Women in Algebra

1. Women in Algebra By : Myra Abrams

2. Was introduced to all systems of religion, by father, Theon, who was a professor of mathematics at the University of Alexandria. She was invited to teach mathematics and philosophy at the University of Alexandria. Young students came from all over Europe, Asia, and Africa to hear her lecture on the Arithmetica of Diophantus. She authored several treaties on Ptolemy’s Almagest. A portion of her work involved Diophantine Algebra, which dealt with first degree and quadratic equations She also wrote On The Conics of Apollonius and she made commentaries on Ptolemy’s Almagest. She belonged to the school of Greek thought called neo-Platonia. Neo-Platonia was the scientific rationalism that ran opposition to the dominant Christian religion. She was murder in 415 AD on her way to the university by a mob of religious fanatics. The fanatics pulled out all of her hair, scrapped off her skin with oyster shells, and threw her into a pit of fire. Hypatia

3. At the age of 16 she was determined to go to Vassar Female College. In order to attend the college she had to convince her grandmother. She wrote her grandmother a letter saying that there were too many females in New England and that she was not pretty enough to get married, so she need an education in order to support herself. She attended Vassar and graduated in 1883. She later attended John Hopkins University (despite the men-only policy) In 1883 she completed her dissertation titled “On the Algebra of Logic”. Although she fulfilled her requirements for a Ph. D., the university would not grant her a degree (because she was a woman). Her dissertation and subsequent publications represented the first work in logic by an American woman. In 1925, John Hopkins University finally offered her a Ph.D., at the age of 78. Christine Ladd-Franklin (1847-1930)

4. Though initially prepared to be a schoolteacher of foreign languages obtaining certification in English and French, she decided to persue her first love, mathematics. Women at the time were only allowed to audit courses. She started auditing classes at the University of Erlangen and later the University of Gottengen. She received her Ph.D., in mathematics, and graduated summa cum laude. Her doctoral thesis centered on computation dealing with “invariants off ternary biquadratic forms”. Her work became part of the research effort related to developing Einsteinium differential invariants. She became a master algebraist who transferred the study of structures such as rings of polynomials and hypercomplex numbers into powerful, abstract algebraic theories. These structures are called Neotherian rings in her honor. These rings can be studied in the branch of abstract algebra. In 1933 she became a teacher in America, due to Hitler’s rule (she was Jewish). Emmy Noether (1882-1935)

5. At age 18, she joined one of the colleges of Cambridge University, Girton College. She scored eighth in mathematics, but was not allowed to attend the award ceremony or have her name read as a recipient. She finished her doctorate in 1855 from the University of London. She wanted to be a research mathematician and decided to work at Bryn Mawr College in Pennsylvania. She was one of two of female professors at the college. She required her students to have had Algebra through quadratic equations and geometric progressions and plane geometry. She also required her students to take solid geometry and trigonometry She was very active in the American Mathematical Society and the American Journal of Mathematics. Her research focused about algebraic curves of degrees higher than two, connecting algebra to geometry. She was one of the first to prove theorems abstractly. Charlotte Angas Scott (1858-1931)

6. She began her mathematical studies by reading Euclid’s Elements of Geometry and later she studied Newton’s Principia. Her main contribution to algebra centered on the solving of Diaphantine equations. She published her work and won a silver medal. Some of her works were The Mechanics of Heavens, Micanique Celestre,The Connection of the Physical Sciences, and Molecules and Microscopic Science She was from a very poor family. She could barely read. By the age of thirteen she taught herself Latin, and could read Caesar’s Commentaries. She obtained her interest of Algebra while reading a fashion magazine. The magazine contained algebraic symbols in a mathematical interest. Mary Fairfax Somerville (1780-1872)

7. She was considered a slow child, but she had a stubbornness that she attributed to her success in mathematics. When she was younger she became ill with scarlet fever. Her parents hired a tutor that brought her through the fifth, sixth, seventh, and eighth grades. In high school she took geometry, algebra, advanced algebra, trigonometry, and solid geometry. She was the only female in these classes. She went to San Diego State University and majored in mathematics. Her Ph.D. thesis looked at how integers could be related to rational numbers. She received her Ph.D. in 1948. She started focusing her work on David Hilbert’s 10th problem, which dealt with Diophantine equations, which she explained her progress in this area in a paper titled “Existential Definability in Arithmetic.” She hypothesized that there were Diophanntine equations that increased faster than polynomials, but slower than exponents. Her hypothesis was later proved correct. Julia Bowman Robinson (1919-1985)

8. As a child she taught herself to read and write. She attended a private girls’ school for six years and then attended high school for six more years. She later studied mathematics at the University of Berlin (1924-1928). She got a job teaching high school math in 1931, but lost her job when Hitler came to power (she was Jewish). She moved to Denmark, and became mathematics professor’s secretary and did research in Algebra. She published her first paper in 1937, and later in 1965 she published two more papers regarding her research in Algebra. Most of her work focused on finite nonabelian groups, particularly the nature of groups of odd order. One area of particular interest to her dealt with vectormodules. In another paper, she used an (n-1)x(n-1) structure matrix for a finite group with n elements. Kate Fenchel (1905-1983)

9. In 1882, she began attending Wellesley College majoring in mathematics. In her day and time woman were being recognized as competent. Yale awarded her a Ph.D. in 1903. Women mathematicians were expected to resign from their college teaching posts upon marriage, so she stayed single. Merrill wrote two algebra textbooks titled, A First Course in Higher Algebra and Selected Topics in Higher Algebra. Helen Merrill (1864-1949)

10. She began her studies in 1925, at the University of Vienna and received her doctoral degree in 1930. While working in the National Bureau of Standards, wrote three chapters in the Handbook of Physics. A chapter each on algebra, operation theory, and ordinary differential equations. Her major work was in topological algebra or algebraic number theory. Her matrix theory fell into three categories: Analytic, Algebraic, and Arithmetical. Her algebraic work focused on commutativity, generalized commutatuvuty, and additive and multiplicative commutators. Olga Tausky-Todd (1906-1995)