Science History Podcast

The history of mathematics extends back millennia. The needs of trade, taxation, and time-keeping drove the development of principles of arithmetic, algebra, and geometry, which had already acquired some sophistication by 5,000 years ago. Perhaps most fundamental to the development of mathematics has been discoveries on the nature of numbers themselves, or what mathematicians refer to as Number Theory. Today’s topic is the history and development of Number Theory, viewed through the lens of numbers and number systems. Our guide to Number Theory is Bryden Cais, professor of mathematics at the University of Arizona and the Director of the Southwest Center for Arithmetic Geometry.  Bryden completed a BA in mathematics at Harvard University in 2002 and a PhD also in mathematics at the University of Michigan in 2007. He was a postdoctoral fellow at McGill University, a visiting scholar at Universität Bielefeld, and a professor at the University of Wisconsin, Madison before joining the faculty at the University of Arizona in 2011. We explore the nature and history of different number systems, highlight the obstacles that mathematicians and civilizations faced with new concepts of number, and touch on some unsolved problems in modern number theory. A study guide for this episode is available in PDF form HERE, or as LaTeX HERE.

The most important book in the history of mathematics is Euclid’s Elements. The book – really 13 short books bound together into a single treatise – dates to approximately 300 BC, and is credited to the Greek mathematician Euclid of Alexandria. It is apparently a compendium and expansion of the work of previous Greek mathematicians, such as Pythagoras, Hippocrates of Chios, and Eudoxus of Cnidus. The Elements is the oldest surviving logical treatment of mathematics as a discipline, and its theorems and constructions are central to the history of scientific discovery and logic. It is likely that only the Bible has been issued in more editions than the Elements since the invention of the printing press. With us to discuss the Elements, and its importance to the development of geometry, is David Acheson. David completed his bachelor’s degree in math and physics at Kings College, London, in 1967, and his Ph.D. in math at the University of East Anglia in 1971. He then held a variety of academic positions and became a Fellow in Mathematics at Jesus College, Oxford in 1977. In addition to his academic and textbook writing, David has written about mathematics for the public, including his books From Calculus to Chaos, published in 1997, 1089 and All That, published in 2002, The Calculus Story, published in 2017, and The Wonder Book of Geometry, published 2020, all by Oxford University Press.

Galileo occupies an inflection point in the history of science and society. Born in 1564, Galileo changed the trajectory of science though his work in astronomy, physics and related fields. He invented various clever devices, and he used the telescope to push the boundaries of knowledge about our solar system and Earth’s place in it. Galileo’s discoveries, and the manner in which he presented them in his 1632 book Dialogue Concerning the Two Chief World Systems, hurled his fate into the judgements of the Roman Inquisition. Galileo recanted after he was found “vehemently suspect of heresy”. The inquisitors sentenced Galileo with the unusual punishment of house arrest, where he remained until his death in 1642. The Dialogue represented much more than a book on Copernican heliocentrism – that is, that the Earth rotates daily and revolves around the sun. The Dialogue also became a cudgel in the European conflicts between Catholics and Protestants, and the fate of the book in the midst of the Inquisition placed Galileo’s lot in a precarious position. Did Galileo give a copy of the book to its Latin translator, which facilitated its distribution throughout Europe? Was Galileo’s recanting of heliocentrism genuine, or did he continue to spread heretical views while under house arrest? How did Galileo run afoul of a Pope who had previously supported his work? The questions surrounding the Dialogue live on, and with us to decipher the controversy is John Heilbron. John received AB and MA degrees in physics from the University of California, Berkeley in 1955 and 1958, respectively. He completed his Ph.D. in history, also at Berkeley, in 1964. He then taught at the University of Pennsylvania before returning to Berkeley in 1967, where he worked his way through the ranks of academia to a full professorship and director of the Office for History of Science and Technology in 1973. He served as Berkeley’s Vice Chancellor in the early 1990s, and since then has been active as a professor emeritus. Since 1996, John has also conducted research at the University of Oxford, and since 2012 at the California Institute of Technology. John is a member of the International Academy of the History of Science, for which he served as president from 2001-2005. He is also a member of The Royal Swedish Academy of Sciences, The American Academy of Arts and Sciences, and The American Philosophical Society. He is the recipient of many awards for his scholarship on the history of science. John has written numerous books, and today we discuss his latest, a beautifully written book entitled, The Ghost of Galileo in a Forgotten Painting from the English Civil War, published in 2021 by Oxford University Press.

The creation of a new discipline based upon a single scientific expedition is a rare occurrence, but this is what resulted from the 1872-1876 expedition of H.M.S. Challenger. With us to explain the history and significance of the Challenger Expedition is Doug Macdougall. Doug is a geochemist who received a BS in geology from the University of Toronto, an MS in geology from McMaster University, and a PhD in Earth Sciences from the Scripps Institution of Oceanography at the University of California, San Diego. After a two-year postdoc in physics at the University of California, Berkeley, Doug returned to Scripps to serve on the faculty. He is now an emeritus professor of Earth Sciences. Doug is a fellow of the Meteoritical Society and the American Geophysical Union. Today we discuss his book Endless Novelties of Extraordinary Interest – The Voyage of H.M.S. Challenger and the Birth of Modern Oceanography, published by Yale University Press.

In the early 1990s, scientists discovered that sperm counts in industrialized countries had declined precipitously over the previous half century. It turns out that the incidence of other reproductive health problems beyond male infertility also increased in the latter part of the 20th century and into the 21st century. With us to discuss human reproductive health, and how it has changed in part due to exposure to pollutants, is Shanna Swan. Shanna received her BS in mathematics at the City College of New York, her MS in biostatistics at Columbia University, and her PhD in statistics at the University of California, Berkeley. She specializes in Environmental and Reproductive Epidemiology, and is a Professor of Environmental Medicine and Public Health at the Icahn School of Medicine at Mount Sinai, New York. Shanna investigates how prenatal and early childhood exposure to stressors, including chemicals commonly found in the environment, impact the reproductive health and development of children. Today we discuss her new book published by Scribner & Sons – the book is called Count Down: How Our Modern World Is Threatening Sperm Counts, Altering Male and Female Reproductive Health, and Imperiling the Future of the Human Race.

The boundaries of science are clear, and can be demarcated by the concept of falsifiability. Or so we learn in our science classes. But with some areas of science, falsifiability is not the critical feature, and may be impossible on theoretical or empirical grounds. Worrying about falsifiability might even get in the way of interesting ideas. With us to discuss the history of problems in science and falsifiability is Sean Carroll, a leading physicist and science communicator. Sean received a BS in astronomy and astrophysics from Villanova University in 1988, and a PhD in astronomy from Harvard University in 1993. He is a research professor of theoretical physics at the California Institute of Technology and an External Professor at the Santa Fe Institute. His research interests include cosmology, astrophysics, and general relativity. Sean regularly appears in the media to discuss science, and he is the host of the podcast Mindscape. He is also the author of popular science books, including From Eternity to Here, The Particle at the End of the Universe, Something Deeply Hidden, and The Big Picture: On the Origins of Life, Meaning, and the Universe Itself. In this conversation we discuss the concepts of an afterlife, black holes and entropy, time travel, the multiverse, and hierarchy theory, all in the context of what is science, how we should judge science, and the importance, or not, of falsifiability.

Human health and environmental health are inextricably linked. We are negatively impacted by the same pollutants that harm other organisms, and we all live in a sea of synthetic chemicals that are part of our food supply, personal care products, the built environment, and just about every aspect of our lives. With us to gain a better understanding of the history of environmental health, especially the impact of pollutants on human health, is Linda Birnbaum. Linda received a B.A. in biology from the University of Rochester in 1967, and M.S. and Ph.D. degrees in microbiology from the University of Illinois in 1969 and 1972. She held various research and administrative positions in academia and government before taking on the directorships of the US National Institute of Environmental Health Sciences and the National Toxicology Program in 2009. She retired from these directorships in 2019. Linda has published over 600 scientific articles, and is the recipient of numerous awards related to public health.

How is it that corporations routinely and successfully obfuscate science and seed public doubt on issues of paramount importance, ranging from climate change to health effects of tobacco and pesticides? Who are the scientists for hire whose job is to muddy the waters on important policy issues? Why doesn’t our government protect us from nefarious corporations that threaten our health and the environment, and how can we change regulatory ethics to favor the public interest? With us to answer these questions is my guest, David Michaels. David is a professor of epidemiology in the Department of Environmental and Occupational Health at George Washington University. From 1998 through 2001, David served as the Assistant Secretary for Environment, Safety and Health at the U.S. Department of Energy, with responsibility for the safety of workers, communities and the environment surrounding nuclear weapons facilities. From 2009 to 2017, David served as the 12th Assistant Secretary of OSHA, the Occupational Safety and Health Administration. He is the longest serving leader of OSHA in its history. David is the author of numerous articles, as well as the books Doubt is their Product: How Industry’s Assault on Science Threatens your Health (2008), and The Triumph of Doubt – Dark Money and the Science of Deception (2020), both published by Oxford University Press.

Whistleblowers are admired or vilified. They are saviors of democracy or traitors to their country. They confront those in power and drive the news, and some, such as Edward Snowden and Chelsea Manning, are household names. But one man is their inspiration, the person who made whistleblowing a phenomenon of modern times, and his name is Daniel Ellsberg. Ellsberg was born in 1931 in Chicago and grew up in Detroit. He graduated with honors from Harvard with an AB in economics in 1952, and then studied at the University of Cambridge. He served in the U.S. Marine Corps from 1954-1957, and then returned to Harvard where he completed his PhD in economics in 1962. Ellsberg worked as a strategic analyst at the RAND Corporation beginning in 1958, and then in the Pentagon beginning in 1964 under Secretary of Defense Robert McNamara. He worked for the U.S. State Department in South Vietnam for two years, and then returned to the RAND Corporation. At the end of 1969, with help from his colleague Anthony Russo, Ellsberg secretly copied the Pentagon Papers. His illegal dissemination of these papers to newspapers and the subsequent aftermath is the subject of today’s interview, along with his work related to nuclear war planning and the prevention of nuclear war. We discuss this history, and how it relates to the Vietnam War and the downfall of President Nixon, along with many other topics stretching from World War II to the disastrous Trump Administration. Our discussion centers on Ellsberg’s two seminal books, Secrets – A Memoir of Vietnam and the Pentagon Papers and The Doomsday Machine: Confessions of a Nuclear War Planner. I hope you enjoy this conversation with Ellsberg as much as I did – his wit, his charm, and his deep historical perspective on critical moments of the 20th century. On top of the many interesting things Ellsberg has to say, he also reveals some new information for the very first time. (Photograph of Ellsberg by Christopher Michel https://commons.wikimedia.org/wiki/File:Daniel_Ellsberg_2020_CM.jpg)

Pete Myers interviews me about my new book, The Chemical Age, published this month by the University of Chicago Press.