ACKNOWLEDGMENTS
The roots of this book go far back, to my first year as a graduate student at Stanford, when I wrote a paper arguing that infinitesimals were politically subversive in seventeenth-century Europe. In the following years my research interests carried me elsewhere, first to the maritime culture of early modern exploration, and then to the “romantic turn” in mathematics in the early nineteenth century. But I never forgot that early insight, and never doubted that I would one day tell the story. It took longer than I thought, but I finally did. And because I have been thinking about this topic for more than two decades, the list of those I have consulted and whose comments helped shape this book is a long one.
I would like to thank Timothy Lenoir, Peter Galison, and Moti Feingold, who commented on that paper years ago, as well as Douglas Jesseph, whose detailed critiques spurred me to refine and improve the argument. I spent hours talking about these issues with Christophe Lecuyer, Jutta Sperling, Phillip Thurtle, Josh Feinstein, and Patricia Mázon, my graduate school peers at the time. In later years my colleagues at UCLA were my sounding board, and I thank Margaret (Peg) Jacob, Mary Terrall, Ted Porter, Norton Wise, Soraya de Chadarevian, and Sharon Traweek for their insights and friendship. Carla Rita Palmerino kindly gave me access to her notes from the Jesuit Archives, and Ugo Baldini helped guide me through the maze of Jesuit sources.
Steven Vanden Broecke became a good friend during a quarter of shared office space, and contributed penetrating comments and a deep knowledge of the early modern world. Conversations with Joan Richards and Arkady Plotnitsky helped shape my thinking on mathematics and broader culture, and Mario Biagioli and Massimo Mazzotti deepened my understanding of early modern Italy and the place of mathematics in its society. Reviel Netz’s “Mathematics as Literature / Mathematics as Text” workshop gave me an opportunity to test-run some of these ideas before a lively and well-informed group, and I benefited greatly from his thoughtful suggestions. Doron Zeilberger, Michael Harris, and Jordan Ellenberg have been generous with mathematical advice, and Siegfried Zielinski has been an example of intellectual open-mindedness. Apostolos Doxiadis, in both his writings and his public outreach, showed me that mathematics, when beautifully presented, has a broad, devoted, and enthusiastic audience.
Amanda Moon of Farrar, Straus and Giroux shepherded the book through all its stages, from acquisition to publication, always providing incisive and helpful advice. Her colleagues Debra Helfand, Delia Casa, Jenna Dolan, Debra Fried, and Jennie Cohen worked diligently on all aspects of the book from copyediting to proofreading to production, turning a bland-looking electronic file into an elegantly written and beautiful final product. Dan Gerstle read every word of an early draft and made many suggestions, and Laird Gallagher brought a sharp editorial eye to later versions of the text. Both unquestionably made this a better book. Lisa Adams of the Garamond Agency was with this project from its earliest conception to its fruition, and I can truthfully say that Infinitesimal would never have come to be without her advice, support, and professionalism. My childhood friend Daniel Baraz has been a constant presence in my life despite living on the other side of the world. His friendship helped sustain me throughout the process.
To Bonnie, my love: thank you for being the best wife any man could wish for. Your intelligence and support are in every page of this book. My children were with me throughout the planning, writing, and production process, but they are now embarking on their own life adventures away from home. I will miss their daily presence and companionship, as well as their energy, intelligence, and creativity, and our long talks about everything from football to the Iliad to the art of writing. Jordan and Ella, wherever your paths may lead, my love will always follow.
INDEX
The index that appears in the print version of this title does not match the pages in your e-book. Please use the search function on your e-reading device to search for terms of interest. For your reference, the terms that appear in the print index are listed below.
absolute infinity
absolute rule of kings
Académie des Sciences
Academy
Academy of the Desirous
Accademia dei Lincei
Achilles and the Tortoise
Acquaviva, Claudio; indivisibles opposed by; innovation disdained by; Revisors created by
Acta Eruditorum (Leibniz)
Act of Toleration (1689)
Adolphus, Gustavus
Aerarium philosophiae mathematicae (Bettini)
aerodynamics
Against the Murderous, Thieving Hordes of the Peasants (Luther)
air currents
Alberti, Leon Battista
Albrecht of Hohenzollern
alchemy
Alcibiades, Albert
Aldobrandini, Cardinal
Alexander VI, Pope
algebra
Algebra (Clavius)
algebraic numbers
“all the lines”
“all the planes”
Alvarado
Ammannati, Bartolommeo
Anabaptists
analysis
Angeli, Stefano degli
Anglican Church, see Church of England
Antwerp Cathedral
Apiaria universae philosophiae mathematicae (Bettini)
Apollonius
Apostolic Clerics of St. Jerome, see Jesuats
Archimedes
Archimedian spiral
architecture
Aristotelian physics
Aristotle; indivisibles opposed by
Aristotle’s wheel
arithmetic
Arithmetica infinitorum (Wallis)
Arriaga, Rodrigo de
Arti, Duke of
Arundel, Earl of
Assayer, The (Galileo)
Assembly of Divines
astrolabe
Astronomia nova (Kepler)
astronomy
atoms
Aubrey, John
Augsburg
Austria
authority
axiom of Archimedes
Babbage, Charles
Bacon, Francis
Bacon, Roger
Baldi, Bernardino
Bamberg
Barberini, Antonio
Barberini, Francesco
Barberini, Maffeo (Pope Urban VIII)
barometers
Barrow, Isaac
Basilica of Santa Croce
Bavaria
Beaugrand, Jean
Belgium
Bellarmine, Robert; death of; heliocentrism edict of; papal supremacy defended by
Benedictines
Berkeley, George, infinitesimals mocked by
Bernini, Gian Lorenzo
Bernoulli, Daniel
Bettini, Mario
Biberus, Nithard
Bible; science vs.
Biblioteca Nazionale Centrale
Bibliotheca selecta (Possevino)
Bidermann, Jacob
black holes
Black Robes
black swans
blood, circulation of
Bockelson, Jan
Bohemia
Boleyn, Anne
Bologna, University of
Bolognese Senate
Bolsheviks
Borgia, Cesare
Borgia, Francis, Duke of Gandia
Borgia, Gaspar
Borromeo, Federico
Boscovich, Roger
Bosse, Abraham
Botticelli, Sandro
Boulliau, Ismael
Boulonois, E. de
Bourbons
Boyle, Robert
Brahe, Tycho
Bramante, Donato
Brazil
Breitenfeld, Battle of
Briggs, Henry
Brouncker, Lord
Brunelleschi, Filippo
Bucer, Martin
Burke, Edmund
business models
calculus; creation of; infinitesim
al
calendar reform
Calvin, John
Calvinism
Cambridge University
Campion, Edmund
Canisius, Peter
Canons Regular
Cappon, Ignace
Carafa, Vincenzo
Cardano, Gerolamo
Cartesian philosophy
Castelli, Benedetto
Castel Sant’Angelo
Catherine of Aragon
Catherine of Siena
Catholic Church, Catholicism; Bible requiring interpretation in; on good works; hierarchy of; Hobbes’s criticism of; infinitesimals and; Luther’s opposition to; Protestantism vs.; suppressed in England
Cavalieri, Bonaventura; Angeli as disciple of; background of; Bettini’s dispute with; on composition of continuum; conservatism of; death of; Guldin’s dispute with; indivisibles supported by; Jesuats joined by; Jesuits’ attack on; mathematics taught by; method of indivisibles created by; paradoxes as seen by; parallelogram proof of; Tacquet’s dispute with; Torricelli vs.
Cavaliers
Cavendish, Charles
Cavendish, Margaret
Cavendish, William
Cavendish family
centers of gravity
Centrobaryca (Guldin)
Cesarini, Virginio
Cesi, Federico
Charlemagne
Charles I, King of England
Charles II, King of England; restoration of
Charles V, Emperor
chemistry
China
Christina of Lorraine
Church of England; creation of; indivisibles opposed by; reform of
Church of St. Ignatius
Ciampoli, Giovanni
circle, area of
civil engineering
Civil War, English; causes of; as context of Leviathan; threat of anarchy in
Clarendon, Earl of
Clavis mathematicae (Oughtred)
Clavius, Christopher; calendar reformed by; death of; Galileo’s astronomical discoveries accepted by; geometry seen as central by; Hobbes vs.; Jesuit reverence for; lack of originality of; mathematical academy created by; mathematical curriculum of; mathematics seen as key to religious disputes by; mathematics seen as stable by; mathematics taught by; received into Society of Jesus; textbooks written by
Clement VII, Pope
Clement VIII, Pope
Clement IX, Pope
codes
cohesion
College of Cardinals
Collegio Romano; founding of; Galileo honored by; Galileo’s dispute with; indivisibles banned by; mathematics academy created at; Pallavicino’s defense of dissertation in
Cologne
Colombini, John
comets
Commandino, Federico
compass
conatus
Concis (Apollonius)
Constitutions (Ignatius of Loyola)
constructive proofs
continuum: Cavalieri on; Galileo and; indivisibles in; paradoxes of, see paradoxes; physical reality and
contradictions, see paradoxes
Copernicus, Nicolaus, heliocentric theory of
cossists
Council of Constance
Council of Nicea
Council of Trent
Counter-Reformation
Crick, Francis
Cromwell, Oliver
Cromwell, Richard
curing wounds at a distance
Cursus philosophicus (Arriaga)
Cylindrica et annularia
Cylindricorum et annularium (Tacquet)
d’Alembert, Jean
Darwin, Charles
d’Aviso, Urbano
Decameron physiologicum (Hobbes)
De centro gravitatis (Guldin)
De centro gravitatis (Valerio)
De cive (Hobbes)
deconstruction
De corpore (Hobbes)
De Corpore Politico, or the Elements of the Law (Hobbes)
deduction
deductive proofs
De homine (Hobbes)
De infinitis parabolis (Angeli)
de la Chaise, François
della Rovere family
del Monte, Guidobaldo
de Lugo, Giovanni
Democritus
de Nemore, Jordanus
Denmark
De revolutionibus (Copernicus)
Descartes, René; infinitesimals disdained by
De sectionibus conicis (Wallis)
de Thou, Jacques-Auguste
Dialogue on the Two Chief World Systems (Galileo)
Dialogues Concerning Two New Sciences (Galileo)
Diet of Worms
differential calculus
Digby, Kenelm
Diggers
Discourse on Floating Bodies (Galileo)
Discourses and Mathematical Demonstrations Relating to Two New Sciences (Galileo)
Disputationes metaphysicae (Suárez)
divine grace
divine omnipotence
divine right of kings
DNA
Dominicans
Donatello
doubling of cube
Drake, Francis
ductus plani in planum
Duperron, Jacques Davy
Dutch Republic
Easter
Eck, Johann
Edward VI, King of England
Einstein, Albert
electricity
electric motors
electrodynamics
electronics
Elementorum philosophiae sectio tertia de cive (Hobbes)
Elements, The (Euclid); Clavius’s edition of
Elenchus geometriae Hobbianae (Wallis)
Elizabeth I, Queen of England
engineering
England; Catholicism suppressed in; Dutch war with; manners in
Enlightenment
Enthusiasts
Estates-General
Eucharist
Euclid
Euclid (Clavius)
Euclidean geometry; as construction of world; deduction in; method of presentation in; pure reasoning in; rigidity of
Eudoxus of Cnidus
Euler, Leonhard
evolution
Exercitationes geometricae sex (Cavalieri)
experiments; in math; as standing for tolerance
Fairfax, Thomas
faith; and scientific research
Faithorne, William
Farnese family
Favre, Pierre
Ferdinand II, Duke of Tuscany
Ferdinand II, Emperor
Fermat, Pierre de
Fifth Monarchy Men
Finland
fluids
fluxions
Fontenelle, Bernard Le Bovier de
Fordinus
fortifications
Foscarini, Paolo
Fourier, Joseph
France; English alliance with; Huguenots expelled from; Jesuits banned from teaching in; manners in; Protestants in
Francisco de Toledo
Francis I, King of France
Francis Xavier
Franck, Sébastian
Franklin, Benjamin
Frederick I, King of Denmark
Frederick the Wise of Saxony
freedom to philosophize
French Academy of Sciences
French Revolution
French Royal Academy of Sciences
Galen
Galileo Galilei; astronomical discoveries of; Barberini’s friendship with; conservatism of; and continuum; death of; denunciation of; fame of; freedom to philosophize advocated by; heliocentrism defended by; Hobbes’s visit to; house arrest and humiliation of; indivisibles accepted by; Jesuits’ tension with; Urban’s discussions and relationship with; Urban’s removal of protection from; Wallis influenced by
Galvani, Luigi
Gandia, Duke of
Gandia, Spain
Gassendi, Pie
rre
General Congregation
generators
Geneva, Switzerland
geography
Geometria indivisibilibus (Cavalieri)
geometrical curves
geometry; as embodiment of order; in Plato’s Academy
Germany
Germany, Nazi
Gilbert, William
Giotto
Glorious Revolution
gnomon; semi-
Goa
Gonzaga, Charles, Duke of Nevers
good works, Catholic belief in
Grassi, Orazio
gravitation
Gregorian Calendar
Gregory XIII, Pope
Gregory XV, Pope
Grienberger, Christoph
Guldin, Paul; Cavalieri disputed by
gunpowder
Gustavus I Vasa, King of Sweden
Habsburgs
Hall of the Consistory
Harriot, Thomas
Harvey, William
Hawking, Stephen
heat diffusion
heliocentrism
Henri IV, King of France
Henry VIII, King of England
hierarchy: of Church; Hobbes’s advocacy of; indivisibles and; of Jesuits; of knowledge; and opposition to indivisibles; papal supremacy in; in religion; of truth
Hieronymites
Hippasus
History (de Thou)
History of the Royal Society (Sprat)
Hitler, Adolf
Hobbes, Francis
Hobbes, Thomas; as Bacon’s secretary; Clavius vs.; education of; as ejected from ranks of mathematicians; flaws in geometry seen by; Galileo visited by; geometry as model of philosophy of; geometry reformed by; grand tours of; indivisibles interpreted by; indivisibles rejected by; introduction to mathematics of; and knowledge as based on logic; material notions in mathematics of; own philosophy praised by; quadrature of circle and; rigidity of; as Royalist in Civil War; Scholasticism disdained by; Sorbière’s praise for; Wallis’s dispute with
Hobbes, Thomas (father)
Holbeach, Martin
Holy Roman Empire
homogenes
Hooke, Robert
Horace
horror vacui
Huguenots
human nature
Human Nature (Hobbes)
Huygens, Christiaan
hydrodynamics
Ignatius His Conclave (Donne)
Ignatius of Loyola; Aquinas as authority of; background of; Clavius received into Society of Jesus by; Jesuits created by; mathematical education valued by; order defended by; sainthood of; and start of Jesuit colleges
Imperial Cortes
impetus
incommensurability
Independents
Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World Page 39