The role of the “crisis” of incommensurables in the development of pre-Euclidean Greek mathematics

Evaluation scheme:

Arguments (50%): The essay presents a concise, well-stated, interesting and non-trivial thesis; and it is argued for persuasively. The student engages with historical sources (primary and/or secondary).

Style: “proper essay” (20%): The essay has a clear introduction, body, conclusion, transitions, thesis statement etc.

Style: writing ability (10%): Clarity, sentences, paragraphs, foot/end notes, formal (academic) style, etc.

Sources (10%): Uses good sources (number, quality, level) and proper bibliographic style (clear, consistent)

Overall effort (10%): General impression – was a lot of work put in, or was it written at the last minute?

Essay Topics

The list below is intended as a general guide in choosing a topic. The essay itself should be fairly specific in developing some theme or exploring some issue that arises in these or any other subject areas. Avoid general descriptive overviews or reports on the literature. Although the essay may contain a synthesis of factual material, it should be focussed, analytical and issue-oriented.

Decomposition of unit fractions in Egyptian mathematics

Babylonian mathematical astronomy

The role of the “crisis” of incommensurables in the development of pre-Euclidean Greek mathematics

Geometric algebra in Euclid’s Elements

The method of exhaustion in Euclid and Archimedes

The place of construction in Greek geometry

Numerical methods in Ptolemy’s Almagest

The role of mathematics in the development of Greek astronomy

Contributions of Islamic mathematical science to algebra and arithmetic

Mathematical astronomy in Islamic science

Trigonometry and Islamic mathematics

Foundations of geometry in Islamic mathematics

Indian work on infinite series

The reception and transmission of Euclid’s Elements in Medieval Europe

Proportion theory in the Middle Ages

Mathematical dynamics in the Middle Ages

Oresme and the latitude of forms

The handling of imaginary numbers by Cardano and Bombelli

Viète and the invention of the analytic art

Mathematics in Copernicus’s De Revolutionibus

Linear perspective in art and the origins of projective geometry

The construction of curves in Descartes’ Géométrie

Number theory in the seventeenth century

Theory of probability in the seventeenth century

Concepts of the continuum in Medieval mahematics

Kepler’s derivation of the elliptical orbit

Napier and the invention of logarithms

The history of the concept of analysis from Pappus to Descartes

Method of indivisibles in 17th-century mathematics

Tangent methods in the pre-calculus period

Transcendental curves in 17th-century mathematics

Optimization problems in seventeenth-century mathematics

Mathematical dynamics and the invention of calculus

The Newton-Leibniz priority dispute