Let us note that Woonsocket, the town in which Anne was born, was only established one year before her birth when three villages combined to form the town. This rapidly expanding town added three further villages to grow bigger in 1871. It was in her home town of Woonsocket that Anne Bosworth attended school. She graduated from Woonsocket High School in 1886 and later in the same year she began her studies at Wellesley College. She graduated with a B.S. in 1890 and, later that year, she was appointed as First Assistant at the Amesbury High School in Massachusetts. She taught there until March 1892. On 23 March 1892 she took up a one year appointment as an Instructor in Mathematics at Rhode Island College of Agriculture and Mechanic Arts situated in Kinston, New York. This institution, which had only received its charter in 1888, changed its name to Rhode Island State College in 1909 and today is known as the University of Rhode Island. The year in which Bosworth joined the College was the first in which it had begun to teach courses beyond the secondary school level. Bosworth's one year appointment was changed to an appointment as Rhode Island College's first Professor of Mathematics and Physics by April 1892 :-
Immediately upon her arrival at the College, Bosworth rolled up her sleeves: She developed a multi-disciplinary curriculum, began the mathematics book collection, and taught courses in algebra, geometry, calculus, various courses in physics, and "this still mysterious force" electricity.These activities are detailed in the 1892 Annual Report of Rhode Island College. Bosworth's department consisted of just herself in 1892 but, in 1893, William Elisha Drake was appointed as Professor of Mechanical Engineering. The Department continued to grow with Arthur Curtis Scott being appointed as Instructor in Physics in 1895 and promoted to Assistant Professor two years later. Bosworth wanted to study more advanced mathematics and, in the summer of 1894 and of 1896, she studied with Eliakim Hastings Moore and Oskar Bolza for a Master's Degree at the University of Chicago. She was awarded a Master's Degree in 1896.
To see how the Department of Mathematics at Rhode Island College of Agriculture and Mechanic Arts developed during her first years as Professor of Mathematics, see an extract from the 1896 Annual Report of the College  at THIS LINK.
The respect that she won from her students at Rhode Island College is clear from the College's student yearbook, The Grist 1898, published in June 1897, which contains a picture of Lucy Bosworth and the Dedication :-
To Miss Bosworth, our professor and classmate, we, who honor her ability and value her friendship, respectfully dedicate this volume.In April 1898, Bosworth was granted leave of absence so that she might attend lectures at the University of Göttingen in Germany. She travelled there with her mother Ellen Bosworth. In Göttingen she attended lectures by Felix Klein on Mechanics as well as lectures by Arthur Schönflies, Issai Schur and Woldemar Voigt. In the winter semester of 1898-99 she attended David Hilbert's lectures on Geometry :-
In spring 1899 Bosworth "was summoned" to tea with Hilbert, whose lectures on non-Euclidean geometry she had attended, and was asked when she would take her doctoral exams. She said she had not any such intention, had not even thought of a dissertation topic. Hilbert said, "But your dissertation is finished"! It appears that she had done a special exercise for him, and it was considered an entirely original approach and acceptable as a thesis. So instead of spending the summer travelling in Italy, Greece, etc. she remained in Göttingen and took her examinations and passed with honour.Bosworth submitted her 57-page thesis Begründung einer vom Parallelenaxiome unabhängigen Streckenrechnung to the University of Göttingen and her oral examination took place on 31 July 1899. Hilbert, as an examiner, wrote that her thesis was :-
... a sound and independent achievement of scientific value.She returned to the United States with her mother in August 1899 and, once the thesis was published in 1900, she was awarded a doctorate. In  George Bruce Halsted writes:-
Professor Anne Bosworth, of Rhode Island, has followed this up by actually constructing in her doctor's dissertation at Göttingen (1900), under Hilbert, a sect-calculus independent of the parallel-axiom. This is a beautiful piece of non-Euclidean geometry, and is, so far as I know, the first feminine contribution to our fascinating subject.Back at Rhode Island College of Agriculture and Mechanic Arts, Bosworth again took up her role as Professor of Mathematics. She lived with her mother in Kingston. However, her life would take a very different turn because of someone she had met while studying at Göttingen.
Theodore Moses Focke (1871-1949) was born in Massillon, Ohio, and had studied civil engineering at Case Institute of Technology in Cleveland, graduating in 1892. After a year as an Instructor in Mathematics at Case and three years as a tutor of physics and chemistry at Oberlin College in Oberlin, Ohio, he went to Göttingen to undertake research. He was awarded a doctorate in 1898 for a thesis, written in German, on the thermal conductivity of various kinds of glass. While in Göttingen he and Bosworth had met. After his studies at Göttingen, Focke returned to the United States and joined the mathematics department at Case Institute of Technology. Bosworth and Focke married on 7 August 1901 in Kingston, Rhode Island. The Fourteenth Annual Report of the Rhode Island College of Agriculture and Mechanic Arts in 1902 reported Bosworth's resignation :-
Anne L Bosworth, Ph.D., who had been professor of mathematics since the establishment of the department in 1892, sent in her resignation, to go into effect in June of this college year. It is with regret that the institution loses Miss Bosworth from the faculty. Her conscientious work has been, from the beginning, highly appreciated by every member of the institution. Laurence I Hewes, Ph.D. (Yale), was appointed professor of mathematics to succeed her.Anne Bosworth Focke joined her husband in Cleveland. They had three children, a son and two daughters. Their first child Helen Metcalfe Focke was born on 10 June 1902 and became a professor at the School of Library Science of Western Cape University. Helen died on 20 October 1997 in Los Angeles. Theodore Brown Focke was born on 16 September 1904. He was awarded a B.S. from Case Institute of Technology in 1926 and a doctorate in engineering from the University of Nancy in France, in 1928. Alfred Bosworth Focke was born on 30 September 1906. He was awarded a B.S. from Case School of Applied Science in 1928, became an assistant in physics at the California Institute of Technology and later professor and chairman of the Physics Department at Harvey Mudd College, Claremont, California. Helen Focke wrote in 1978 :-
After their marriage, Mother did not teach again but worked with Father grading papers, being a good faculty wife and having three children of whom I am the oldest.Anne Focke contacted pneumonia and died at the age of thirty-eight. She was buried in Massillon, Ohio. In 1910, three years after her death, her mother Ellen and her aunt Anna were both living with Theodore Focke in Cleveland.
Article by: J J O'Connor and E F Robertson