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Numbers and the World: Essays on Math and Beyond

About this Title

David Mumford, Brown University, Providence, RI

Publication: AMS Non-Series Monographs
Publication Year: 2023; Volume 149
ISBNs: 978-1-4704-7051-7 (print); 978-1-4704-7449-2 (online)
DOI: https://doi.org/10.1090/mbk/149

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Table of Contents

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Front/Back Matter

Opening more eyes to mathematics

The history of mathematics

AI, neuroscience, and consciousness

And now, some bits of real math

Coming to terms with the quantum

Nothing is simple in the real world

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References
  • Jennifer Ackerman, The Genius of Birds, Penguin Press, 2016.
  • Douglas Arnold, Guy David, David Jerison, Svitlana Mayboroda, and Marcel Filoche, Effective confining potential of quantum states in disordered media, Physical Review Letters, 2016.
  • T. A. Sarasvati Amma, Geometry in ancient and medieval India, Motilal Banarsidass, Delhi, 1979. With a foreword by V. Raghavan. MR 685920
  • Michael Artin and Jean-Louis Verdier, Seminar on “Etale cohomology of number fields”, 1964. Thanks to John Milne, available online at https://www.jmilne.org/math/Documents/woodshole.pdf.
  • A. Auersperg, A. von Bayern, G. Gaidon, L. Huber, and A. Kacelnik, Flexibility in problem solving and tool use of kea and New Caledonian crows in a multi access box paradigm, PLOS ONE, 2011.
  • Pascal Auscher, Guido Weiss, and Victor Wickerhauser, Local sine and cosine bases of Coifman and Meyer, in C. K. Chui, editor, Wavelets – a tutorial, Academic Press, 1991.
  • Srdjan Antic, Wen-Liang Zhou, Anna Moore, Shaina Short, and Katerina Ikonomu, The decade of the dendritic NMDA spike, Journal of Neuroscience Research 88 (2010), 2991–3001.
  • J. S. Bell, On the Einstein Podolsky Rosen paradox, Phys. Phys. Fiz. 1 (1964), no. 3, 195–200. MR 3790629, DOI 10.1103/PhysicsPhysiqueFizika.1.195
  • John Bell, Against ‘measurement’, Physics World, pages 33–40, August 1990.
  • Henri Bergson, Essai sur les données immédiates de la conscience, Félix Alcan, Paris, 1889.
  • J. J. Bastian and K. J. Harrison, Subnormal weighted shifts and asymptotic properties of normal operators, Proc. Amer. Math. Soc. 42 (1974), 475–479. MR 380491, DOI 10.1090/S0002-9939-1974-0380491-X
  • Christopher Bishop, Weil-Petersson curves, conformal energies, $\beta$-numbers, and minimal surfaces, under preparation for publication, 2020.
  • Bruce Blausen, Blausen 0114 brainstemanatomy.png, 2014. From Wikimedia Commons, Medical gallery of Blausen Medical 2014, WikiJournal of Medicine 1 (2). DOI:10.15347/wjm/2014.010, ISSN 2002-4436.
  • Jean Bricmont, Making sense of quantum mechanics, Springer, [Cham], 2016. MR 3525766, DOI 10.1007/978-3-319-25889-8
  • Stefan Banach and Alfred Tarski, Sur la décomposition des ensembles de points en parties respectivement congruentes, Fundamenta Mathematicae, pages 244–277, 1924.
  • Stephen Buranyi, Is the staggeringly profitable business of scientific publishing bad for science?, 2017.
  • Irwan Bello, Barret Zoph, Ashish Vaswani, Jonathon Shlens, and Quoc Le, Attention augmented convolutional networks, 2019. Online at arXiv: 1904.09925v5.
  • John Calhoun, Death squared: The explosive growth and demise of a mouse population, Proceedings of the Royal Society of Medicine 66 (1973), 80–86.
  • J. L. Carr, Harpole and Foxberrow, General Publishers, Gardner Books, 1992.
  • Marie-Claire Cammaerts and Roger Cammaerts, Are ants (hymenoptera formicidae) capable of self recognition?, Journal of Science 5 (2015), 521–532.
  • Al Cuoco and E. Paul Goldenberg, Computational thinking in mathematics and computer science: what programming does to your head, J. Humanist. Math. 11 (2021), no. 1, 346–363. MR 4212369, DOI 10.5642/jhummath.202101.17
  • Alexis Clairaut, Sur l’orbite apparente du soleil autour de la terre, Mèmoires de Mathèmatiques et de la Physique, Acadèmie des Sciences, pages 521–561, 1754.
  • Ronald R. Coifman and Yves Meyer, Remarques sur l’analyse de Fourier à fenêtre, C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 3, 259–261 (French, with English summary). MR 1089710
  • Bernard Comrie, Language Universals and Linguistic Typology: Syntax and Morphology, University of Chicago Press, 1981.
  • Hyla Stuntz Converse, The Agnicayana rite: Indigenous origin?, History of Religions, pages 81–95, 1974.
  • Christopher Cullen, An eighth century table of tangents, Chinese Science 1 (1982), 1–33.
  • Al Cuoco, CME Project: Algebra 1, Pearson, CME Project, 2010.
  • Al Cuoco, Calculating the monthly payments on a loan, 2019. Available online at https://go.edc.org/essays.
  • Charles Darwin, The Expression of the Emotions in Man and Animals, 1872.
  • Stanislas Dehaene, Consciousness and the Brain: Deciphering How the Brain Codes Our Thoughts, Viking, 2014.
  • René Descartes, La Geometrie, a facsimile of the 1637 French text plus an English translation, Dover Publications, 1954.
  • Christopher M. Dawson, Andrew P. Hines, Duncan Mortimer, Henry L. Haselgrove, Michael A. Nielsen, and Tobias J. Osborne, Quantum computing and polynomial equations over the finite field $\Bbb Z_2$, Quantum Inf. Comput. 5 (2005), no. 2, 102–112. MR 2132049
  • Jared Diamond, Collapse, Viking Press, 2005.
  • P. P. Divakaran, The mathematics of India, Sources and Studies in the History of Mathematics and Physical Sciences, Springer, Singapore; Hindustan Book Agency, New Delhi, 2018. Concepts, methods, connections. MR 3838418, DOI 10.1007/978-981-13-1774-3
  • Ingrid Daubechies, Stéphane Jaffard, and Jean-Lin Journé, A simple Wilson orthonormal basis with exponential decay, SIAM J. Math. Anal. 22 (1991), no. 2, 554–573. MR 1084973, DOI 10.1137/0522035
  • A. I. Dyachenko, E. A. Kuznetsov, M. D. Spector, and V. E. Zakharov, Analytical description of the free surface dynamics of an ideal fluid, Physics Letters A 221 (1996), 73–79.
  • Wendy Doniger, The Hindus, Viking/Penguin, 2009.
  • Benedictus de Spinoza, Ethica Ordine Geometrico Demonstrata, 1677. Available free online in Project Gutenberg as ‘The Ethics’, https://www.gutenberg.org/files/3800/3800-h/3800-h.htm.
  • Robin Dunbar, Grooming, gossip, and the evolution of language, Harvard University Press, 1998.
  • Frans de Waal, Mama’s Last Hug, W. W. Norton, 2019.
  • Jia Du, Laurent Younes, and Anqi Qiu, Whole brain diffeomorphic metric mapping via integration of sulcal and gyral curves, cortical surfaces, and images, Neuroimage 56 (2011), 162–173.
  • Freeman Dyson, Disturbing the Universe, Basic Books, 1981.
  • Freeman Dyson, The question of global warming, New York Review of Books, 2008. Issue June 12.
  • John Eccles, A unitary hypothesis of mind-brain interaction in the cerebral cortex, Proceedings of the Royal Society London B 240 (1990), 433–451.
  • Willis D. Ellis, A source book of Gestalt psychology, Psychology Press, 1999.
  • A. Ehrenfeucht and A. Mostowski, Models of axiomatic theories admitting automorphisms, Fund. Math. 43 (1956), 50–68. MR 84456, DOI 10.4064/fm-43-1-50-68
  • Volker Enss, Asymptotic observables on scattering states, Comm. Math. Phys. 89 (1983), no. 2, 245–268. MR 709466
  • John Eccles and Karl Popper, The Self and Its Brain, Routledge, 1977.
  • Albert Einstein, Boris Podolsky, and Nathan Rosen, Can quantum-mechanical description of physical reality be considered complete?, Physical Review 47 (1935), 777–780.
  • Leonhard Euler, Recherches sur la courbure des surfaces, Mémoires de l’Académie des Sciences de Berlin, pages 119–143, 1760.
  • Daniel Everett, Don’t sleep, there are snakes: Life and Language in the Amazonian Jungle, Vintage, 2009.
  • Richard Feynman, Surely you’re joking Mr. Feynman, W. W. Norton, 1985.
  • Ronald Fagin, Joseph Y. Halpern, Yoram Moses, and Moshe Y. Vardi, Reasoning about knowledge, MIT Press, Cambridge, MA, 1995. MR 1345612
  • Gerald B. Folland, Quantum field theory, Mathematical Surveys and Monographs, vol. 149, American Mathematical Society, Providence, RI, 2008. A tourist guide for mathematicians. MR 2436991, DOI 10.1090/surv/149
  • Chris Freiling, Axioms of symmetry: throwing darts at the real number line, J. Symbolic Logic 51 (1986), no. 1, 190–200. MR 830085, DOI 10.2307/2273955
  • Jöran Friberg, Amazing traces of a Babylonian origin in Greek mathematics, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007. MR 2388891, DOI 10.1142/9789812708847
  • Harvey Friedman, Invariant maximal cliques and incompleteness, 2011. Online at https://u.osu.edu/friedman.8/foundational-adventures/downloadable-manuscripts/, manuscript 81. You can find all Friedman’s recent work in preprint form here.
  • Jürg Frölich, A brief review of the ETH-approach to quantum mechanics, 2019. ArXiv:1905.06603v2.
  • Jürg Frölich, Irreversibility and the arrow of time, 2022. ArXiv:2202.04619v1.
  • Susan Forman and Lynn Steen, Beyond eighth grade: Functional mathematics for life and work, University of California at Berkeley, 1999. Available online at https://eric.ed.gov/?id=ED434271.
  • R. P. Feynman and F. L. Vernon Jr., The theory of a general quantum system interacting with a linear dissipative system, Ann. Physics 24 (1963), 118–173. MR 157605, DOI 10.1016/0003-4916(63)90068-X
  • Howard Gardner, Frames of Mind: The Theory of Multiple Intelligences, Basic Books, 1983.
  • Lars Gårding, Encounters with science: dialogues in five parts, Perspectives in analysis, Math. Phys. Stud., vol. 27, Springer, Berlin, 2005, pp. 295–376. MR 2215731, DOI 10.1007/3-540-30434-7_{1}4
  • Loren Graham and Jean-Michel Kantor, Naming infinity, The Belknap Press of Harvard University Press, Cambridge, MA, 2009. A true story of religious mysticism and mathematical creativity. MR 2526973
  • Ulf Grenander and Michael I. Miller, Pattern theory: from representation to inference, Oxford University Press, Oxford, 2007. MR 2285439
  • Ulf Grenander, Lectures in Pattern Theory I, II and III, Pattern Analysis, Pattern Synthesis, Regular Structures, Springer, 1981. Three parts published starting in 1976.
  • Ulf Grenander, A Calculus of Ideas: A Mathematical Study of Human Thought, World Scientific, 2012.
  • Alexander Grothendieck, Recoltes et semailles, https://www.quarante-deux.org/archives/klein/prefaces/Romans_1965-1969/Recoltes_et_semailles.pdf, 1986. Online; distribution restricted by his family.
  • Peter Godfrey-Smith, Other Minds: the Octopus, the Sea and the Deep Origins of Consciousness, Farrar, Straus, and Giroux, 2016.
  • Giorgio Gans, William Thompson, and Stephen Kosslyn, Brain Areas Underlying Visual Mental Imagery and Visual perception, Brain Research and Cognitive Brain Research 20 (2004), 226–241.
  • M. Giustina and A. Zeilinger, Significant-loophole-free test of bell’s theorem with entangled photons, Physical Review Letters, 115, 2015.
  • Rudolf Haag, Local quantum physics, 2nd ed., Texts and Monographs in Physics, Springer-Verlag, Berlin, 1996. Fields, particles, algebras. MR 1405610, DOI 10.1007/978-3-642-61458-3
  • Jonathan Haidt, The Righteous Mind, Pantheon, 2012.
  • Guershom Harel, The DNR system as a conceptual framework for curriculum development and instruction, in R. Lesh, J. Kaput, and E. Hamilton, editors, Foundations for the Future in Mathematics Education, Lawrence Erlbaum Inc., 2007.
  • Werner Heisenberg, The Physicist’s Conception of Nature, Harcourt, Brace, 1958.
  • Deborah Hughes-Hallett and William McCallum, Calculus: Single and Multivariable, Wiley, 2nd edition, 1998.
  • Fiona Hill, There Is Nothing For You Here: Finding Opportunity in the Twenty-First Century, Mariner Books, 2021.
  • Joe Harris and David Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math. 67 (1982), no. 1, 23–88. With an appendix by William Fulton. MR 664324, DOI 10.1007/BF01393371
  • Jens Høyrup, Length, Width, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin, Springer, 2002.
  • W. Hunziker and I. M. Sigal, The quantum $N$-body problem, J. Math. Phys. 41 (2000), no. 6, 3448–3510. MR 1768629, DOI 10.1063/1.533319
  • Marc Hauser, Charles Yang, Robert Berwick, Ian Tattersall, Michael Ryan, Jeffrey Watumull, Noam Chomsky, and Richard Lewontin, The mystery of language evolution, Frontiers of Psychology, 2014.
  • Feng Han and Song Chun Zhu, Bottom-up/top-down image parsing by attribute graph grammar, IEEE Transactions on Pattern Analysis and Machine Intelligence, pages 59–73, 2009.
  • Annette Imhausen, Traditions and myths in the historiography of Egyptian mathematics, in Oxford Handbook of the History of Mathematics, pages 781–800, Oxford University Press, 2009.
  • H. W. Janson, History of Art, Thames and Hudson, 1963.
  • Thomas Jech, Set theory, 2nd ed., Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1997. MR 1492987, DOI 10.1007/978-3-662-22400-7
  • Gaetano Kanisza, Grammatica del Vedere, Il Mulino, Bologna, Italy, 1980. French translation, La Grammaire du Voir, Diderot, 1997.
  • Akihiro Kanamori, The higher infinite, 2nd ed., Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003. Large cardinals in set theory from their beginnings. MR 1994835
  • Tosio Kato, Continuity of the map $S\mapsto \mid S\mid$ for linear operators, Proc. Japan Acad. 49 (1973), 157–160. MR 405148
  • Felix Klein, Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert, Springer-Verlag, Berlin-New York, 1979 (German). Two volumes reprinted as one; With a foreword by R. Courant and O. Neugebauer. MR 529278
  • A. Kanamori and M. Magidor, The evolution of large cardinal axioms in set theory, Higher set theory (Proc. Conf., Math. Forschungsinst., Oberwolfach, 1977) Lecture Notes in Math., vol. 669, Springer, Berlin, 1978, pp. 99–275. MR 520190
  • Andreas Kriegl and Peter W. Michor, The convenient setting of global analysis, Mathematical Surveys and Monographs, vol. 53, American Mathematical Society, Providence, RI, 1997. MR 1471480, DOI 10.1090/surv/053
  • Andrey Kolomogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung, 1933. English translation published by Chelsea Books in 1956 and reprinted many times.
  • Elizabeth Kolbert, The Sixth Extinction, Henry Holt and Company, New York City, 2014.
  • Saul Kripke, Transfinite recursion on admissible ordinals, Journal of Symbolic Logic, pages 161–162, 1964.
  • Sergey Kushnarev, Teichons: solitonlike geodesics on universal Teichmüller space, Experiment. Math. 18 (2009), no. 3, 325–336. MR 2555702
  • Nick Lane, The Vital Question: Energy, Evolution, and the Origins of Complex Life, W. W. Norton, 2015.
  • A. J. Leggett, S. Chakravart, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zweiger, Dynamics of the dissipative two-state system, Review Modern Physics 59 (1987).
  • Tsung-Yi Lin, Piotr Dollar, Ross Girshick, Kaiming He, Bharath Hariharan, and Serge Belongie, Feature pyramid networks for object detection, 2017. Online at arXiv: 1612.03144v2.
  • L. Haggerty, What a two-and-a-half-year-old child said in one day, Journal of Genetic Psychology, pages 75–85, 1929.
  • Philip Lieberman, The Biology and Evolution of Language, Harvard University Press, 1984.
  • C. C. Lin, Almost commuting self-adjoint matrices and applications, Fields Institute Communications, 13, 1997.
  • L. D. Landau and E. M. Lipschitz, Quantum Mechanics: Non-Relativistic Theory, Pergamon Press, 1965.
  • Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo, Swin transformer: Hierarchical vision transformer using shifted windows, 2022. Online at arXiv: 2103.14030v2.
  • Zhuand Liu, Hanzi Mao, Chao-Yuan Wu, Christoph Feichtenhofer, Trevor Carrell, and Saining Xie, A convnet for the 2020s, 2022. Online at arXiv: 2201.03545v2.
  • Kazimir Malevich, https://www.azquotes.com/author/28541-Kazimir_Malevich.
  • Thomas Robert Malthus, An Essay on the Principle of Population, William Goodwin, London, 1798.
  • Manu. alexanderManusmrti, English translation by George Bühler, online at \breakurl{http://www.sacred-}texts.com/hin/manu.htm.
  • Daniel Mansfield, Perpendicular lines and diagonal triples in old babylonian surveying, Journal of Cuneiform Studies 72 (2020), 87–99.
  • Daniel F. Mansfield, Plimpton 322: a study of rectangles, Found. Sci. 26 (2021), no. 4, 977–1005. MR 4334265, DOI 10.1007/s10699-021-09806-0
  • David Marr, Vision, W. H. Freeman and Co., 1982. Reprinted by MIT Press.
  • Richard Mattessich, The Beginnings of Accounting and Accounting Thought, Garland Publishing, 2000.
  • Manuel Blum and Lenore Blum, A theoretical computer science perspective on consciousness, Journal of Artificial Intelligence and Consciousness 8 (2021), 1–42.
  • Colin McCann, Apeirogon, Random House, 2020.
  • Tomas Mikolov, Kai Chen, Greg Corrado, and Jeffrey Dean, Efficient estimation of word representations in vector space, 2013. Online: arXiv:1301.3781v3.
  • Alan McIntosh, Counterexample to a question on commutators, Proc. Amer. Math. Soc. 29 (1971), 337–340. MR 276798, DOI 10.1090/S0002-9939-1971-0276798-4
  • Ian McKewan, Machines Like Me, Nan A. Talese, 2019.
  • Bartlett Mel, Toward a simplified model of an active dendritic tree, in Dendrites, Oxford University Press, 2016.
  • Bjorn Merker, Consciousness without a cerebral cortex: A challenge for neuroscience and medicine, Behavioral and Brain Sciences 30 (2007), 63–134.
  • N. Metropolis, The beginning of the Monte Carlo method, Los Alamos Sci. 15, Special Issue (1987), 125–130. Stanislaw Ulam 1909–1984. MR 935771
  • Thomas Metzinger, The Ego Tunnel: the Science of Mind and the Myth of the Self, Basic Books, 2009.
  • Chris Manning and John Hewitt, A structural probe for finding syntax in word representations, 2019. Online: arXiv: 1803.00188.
  • John Mitchell, An inquiry into the probable parallax, and magnitude, of the fixed stars, from the quantity of light which they afford us, and the particular circumstances of their situation, Philosophical Transactions 57 (1767), 234–264.
  • Colin McEvedy and Richard Jones, Atlas of World Population History, Puffin-Penguin, London, 1978.
  • Piet Mondrian, Plastic Art and Pure Plastic Art, Wittenborn and Company, 1945.
  • Sy Montgomery, The Soul of an Octopus, Simon & Schuster, 2015. You must see also her lecture https://www.youtube.com/watch?v=_N2yDf7_1oc.
  • Masanori Morishita, Knots and primes, Universitext, Springer, London, 2012. An introduction to arithmetic topology. MR 2905431, DOI 10.1007/978-1-4471-2158-9
  • Yiannis N. Moschovakis, Descriptive set theory, 2nd ed., Mathematical Surveys and Monographs, vol. 155, American Mathematical Society, Providence, RI, 2009. MR 2526093, DOI 10.1090/surv/155
  • David Mumford, Caroline Series, and David Wright, Indra’s pearls, Cambridge University Press, New York, 2002. The vision of Felix Klein. MR 1913879, DOI 10.1017/CBO9781107050051.024
  • Michael Miller, Alain Trouvé, and Laurent Younes, On the metrics and Euler-Lagrange equations of computational anatomy, Annual Reviews Biomedical Engineering 4 (2002), 375–405.
  • W. Bryant Mumford, Malangali school, Atrica 3 (1930), 265–292.
  • Nikola Markov, Julien Vezoli, Pierre Chameau, Arnold Falchier, René Quilodran, and Shimon Ullman et al., Anatomy of hierarchy: Feedforward and feedback pathways in macaque visual cortex, Journal of Comparative Neurology 522 (2014), 225–259.
  • Tsukane Ogawa and Mitsuo Morimoto (eds.), Mathematics of Takebe Katahiro and history of mathematics in East Asia, Advanced Studies in Pure Mathematics, vol. 79, Mathematical Society of Japan, [Tokyo], 2018. Papers from the ICM 2014 satellite conference: International Conference on Traditional Mathematics in East Asia and Related Topics held at Ochanomizu University, Tokyo, August 25–30, 2014. MR 3929745
  • Alfred R. Osborne, Nonlinear ocean waves and the inverse scattering transform, International Geophysics Series, vol. 97, Elsevier/Academic Press, Boston, MA, 2010. MR 2654218
  • Jaak Panksepp, Affective Neuroscience: The Foundations of Human and Animal Emotions, Oxford University Press, 2004.
  • Jaak Panksepp and Lucy Biven, The Archeology of Mind: Neuroevolutionary Origins of Human Emotions, W. W. Norton, 2004.
  • Guiseppe Peano, Arithmetices principia, nova methodo exposita, Fratres Bocca, Rome, 1889. Avaliable at https://archive.org/details/arithmeticespri00peangoog.
  • Judea Pearl, Causality, 2nd ed., Cambridge University Press, Cambridge, 2009. Models, reasoning, and inference. MR 2548166, DOI 10.1017/CBO9780511803161
  • Jeff Paris and Leo Harrington, A mathematical incompleteness in Peano arithmetic, Handbook of mathematical logic, Stud. Logic Found. Math., vol. 90, North-Holland, Amsterdam, 1977, pp. 1133–1142. MR 3727432
  • Mark D. Penney, Dax Enshan Koh, and Robert W. Spekkens, Quantum circuit dynamics via path integrals: is there a classical action for discrete-time paths?, New J. Phys. 19 (2017), no. July, 073006, 29. MR 3686533, DOI 10.1088/1367-2630/aa61ba
  • Emma Previato, Hyperelliptic quasiperiodic and soliton solutions of the nonlinear Schrödinger equation, Duke Math. J. 52 (1985), no. 2, 329–377. MR 792178, DOI 10.1215/S0012-7094-85-05218-4
  • Mingtao Pei, Zhangzhang Si, Benjamin Yao, Y. Jia, and Song-Chun Zhu, Learning and parsing video events with goal and intent prediction, Computer Vision and Image Understanding, pages 1203–1548, 2013.
  • Claudius Ptolemy, Geography of Claudius Ptolemy, Cosimo Classics, 2011. Translated by Edward Luther Stevenson originally in 1932, reprinted often.
  • Michael Rappenglueck, BBC News, 2003, Broadcast on Jan. 21, 2003.
  • Gabriele Radnikow and Dirk Feldmeyer, Layer- and cell type-specific modulation of excitatory neuronal activity in the neocortex, Frontiers in Neuroanatomy 12 (2018).
  • Ben Rudiak-Gould, The sum-over-histories approach to quantum computing, 2006. ArXiv: quant-ph/0607151.
  • Eleanor Robson, Words and pictures: new light on Plimpton 322, Amer. Math. Monthly 109 (2002), no. 2, 105–120. MR 1903149, DOI 10.2307/2695324
  • Alex Rosenberg, Why you don’t know your own mind, https://www.nytimes.com/2016/07/18/opinion/why-you-dont-know-your-own-mind.html, 2016. OpEd piece in The New York Times, July 18, 2016.
  • S. N. Sen and A. K. Bag, The Sulbasutras, Indian National Science Academy, 1983.
  • Denise Schmandt-Besserat, Before Writing: from Counting to Cuneiform, Univ. Texas Press, 1992.
  • Maximilian Schlosshauer (ed.), Elegance and enigma, The Frontiers Collection, Springer, Heidelberg, 2011. The quantum interviews. MR 2895172, DOI 10.1007/978-3-642-20880-5
  • Peter Scholze, Perfectoid spaces, Publ. Math. Inst. Hautes Études Sci. 116 (2012), 245–313. MR 3090258, DOI 10.1007/s10240-012-0042-x
  • Arthur Schopenhauer, The World as Will and Representation, translated by E. F. J. Payne, Dover Publications, 1966.
  • Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/.
  • Igor Shafarevich, The Socialist Phenomenon, Harper and Row, 1980.
  • Igor Shafarevich, Russophobia, https://apps.dtic.mil/dtic/tr/fulltext/u2/a335121.pdf, 1990. Online English translation.
  • Peter W. Shor, Algorithms for quantum computation: discrete logarithms and factoring, 35th Annual Symposium on Foundations of Computer Science (Santa Fe, NM, 1994) IEEE Comput. Soc. Press, Los Alamitos, CA, 1994, pp. 124–134. MR 1489242, DOI 10.1109/SFCS.1994.365700
  • Laurence Sigler, Fibonacci’s Liber Abaci, Springer, 2003. Latin original appeared in 1202 by the author whose proper name is Leonardo de Pisa.
  • Jack H. Silver, Some applications of model theory in set theory, Ann. Math. Logic 3 (1971), no. 1, 45–110. MR 409188, DOI 10.1016/0003-4843(71)90010-6
  • Ruth Silcock, Albert John out Hunting, Viking Kestral Picture Books, 1980.
  • Stephen Simpson, Subsystems of Second Order Arithmetic, Cambridge University Press, Cambridge, UK, 2010.
  • L. K. Shaim and S. W. Nam, Significant-loophole-free test of Bell’s theorem with entangled photons, Physical Review Letters 115 (2015).
  • Robert M. Solovay, A nonconstructible $\Delta _3^1$ set of integers, Trans. Amer. Math. Soc. 127 (1967), 50–75. MR 211873, DOI 10.1090/S0002-9947-1967-0211873-5
  • Robert M. Solovay, A model of set-theory in which every set of reals is Lebesgue measurable, Ann. of Math. (2) 92 (1970), 1–56. MR 265151, DOI 10.2307/1970696
  • Robert M. Solovay, Real-valued measurable cardinals, Axiomatic Set Theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967) Proc. Sympos. Pure Math., XIII, Part I, Amer. Math. Soc., Providence, RI, 1971, pp. 397–428. MR 290961
  • Nelson Spruston, Greg Stuart, and Michael Hausser, Principles of dendritic integration, in Dendrites, Oxford University Press, 2016.
  • Frits Staal, Ritual and Mantras, Rules without Meaning, Motilal Banarsidass, 1996.
  • Frank J. Swetz, The Sea Island mathematical manual: surveying and mathematics in ancient China, Pennsylvania State University Press, University Park, PA, 1992. MR 1180323
  • Sarah Thornton, Seven Days in the Art World, W. W. Norton, 2008.
  • Eckhart Tolle, The Power of Now, Namaste Publishing, 1997.
  • John von Neumann, Mathematical foundations of quantum mechanics, Princeton University Press, Princeton, NJ, 1955. Translated by Robert T. Beyer. MR 66944
  • Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Aidan Gomez, Likasz Kaiser, and Illia Polosukhin, Attention is all you need, 2017. Online: arXiv: 1706.03762.
  • Ulrich Weiss, Quantum Dissipative Systems, World Scientific, 2012.
  • Susan Whitfield, Life along the Silk Road, University of California Press, 2015.
  • Eugene Wigner, Symmetries and Reflections, Ox Bow Press, 1962.
  • Tom Wolfe, The Painted Word, Farrar, Straus, and Giroux, 2008.
  • Harry Woolf (ed.), Some strangeness in the proportion, Addison-Wesley Publishing Co., Reading, MA, 1980. A Centennial Symposium to celebrate the achievements of Albert Einstein; Lectures presented at the Einstein Centennial Symposium held at the Institute for Advanced Study, Princeton, N.J., March 4–9, 1979. MR 610078
  • V. E. Zakharvov, Stability of periodic waves of finite amplitude on the surface of a deep fluid, Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki 9 (1968), 86–94.
  • Vladimir E. Zakharov, Alexander I. Dyachenko, and Oleg A. Vasilyev, New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface, Eur. J. Mech. B Fluids 21 (2002), no. 3, 283–291. MR 1907496, DOI 10.1016/S0997-7546(02)01189-5
  • Heinrich Zimmer, Myths and Symbols in Indian Art and Civilization, Princeton University Press, 1946.
  • Semir Zeki, John Romaya, Dionigi Benincasa, and Michael Atiyah, The experience of mathematical beauty and its neural correlates, Frontiers in Human Neuroscience 8 (2014), 1–12.