Monday, June 3, 2019 – Paris, France

Quotes
“There are only two kinds of certain knowledge: Awareness of our own existence and the truths of mathematics.”
“Any institution which does not suppose the people good, and the magistrate corruptible, is evil.”
“It matters little who first arrives at an idea, rather what is significant is how far that idea can go.”
Agenda .
 (8:45 a.m.) Depart our hotel
 (9:30 a.m.) Pantheon
 Student presentation
 Onehour audio tour
 Visit the crypt to hang out with some famous Enlightenment thinkers and mathematicians.
 (11:00) Two homes of mathematical importance:
 Sophie Germain’s House (13 Rue de Savoie)
 Condorcet’s hideout (15 Rue Servandoli)
 (12:00) Lunch Break
 (2:00 p.m.) Conciergerie tour
Introduction .
A convenient starting point for the Enlightenment in France is the death of Louis XIV in 1715, and le Siècle des Lumières (Century of Light) came to a violent end with the French Revolution of 1789. During the Enlightenment, reason became the primary source of authority and legitimacy, leading to the advance of ideas such as democratic government, separation of church and state, and the scientific method. Ideas have consequences, and the ideals of the Enlightenment had worldwide effects. They undermined the authority of the monarchy, and led to increased questioning of the role of the church in our life.
The French Revolution profoundly influenced the history of Europe, the United States, and much of our modernday world. It led to the worldwide decline of monarchies and the rise of democracy. It also created violent shockwaves that rippled across the globe in a series of wars and revolutions (that, in some sense, continue to this day). Some historians would rank the French Revolution as one of the pivotal events in world history. Today, we try to get just a small taste of the ideas that led to revolution, the results of the revolution, and the effects it had on the history of mathematics.
Maximillian de Robespierre was one of the architects of the Revolution. After the execution of Louis XIV in 1793, Robespierre led the Reign of Terror during which (as director of the Committee on Public Safety) he condemned thousands of French people (including the mathematicians Condorcet and Fourier) to execution for not being “sufficiently liberal” (though both Condorcet and Fourier escaped the guillotine—in different ways … .)
During the Reign of Terror, a young woman named Sophie Germain remained hidden in her parents' house where (against her father’s wishes) she became a master mathematician, and an inspiration for generations of young women in mathematics and science. Her untimely death from breast cancer is one of the great tragedies in math history. Robespierre also experienced an untimely death. As the very committee he once led became increasingly bloodthirsty, Robespierre became a target. He was executed at the guillotine in 1794 at age 36.
The French Revolution is a complicated era that is tricky to get a handle on, and we certainly won’t get a full picture today. Our goals are to understand some of the major events, people, and places. Surprisingly, these events had important effects on the field of mathematics, and what it means to be a mathematician.
Notebook Assignments .
 There are several famous mathematicians buried in the Panthéon, including JosephLouis Lagrange, Lazare Carnot, Marquis de Condorcet, and Gaspard Monge. Why are they buried here? What does their inclusion, along with figures such as Voltaire and Rousseau, say about mathematicians during the 18^{th} century?
 What’s the connection between the French Revolution and Sophie Germain? What mathematical accomplishments is Sophie Germain known for?
 The playwright Honore de Balzac wrote about life during the Revolution: “Life is a series of combinations, and you have to study and adapt to them if you are to succeed in maintaining a good position.” Describe some ways in which mathematicians either “adapted” or “resisted” during the French Revolution. Then answer this question: In your own life, how do you decide when to “adapt”, and when to “resist”? Take a few moments to be honest with yourself about this question.
 (MTH 490 Students Only) Read “Selections from the Preliminary Discourse to the Encyclopedia” by Jean le Rond d’Alembert (posted online). Then answer this question: For d’Alembert, what branch of mathematics is the highest level of abstraction? Why (according to d’Alembert) should mathematicians not go beyond that point? What does this say about mathematics during the Enlightenment?