Equation Solving from Babylon to Galois

Bridget Ruff, Bates College


Galois Theory represents a pivotal moment in Mathematics. Through a single theorem, ancient problems in equation solving and ruler and compass geometry were solved and modern ideas of Algebra emerged. Further, by using the Galois Theory as a case study for the search for understanding in Mathematics, this thesis argues that the search for solutions to equations is part of a search for human understanding of the world. By tracing the roots of early Mathematics in Babylon, China, and the Middle East to the Renaissance, Enlightenment and French Revolution, the search for solutions connects people with vastly different conceptions of numbers to a single theory. The impossibility of certain ruler and compass constructions and the insolubility of the quintic end a centuries long search for solutions and retain meaningful results for mathematicians today.