User:CountingKoalas/GraceBates

Grace Elizabeth Bates (13 August 1914 – 19 November 1996) was an American mathematician and one of few women in the United States to be granted a Ph.D. in mathematics in the 1940s. She became an emeritus professor at Mount Holyoke College. Bates specialized in algebra and probability theory, and she co-authored two books: The Real Number System and Modern Algebra, Second Course. Throughout her own education, Bates overcame obstructions to her pursuit of knowledge, opening the way for future women learners.

Early life and education
She was born on 13 August 1914. Interested in mathematics from a very young age, Bates was encouraged to pursue by her family. Bates maintained a close relationship with her brother, reinforced by the early death of their mother. Upon completing high school, her brother used his salary to help her continue her education through high school and college.

During her studies, Bates would petition several times to take more advanced math courses than were typically available. Bates attended the Cazenovia Seminary for high school, where she petitioned to take intermediate algebra. She pursued her undergraduate studies at Middlebury College. At this time, Middlebury College was segregated by sex and had one female math professor teaching the entire women's math curriculum. For her senior year, Bates petitioned to take differential equations, which was only offered to male students. She would become the only woman in the course. After completing her B.S. in mathematics in 1935, she continued in her studies and obtained a master's degree at Brown University in 1938.

Bates entered her doctoral program at the University of Illinois in 1944. Initially interested in geometry, Bates instead decided to pursue algebra and work under Reinhold Baer. She completed her doctoral thesis, titled "Free Loops and Nets and their Generalizations", in 1946.

Professional life and continuing education
Having aspired to be a teacher most of her life, Bates began teaching mathematics and English to elementary and secondary school children. The idea of teaching at the collegial level drew her back to continue her education. While pursuing her doctorate, Dr. Bates discovered her love for research. For her dissertation, Dr. Bates worked with Reinhold Baer and rose to his frequent challenges. In her words,"'[T]he one thing about getting a doctorate I had dreaded was this original thesis you were supposed to write ... I didn’t think I could do it, and I [thought] it would be all drudgery. Well, it wasn’t that way at all with Baer ... I have it [the dissertation] here — it’s on free loops and nets. He gave me the definition of a loop, of which I’d never heard before, and [the] idea of using a graphic approach to some of the theory he had [believed] ought to be true, and said, “Oh, go ahead now, let’s see what you can do.”  And I’d fumble around, and I didn’t think I had much.  I’d go into the study room we graduate students had, and he’d be in the very next day to see.  And he’d say, “Miss Beets!”  He never did get my name right.  And...after I’d give him something that I’d done... he’d say, “Well, this is all wrong.  This theorem is all wrong.  I don’t think it’s true.” ... I thought, “I’m going to stay up all night till I find a counterexample!”  And I really worked like a dog, and I got into my study place there the next day, and sure enough he came in and said, “Ah, Miss Beets, I found a counterexample!” And I said, “So did I!”  And that was the first [time], really, that I began to have confidence in myself'"In 1949, Bates graduated from the University of Illinois with a Ph.D. in mathematics. After teaching briefly at Sweet Briar College, she joined the faculty of Mount Holyoke College where she advanced to become a full and emeritus professor. She worked here till her retirement in 1979. It was while working at Mount Holyoke Dr. Bates discovered her love of statistics. "It was a tradition everywhere that statistics-probability was given to the youngest person. Nobody wanted to teach it!  And so I was given a course in probability and a course in statistics at Mount Holyoke.  And I worked like a dog.  And I found I was getting really interested in it.  My predecessor was a famous mathematician, [Antoni Zygmund,] who went to the University of Chicago from Mount Holyoke.  Well, he had taught [probability and statistics before me].  And I’d come in after him and struggled along as he did.  But [Zygmund] came back from a social occasion [some] time later.  And I was telling him how interested I was getting in the subject, but I really needed more education in it.  And he said, “Well, I’ll write to my friend out in California, Neyman, Jerzy Neyman”—a Polish mathematician.  “I think maybe he could help you.”  And he apparently did, and I got this letter offering me an assistantship for the summer session there at the University of California at Berkeley." Thanks to the introduction from Antoni Zygmund, Dr. Bates spent several summers in the 1950s working with Jerzy Neyman at Berkeley. Together they wrote a number of research articles.

Throughout her life, Bates found she was drawn to teaching, which sparked her love of research which in turn, brought her back to teaching. She died on 19 November 1996.