were not allowed to take classes together with men, or to take degrees, even after Philippa Fawcett achieved the exploit of coming out first in the famous Cambridge Tripos examination in 1890. The exclusion of women was openly unrelated to any belief in their unsuitability for academic studies. In the Victorian mind, it was because women were to be kept pure, unsullied by competition and the professional struggle.

Probably the greatest woman mathematician who ever lived was the German Jewish mathematician Emmy Noether (1882-1935), daughter of an enlightened mathematician father. Emmy had the misfortune to reach her prime around the same time that the Nazis came to power in Germany, so that after having overcome all the obstacles that being a woman threw in her path, to being allowed to take courses at the university, then being allowed to pass exams, then to defend a doctoral thesis, then to teach, she finally succeeded in all this only to be thrown out of the university in 1933 for being Jewish.

While the twentieth century (in Western countries) has removed most of the legal obstacles obstructing women's access to higher education, it is important to realise that many forms of unspoken discrimination still exist. For various reasons, women are still drastically underrepresented on the faculties of major American universities (although they are better off in many European countries). Jenny Harrison's internationally famous and still very controversial 1993 tenure case is a particularly striking example. (Note an interesting detail: there were no women on the US Math Olympiad teams until 1998 whereas a quick look at Olympiad results show women on top-scoring Eastern European -- Russia, Ukraine, teams already in 1995, probably farther back than that).

American students will not need to be told about the difficulties faced by blacks in the United States, first to accede to education, then to higher education, and finally to academic professorships allowing them to flourish in research. It is not easy to find explicit tales of discrimination on this subject, because the available information tends to take the form of celebrating their remarkable achievements. We can be proud the that second and third Ph.D.'s in mathematics awarded to African Americans in the United States were awarded here at Penn, in 1927 and 1933 (the first was awarded in 1924 at Cornell). Unlike women, who are numerous in Ph.D. programs across the country but too rare among the faculty, black mathematicians are severely underrepresented already at the Ph.D. level. These numbers speak for themselves of the subtle silent discrimination that still exists.

Discrimination barring university access to Jews has been historically much less of a problem in the West, but the Soviet Union developed particularly pernicious forms of such discrimination, developing for example two sets of problems for the oral university entrance exam, of which one, much harder than the other, was applied to students with Jewish-sounding names (see page 4 of this article.

The second, even more pernicious type of discrimination that has historically hit the mathematical community takes the form of discrimination against already accomplished mathematical work. The most flagrant example is the effort made by Nazi philosophers, starting in the 1930's, to distinguish between "Aryan mathematics" and "Jewish mathematics". The mathematician Ludwig Bieberbach became one of the major Nazi theorists on this subject. He developed the theory that mathematics done by Jews tends to be highly complex, highly abstract, algebraic, and far removed from deep intuitive considerations coming from closeness to nature. He also claimed that Jewish mathematicians are quick but shallow, making brilliant use of already existing results to spin off as many consequences as possible, whereas the true new ideas come from Aryans. Bieberbach's work provided the official justification (if any was needed) for the Nazis to remove all Jewish professors from German universities starting in 1933, on the grounds that their teaching was "tainting" the minds of the Aryan students. The University of Göttingen in particular lost six of its best professors in a single swoop. David Hilbert, one of the very greatest mathematicians of his time, had worked hard to have these particular professors hired, thus lost six of his colleagues and remained isolated in the department. It is reported that when Hilbert found himself sitting next to the Minister of Education at a banquet, who proudly asked him "How is mathematics at Göttingen now that it has been freed of the Jewish influence?", Hilbert quietly responded "Mathematics at Göttingen? There is none any more." For specific instances of mathematicians who suffered such discrimination, see for example Issai Schur or Edmund Landau.