After attending schools in Boston, Olive Clio Hazlett entered Radcliffe College. This College, which existed from the 1870s as somewhere women could obtain informal education by Faculty members from Harvard University, was given the right to award degrees in 1894 after moves to admit women directly to Harvard failed. Hazlett graduated from Radcliffe College in 1912 and then went to the University of Chicago to undertake research in algebra. There she undertook :-
... graduate training in the Department of Mathematics and Astronomy of the University of Chicago (chiefly under Professors E H Moore and L E Dickson, writing my theses under the latter) ...
She was awarded her Master's Degree in 1913 and a Ph.D. in 1915 for a thesis entitled On the Classification and Invariantive Characterization of Nilpotent Algebras. Following the award of the doctorate Hazlett was awarded an Alice Freeman Palmer which enabled her to attend Harvard during 1915-1916. Her first appointment was at Bryn Mawr in 1916 where Charlotte Scott, the first Head of Mathematics was still in that role. The College was headed by Martha Carey Thomas who by this time had built it into a college with a very high quality of education for women.
After two years at Bryn Mawr, Hazlett was appointed as Assistant Professor at Mount Holyoke. In 1924 Mount Holyoke promoted her to Associate Professor, but Hazlett was dedicated to research in algebra and she was unhappy with the many classes she had to teach leaving her little time for research. Other facilities, such as the library, were not really what an ambitious researcher required so Hazlett decided to move on. She applied for a post at the University of Illinois and already she had a high research reputation being described by L E Dickson as :-
... one of the two most noted women in America in the field of mathematics.
She was offered a post at the University of Illinois and she knew that there she would have all the facilities she needed to concentrate on her algebra research. She wrote in  that after her doctoral training:-
... it was inevitable that I should continue research in algebra: linear algebras, nilpotent algebras, matrices, quaternions, division algebras; modular invariants and convariants in a Galois Field, GF(pn), of order pn- both formal and otherwise; and ideals of a matrix algebra. The resulting papers were published in Bulletin of the American Mathematical Society, Transactions of the American Mathematical Society, Annals of Mathematics, Journal of Mathematics, and Journal de Mathématiques Pures et Appliquées as well as in Proceedings of the International Mathematical Congress (Toronto, 1924) and Atti del Congresso Internazionale dei Matematici (Bologna, 1928).
The International Congress of Mathematicians in Bologna which Hazlett mentions at the end of this quote was one to which she presented a paper Integers as Matrices. She was able to attend it while holding a Guggenheim Fellowship which enabled her not only to visit Italy, but also to visit Göttingen in Germany and Zürich in Switzerland during 1928 and 1929. Back at the University of Illinois in 1930, she was promoted to Associate Professor. However, she found the teaching workload high and she felt that Illinois never quite gave her the research opportunities that she felt she had been promised when she was first appointed. She did not publish any further papers on algebra after 1930 but she was active in other ways, both before and after that time :-
I did refereeing of research papers in above lines of algebra offered for publication to Transactions of the A.M.S., Annals of Mathematics, and (I think) Journal of Mathematics. For some years, I was an Associate Editor of the Transactions of the A.M.S., a research journal. Also, I wrote the article on Quaternions for the Encyclopaedia Britannica (14th edition). - Around 1930, the International Association of University Women formed a committee to award fellowships and I was made the judge of any mathematical manuscript submitted to it.
In 1934-35 one of the students taking her algebra class was Paul Halmos. He writes :-
Algebra was taught by Olive Hazlett who was, by our lights, a famous and important mathematician: she published papers and she taught advanced courses... Hazlett's course was based mainly on the first volume of van der Waerden, with, of course, some deletions and additions. She enjoyed telling us about one of her papers whose title she gave as "Embedding a ring in a field," and she enjoyed telling us how her colleague Shaw teased her about it - it evoked a picture of nefarious agricultural activities, he said.
The difficulties were about to take their toll, however. Rossiter writes in :-
Isolated and moderately successful but with aspirations of full equality, [she] denied the potential psychological dangers in [her] position.
She wrote to the Chairman of the Mathematics Department in 1935 complaining about the large service courses she was required to teach. By December 1936 she was forced to take sick leave which was supposed to end in August 1937 so that she could take up teaching again for the academic year 1937-38. However her health was not good enough to allow this and she was forced to take another year off on sick leave. We have a description of Hazlett teaching a second semester course on algebra in 1940-41 by one of the students taking the class who writes that she was :-
... tall, thin, her long grey hair done up in a bun, wisps of hair always hanging down in her face. She seemed so different that we in her class were rather frightened of her.
World War II led to a second phase in Hazlett's research. She describes that as follows :-
... in 1940 came the second World War and I found myself caught up in its tentacles. The American Mathematical Society appointed a Cryptanalysis Committee with (as I recall) five members of whom Professor A A Albert of the University of Chicago was chairman and Commander H T Engstrom the military (and hence the most important) member. Later, they apparently added some members and I was one of them. Accordingly, I had entrusted to me several classified military documents of the U.S. Signal Corps.
Her description of the lengths she had to go to in order to keep her work secret makes interesting reading :-
This meant that I had to exercise great caution as to [the documents] safety. Naturally, as a naive self-protection, I told the head of my department about the work and the documents, showing him the letter from Commander Engstrom. Otherwise, I did not mention documents or work to a soul except to an officer of the U.S.S.C. or to the F.B.I. when need arose. [In a subsequent letter Hazlett corrected this by giving the names of one or two others she had confided in, including G E Moore.] I never had them in my office at the University and I used them only in my apartment which I shared only with a loyal dog. If the door-bell rang when I was working with them, I quickly scuttled them out of sight and reach, replacing them with innocent stuff (research in progress) in algebra that was waiting. At my summer place, I had installed a Diebold Treasure Chest with triple-combination lock and then changed combinations single-handed.
It so happened that one of my ideas was, apparently, the bit that was featured by Commander Enstrom when he gave [the preliminary report of the Cryptanalysis Committee] to the A.M.S. at the Museum of Science and Industry in Chicago in the spring 1943 or 1944. - Later, they suggested that I go to D.C. to make certain contacts and I so did on my way back to my job in early fall of 1944. Of all my various reports, I kept a carbon copy, sent original "registered, return receipt requested" and then burned my copy in a galvanized iron pail, pouring ashes down toilet.
Hazlett retired in 1959 and she was made professor emeritus. She spent the 15 years of her retirement in her home at Peterborough, New Hampshire.
Article by: J J O'Connor and E F Robertson