Women in Algebra

1
Women in Algebra

• By
• Myra Abrams

2
Hypatia

• 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 Ptolemys
  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 Ptolemys 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.

3
Christine Ladd-Franklin (1847-1930)

• 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.

4
Emmy Noether (1882-1935)

• 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
  Hitlers rule (she was Jewish).

5
Charlotte Angas Scott (1858-1931)

• 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.

6
Mary Fairfax Somerville (1780-1872)

• She was from a very poor family. She could
  barely read.
• By the age of thirteen she taught herself Latin,
  and could read Caesars Commentaries.
• She obtained her interest of Algebra while
  reading a fashion magazine. The magazine
  contained algebraic symbols in a mathematical
  interest.

• She began her mathematical studies by reading
  Euclids Elements of Geometry and later she
  studied Newtons 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

7
Julia Bowman Robinson (1919-1985)

• 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 Hilberts
  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.

8
Kate Fenchel (1905-1983)

• 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
  professors 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.

9
Helen Merrill (1864-1949)

• 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.

10
Olga Tausky-Todd (1906-1995)

• 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.