- Apollonius and conics
- Archimedes and measurement of circle
- Diophantus and number theory
- origins of trigonometry
- origin of logarithms
- early history of Fermat's last theorem
- Fermat and analytic geometry
- Kepler
- Cavalieri
- Desargues
- Wallis
- early use of complex numbers (Bombelli,...)
- Pascal
- Newton and fluxions
- Leibniz and calculus
- pi (up to 1700)
- Fibonacci
- Mersenne
- Stevin and decimal notation
- Cardano and cubic equation
- Gauss and fundamental theorem of algebra
- Galois and the Galois group of a polynomial
- Abel and the quintic equation
- Euler: Introductio in analysin infinitorum
- Cauchy and continuity
- Hamilton and quaternions
- Riemann and Riemann surfaces
- Klein and Erlanger program
- projective geometry: Poncelet, von Staudt, Steiner
- Hermite and transcendence of e
- Lindemann and transcendence of pi
- fundamental theorem of calculus
- Gauss and quadratic residues
- Maria Gaetana Agnesi
- Sophie Germain's work on Fermat's last theorem
- Kummer and unique factorization into ideals
- Lagrange and the four-squares theorem
- Poincaré and beginning of topology
- Sylow's theorems in group theory
- The nine-point circle
- Cayley-Hamilton theorem
- Dirichlet and analytic number theory
- Cauchy's integral formula
- Jordan normal form of a matrix
- Riemann mapping theorem
- Fourier series
- genus of an algebraic curve or of a compact Riemann surface
- Weierstrass
- Jordan curve theorem
- finite fields: existence and uniqueness for each prime power order
- Cantor and cardinal/ordinal numbers
- space-filling curves
- the concept of vector space
You are also free to choose a topic not on this list,
but in that case you should talk about your plans with me
as early as possible.
In any case, the topic should have some aspect that you can treat
at a mathematical level appropriate for an upper-division
math course.
It might help to have someone within your group who has some familiarity
with the original language of the work, though it's probably
not necessary, since many of these things have been translated
into English, and in any case you can use a dictionary.