Mathematics

What is the relation between geometry and arithmetic? How can we model the motion of the heavenly bodies? What roles do diagrams and imagination play in a demonstrative proof? What is the structure of good reasoning? Can there be mathematics of the infinite and the infinitesimal? Are there multiple geometries? Students study original and influential works of mathematics, demonstrating hundreds of theorems to one another in class, and inquiring into the foundations of geometry, mathematical physics, logic, number theory, set theory, algebra, analysis, multi-variable calculus, differential equations, and astronomy.

Reading List

Archimedes “On the Equilibrium of Planes,” “On Floating Bodies”

Aristotle Poetics, Physics, Metaphysics, Nicomachaen Ethics, On Generation and Corruption, Politics, Parts of Animals, Generation of Animals

Amedeo Avogadro "Essay on a Manner of Determining the Relative Masses of the Elementary Particles of Bodies”

Claude Berthollet “Excerpt from Essai de Statique Chimique”

Joseph Black “Extracts from Lectures on the Elements of Chemistry”

Stanislao Cannizzaro “Letter to Professor S. De Luca”

John Dalton “Extracts from A New System of Chemical Philosophy”

Hans Driesch “The Science and Philosophy of the Organism”

Euclid Elements

Daniel Fahrenheit “The Fahrenheit Scale”

Joseph Gay-Lussac “On the Expansion of Gases by Heat,” “Memoir on the Combination of Gaseous Substances with Each Other”

William Harvey Motion of the Heart and Blood

Antoine Lavoisier Elements of Chemistry

Lucretius On the Nature of Things

Edme Mariotte Essays

Dmitri Mendeleev “The Periodic Law of the Chemical Elements”

Nicomachus Arithmetic

Blaise Pascal Treatise on the Equilibrium of Liquids

J.L. Proust “Excerpt from Sur Les Oxidations Metalliques”

Ptolemy Almagest

Hans Spemann “The Organizer-Effect in Embryonic Development” (Nobel Lecture 1935), “Embryonic Development and Induction”

J. J. Thomson “Extracts from System of Chemistry”

Rudolf Virchow “Cellular Pathology Lectures”

Apollonius Conics

Aristotle De Anima, On Interpretation, Prior Analytics, Categories

Francis Bacon Novum Organum

Nicolaus Copernicus On the Revolution of the Spheres

René Descartes Geometry, Discourse on Method

Johannes Kepler Astronomia Nova

Blaise Pascal Generation of Conic Sections

Ptolemy Almagest

François Viète Introduction to the Analytical Art

André-Marie Ampère Essays

Daniel Bernoulli “On the Vibrating String”

Charles-Augustin Coulomb “Excerpts from Coulomb’s Mémoires sur l’électricité et le magnétisme”

Richard Dedekind Essay on the Theory of Numbers

René Descartes Meditations, Rules for the Direction of the Mind

Leonhard Euler “Remarks on the Preceding Papers by Mr. Bernoulli”

Michael Faraday “Experimental Researches in Electricity”

Benjamin Franklin “Excerpt from several letters to Peter Collinson on the nature of electricity”

Galileo Galilei Two New Sciences

William Gilbert “De Magnete”

David Hume Treatise on Human Nature

Christiaan Huygens Treatise on Light, On the Movement of Bodies by Impact

Gottfried Wilhelm Leibniz Monadology, Discourse on Metaphysics, Principles of Nature and Grace, Essays

James Clerk Maxwell “On Faraday’s Lines of Force.” “On Physical Lines of Force,” “A Dynamical Theory of the Electromagnetic Field”

Isaac Newton Principia Mathematica

Jean-Antoine Nollet “Observations on Several New Electrical Phenomena”

Hans Christian Ørsted “Experiments concerning the efficacy of electric conflict on the magnetic needle”

Brook Taylor “On the motion of the stretched string”

Alessandro Volta “On the Electricity excited by the mere contact of conducting substances of different kinds”

Thomas Young “On the Nature of Light and Colors”

Niels Bohr “On the Spectrum of Hydrogen”

Theodor Boveri Essays

Louisde Broglie “Matter Waves”

Charles Darwin Origin of Species

Albert Einstein “Relativity,” “On the Electrodynamics of Moving Bodies,” “On the Influence of Gravitation on the Propagation of Light,” “The Foundation of the General Theory of Relativity,” “Does the Inertia of a Body Depend upon its Energy Content?”

Michael Faraday “On the Absolute Quantity of Electricity Associated with the Particles or Atoms of Matter”

François Jacob & Jacques Monod Essays

George Beadle & Edward Tatum Essays

G. H. Hardy “Mendelian Proportions in a Mixed Population”

Georg Hegel Phenomenology of Mind

Werner Karl Heisenberg “Critique of the Physical Concepts of the Particle Picture”

Edmund Husserl Crisis of the European Sciences

James Watson & Francis Crick Essays

Jean-Baptiste Lamarck “Zoological Philosophy”

Nikolay Lobachevsky Theory of Parallels

Gregor Mendel “Experiments with Plant Hybridization”

Robert Andrews Millikan “The Electron”

Hermann Minkowski “Space and Time”

Thomas Morgan “Evolution and Genetics,” “The Chromosomes and Mendel's Two Laws,” “The Linkage Groups and the Chromosomes,” “Sex-Linked Inheritance,” “Crossing-Over”

Max Planck “The Quantum Hypothesis”

Ernest Rutherford “The Scattering of α & β Particles by Matter and the Structure of the Atom”

Erwin Schrödinger “Four Lectures of Wave Mechanics—First Lecture”

Joel Sussman Essays

Walter Sutton Essays

J. J. Thomson “Cathode Rays”

Albert Einstein Essays

Richard Feynman QED

G. H. Hardy A Course of Pure Mathematics

Georg Hegel Philosophy of Nature

Konrad Lorenz Studies in Animal and Human Behavior

Bertrand Russell An Introduction to Mathematical Philosophy

Computation

Computing Technology and Human Society

The information presented is for illustration purposes only and may not reflect the current reading list and preceptorial and study group offerings. Works listed are studied at one or both campuses, although not always in their entirety.

Senior Essay

Rousseau on Civil Society: Two Provocative and Troubling Accounts

Senior Essay

Relating Space and Geometry: The Necessity of Spatial Experience in Association with Multiple Versions of Geometry

Senior Essay

Close Your Eyes and Learn Geometry: Embracing Radical Ideas in Lobachevskian Geometry

Senior Essay

Outer Spaces Inner Intuitions – How Proofs Shape our Relation to Mathematics in Euclid and Lobachevsky

Senior Essay

Necessity, Contingency, and Freedom: An Analysis of Leibniz’s World Through the Lens of Computer Science

Senior Essay

Turning the World Inside-Out: Why the Newtonian Theory of Planetary Motion Supersedes the Ptolemaic

Senior Essay

Number, Perception and Continuity

Senior Essay

Imaginary Geometry and Our Understanding of Space

Senior Essay

Hume’s Empirical Mathematics

Senior Essay

The Role of Beauty in Science as Seen in the Einstein, Podolsky, and Rosen Paper and Responses to it Within the Context of Quantum Theory

Senior Essay

Mind the Gap: The Philosophical Implications of the Divide of Logic and Intuition in Lobachevski

Senior Essay

What is a Curve? A Search for Continuity in Leibniz’s Calculus