XVI. В литературных кругах
● Паскаль Б. Мысли / Пер. с фр., вступ. статья, коммент. Ю. А. Гинзбург. – М.: Изд-во имени Сабашниковых, 1995. – С. 132.
● Dauben, Joseph W. “Chinese Mathematics.” In The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, edited by Victor Katz, 186–384. Princeton, NJ: Princeton University Press, 2007.
● Донн Дж. Прощание, запрещающее грусть / Пер. И. Бродского. (http://litcult.ru/lyrics.ljubimie-stihi/91).
● Hidetoshi, Fukagawa, and Tony Rothman. Sacred Mathematics: Japanese Temple Geometry. Princeton, NJ: Princeton University Press, 2008.
● Joseph, George Gheverghese. The Crest of the Peacock.
● Ken’ichi, Sato. “Chapter 2: Seki Takakazu.” In Japanese Mathematics in the Edo Period. National Diet Library of Japan, 2011. http://www.ndl.go.jp/math/e/s1/2.html.
● Strogatz, Steven. The Joy of x: A Guided Tour of Math, from One to Infinity. New York: Mariner Books, 2013.
● Шимборска В. Число Пи. https://antipodes.org.au/pr_pi_61.html.
XVII. Война, мир и интегралы
● Берлин И. История свободы. Россия / Предисл. А. Эткинда. – М.: Новое литературное обозрение, 2001.
● Dirda, Michael. “If the World Could Write…” Washington Post. October 28, 2007. http://www.washingtonpost.com/wp-dyn/content/article/2007/10/25/AR2007102502856.html.
● Толстой Л. Н. Война и мир. Т. 3, 4. – М.: Художественная литература, 1983.
XVIII. Линия городского горизонта Римана
● Corrigan, Maureen. Leave Me Alone, I’m Reading: Finding and Losing Myself in Books. New York: Random House, 2005.
● Dunham, William. The Calculus Gallery.
● Hamill, Pete. “A New York Writer’s Take on How His City Has Changed,” National Geographic, November 15, 2015. https://www.nationalgeographic.com/new-york-city-skylinetallest-midtown-manhattan/article.html.
● Lindner, Christoph. “New York Vertical: Reflections on the Modern Skyline.” American Studies 47, no. 1 (Spring 2006): 31–52. https://core.ac.uk/download/pdf/148648368.pdf.
● Айн Рэнд. Источник. В 2 т. – М.: Альпина Паблишер, 2020.
XIX. Великая работа синтеза
● Knill, Oliver. “Some Fundamental Theorems in Mathematics.” Harvard University. http://www.math.harvard.edu/~knill/graphgeometry/papers/fundamental.pdf.
● Mazzotti, Massimo. The World of Maria Gaetana Agnesi, Mathematician of God. Baltimore: Johns Hopkins University Press, 2007.
● Navarro, Joaquin. “Women in Maths: From Hypatia to Emmy Noether.” In Everything Is Mathematical. Barcelona: RBA Coleccionables, 2013.
● Ouellette, Jennifer. The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse. New York: Penguin Books, 2010.
ХХ. Что происходит под знаком интеграла, остается под знаком интеграла
Мои благодарности Инне Захаревич за полезный и приятный обмен письмами.
● Фейнман Р. Ф. Вы, конечно, шутите, мистер Фейнман! / Пер. с англ. С. Б. Ильина. – М.: АСТ, 2014.
● Gaither, Carl C. and Alma E. Cavazos-Gaither, eds. Gaither’s Dictionary of Scientific Quotations. New York: Springer Science & Business Media, 2008.
● Gleick, James. Genius: The Life and Science of Richard Feynman. New York: Pantheon Books, 1992.
● Ouellette, Jennifer. The Calculus Diaries.
● Ury, Logan R. “Burden of Proof.” Harvard Crimson. December 6, 2006. https://www.thecrimson.com/article/2006/12/6/burden-of-proof-at-1002-am/.
● Zakharevich, Inna. “Another Derivation of Euler’s Integral Formula.” Reported by Noam D. Elkies. Harvard University. http://www.math.harvard.edu/~elkies/Misc/innaz.pdf.
XXI. Отказать в существовании одним росчерком пера
Моя огромнейшая благодарность Полу Рамонду, студенту докторантуры по физике, который консультировал меня по космологии по Skype. Все допущенные ошибки – целиком на моей совести.
● Эйнштейн А. К космологической проблеме общей теории относительности // Эйнштейн А. Собрание научных трудов в 4 т. Т. 2. Работы по теории относительности 1921–1955 / Под ред. И. Е. Тамма, Я. А. Смородинского, Б. Г. Кузнецова. – М.: Издательство «Наука», 1966. – Серия «Классики науки». – С. 349–362.
● Harvey, Alex, “The Cosmological Constant.” New York University, November 23, 2012. https://arxiv.org/pdf/1211.6337.pdf.
● Isaacson, Walter. Einstein.
● Janzen, Daryl. “Einstein’s Cosmological Considerations.” University of Saskatchewan. February 13, 2014. https://arxiv.org/pdf/1402.3212.pdf.
● Munroe, Randall. “The Space Doctor’s Big Idea.” New Yorker, November 18, 2015.
● Ohanian, Hans. Einstein’s Mistakes: The Human Failings of Genius. New York: W. W. Norton & Company, 2008.
● O’Raifeartaigh, C., and B. McCann. “Einstein’s Cosmic Model of 1931 Revisited: An Analysis and Translation of a Forgotten Model of the Universe.” Waterford Institute of Technology. https://arxiv.org/ftp/arxiv/ papers/1312/1312.2192.pdf.
● O’Raifeartaigh, Cormac, Michael O’Keeffe, Werner Nahm, and Simon Mitton. “Einstein’s 1917 Static Model of the Universe: A Centennial Review.” https://arxiv.org/ftp/arxiv/papers/1701/1701.07261.pdf.
● Rovelli, Carlo. Seven Brief Lessons on Physics. New York: Riverhead Books, 2016.
● Straumann, Norbert. “The History of the Cosmological Constant Problem.” Institute for Theoretical Physics, University of Zurich, August 13, 2001. https://arxiv.org/pdf/gr-qc/0208027.pdf.
XXII. 1994-й, год, когда родился математический анализ
● Łaba, Izabella. “The Mathematics of Wheel Reinvention.” The Accidental Mathematician. January 18, 2016. https://ilaba.wordpress.com/2016/01/18/the-mathematics-ofwheel-reinvention/.
● Письма в журнал Diabetes Care, № 10 (октябрь 1994). Среди процитированных авторов были Ральф Бендер, Томас Волевер, Джейн Монако, Рэнди Андерсон и Мэри Тай.
● Medical Researcher Discovers Integration, Gets 75 Citations.” An American Physics Student in England. March 19, 2007. https://fliptomato.wordpress.com/2007/03/19/medical-researcher-discovers-integration-gets-75-citations/.
● Ossendrijver, Mathieu. “Ancient Babylonian Astronomers Calculated Jupiter’s Position from the Area under a Time-Velocity Graph.” Science 351, no. 6272 (January 29, 2016): 482–84.
● Tai, Mary. “A Mathematical Model for the Determination of Total Area under Glucose Tolerance and Other Metabolic Curves.” Diabetes Care 17, no. 2 (February 1994): 152–54.
● Trefethen, Lloyd N. “Numerical Analysis.” In Princeton Companion to Mathematics, edited by Timothy Gowers, June Barrow-Green, and Imre Leader. Princeton, NJ: Princeton University Press, 2008. http://people.maths.ox.ac.uk/trefethen/NAessay.pdf.
● Wolever, Thomas. “How Important Is Prediction of Glycemic Responses?” Diabetes Care 12, no. 8 (September 1989): 591–93.
XXIII. Если страдание должно прийти
● Бентам И. Введение в основания нравственности и законодательства. – М.: РОССПЭН, 1998. – (История политической мысли).
● Bradbury, Ray. Bradbury Speaks: Too Soon From the Cave, Too Far from the Stars. New York: William Morrow, 2006.
● Dickinson, Emily. “Bound – a Trouble.” (No. 269.) https://en.wikisource.org/wiki/Bound_ttps://en.wiki.
● Фрост Р. Чем счастье короче, тем ярче / Пер. Н. Голя. Источник: https://www.stihi.ru/2010/09/18/8591.
● Jevons, William Stanley. “Brief Account of a General Mathematical Theory of Political Economy.” Journal of the Royal Statistical Society, London XXIX (June 1866): 282–87. https://www.marxists.org/reference/subject/economics/jevons/mathem.htm.
● Kahneman, Daniel, Barbara L. Fredrickson, Charles A. Schreiber, and Donald A. Redelmeier. “When More Pain Is Preferred to Less: Adding a Better End. Psychological Science 4, no. 6 (November 1993): 401–5.
● Mill, John Stuart. Utilitarianism (edited by George Sher). Indianapolis: Hackett Publishing Co., 2002. Page 10.
● Singer, Peter. Animal Liberation: Updated Edition. New York: Harper Perennial, 2009.
* Здесь обыгрывается словосочетание «head crimes» – «главные» или «головные преступления» как «преступления голов». – Прим. ред.
XXIV. Сражение с богами
● Архимед. Сочинения / Пер. и вступ. статья И. Н. Веселовского, перевод арабских текстов Б. А. Розенфельда. – М.: Физматгиз, 1962.
● Brown, Kevin. “Archimedes on Spheres and Cylinders.” Math Pages. https://www.mathpages.com/home/kmath343/kmath343.htm.
● Leibniz, Gottfried Wilhelm Freiherr, and Antoine Arnauld. The Leibniz-Arnauld Correspondence. New Haven, CT: Yale University Press, 2016.
● Lockhart, Paul. Measurement. Cambridge, MA: Belknap Press, 2012.
● Плутарх. Сравнительные жизнеописания: В 3 т. / Изд. подготовили С. С. Аверинцев, М. Л. Гаспаров, С. П. Маркиш; отв. ред. С. С. Аверинцев. – М.-Л.: Издательство АН СССР, 1961–1964. – (Литературные памятники). (2-е изд., испр. и доп. – Сравнительные жизнеописания: В 2 т. – М.: Наука, 1994.)
● Polster, Burkard. Q. E. D.: Beauty in Mathematical Proof. New York: Bloomsbury, 2004.
● Полибий. Всеобщая история / Отв. ред. А. Я. Тыжов. (Серия «Историческая библиотека»). – СПб.: Ювента, 1994–1995.
● Rorres, Chris. “Death of Archimedes: Sources.” New York University. https://www.math.nyu.edu/~crorres/Archimedes/Death/Histories.html.
● Sharratt, Michael. Galileo: Decisive Innovator. Cambridge, UK: Cambridge University Press, 1994. P. 52.
● Whitehead, Alfred North. An Introduction to Mathematics. New York: Henry Holt and Company, 1911.
XXV. Из невидимых сфер
Спасибо моим друзьям из Twitter Бену Блам-Смиту (@benblunsmith) и Майку Лоулеру (@mikeandallie) за помощь с вычислением объема четырехмерной сферы.
● Эббот Э., Бюргер Д. Флатландия. Сферландия / Пер. Ю. А. Данилова. – СПб.: Амфора, 2015. Цит. по: https://e-libra.ru/read/465581-flatlandiya-sferlandiya.html.
● Strogatz, Steven. The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math. Princeton, NJ: Princeton University Press, 2009.
XXVI. Пахлава исполинских размеров
● Арнольд В. И. О преподавании математики // Успехи математических наук. 1998. Т. 53. Вып. 1 (319).
● Cheng, Eugenia. Beyond Infinity: An Expedition to the Outer Limits of Mathematics. New York: Basic Books, 2017.
● Элленберг Дж. Как не ошибаться. Сила математического мышления / Пер. Н. Яцюк; науч. ред. М. С. Гельфанд – М.: Манн, Иванов и Фербер, 2017.
● Kakutani, Michiko. “A Country Dying of Laughter. In 1,079 Pages.” New York Times, February 13, 1996. https://www.nytimes.com/1996/02/13/books/books-of-the-times-acountry-dying-of-laughter-in-1079-pages.html.
● Max, Daniel T. Every Love Story is a Ghost Story: A Life of David Foster Wallace. New York: Viking, 2012.
● McCarthy, Kyle. “Infinite Proofs: The Effects of Mathematics on David Foster Wallace.” Los Angeles Review of Books, November 25, 2012. https://lareviewofbooks.org/article/infinite-proofs-the-effects-of-mathematics-on-david-foster-wallace/.
● Papineau, David. “Room for One More.” New York Times, November 16, 2003. http://www.nytimes.com/2003/11/16/books/room-for-one-more.html.
● Scott, A. O. “The Best Mind of His Generation.” New York Times, September 20, 2008. https://www.nytimes.com/2008/09/21/weekinreview/21scott.html.
● Wallace, David Foster. “Tennis, Trigonometry, Tornadoes: A Midwestern Boyhood.” Harper’s Magazine, December 1991.
● Wallace, David Foster. “Rhetoric and the Math Melodrama.” Science 290, no. 5500 (December 22, 2000): 2263–67.
● Wallace, David Foster. Everything and More: A Compact History of Infinity. New York: W. W. Norton, 2003.
XXVII. Труби, Гавриил, труби!
● Alexander, Amir. Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World. New York: Farrar, Straus and Giroux, 2014.
● Cucić, Dragoljub. “Types of Paradox in Physics.” Regional Centre for Talents Mihajlo Pupin. https://arxiv.org/ftp/arxiv/papers/0912/0912.1864.pdf.
● Gethner, Robert M. “Can You Paint a Can of Paint?” College Mathematics Journal 36, no. 4 (November 2005): 400–402.
● Hofstadter, Douglas. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basic Books, 1979.
● Smith, Wendy, and Marianne Lewis. “Leadership Skills for Managing Paradoxes.” Industrial and Organizational Psychology 5, no. 2 (June 2012).
XXVIII. Сцены из невозможности
Мои благодарности Тарин Флок за то, что она провела меня через доказательство интеграла Гаусса.
● Chiang, Ted. Stories of Your Life and Others. New York: Tom Doherty Associates, 2002.
● Oliva, Philip B. Antioxidants and Stem Cells for Coronary Heart Disease. Singapore: World Scientific Publishing, 2014. Page 534.