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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





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