SEE ALSO Reimann Hypothesis (1859), Proof of the Prime Number Theorem (1896), Hilbert’s 23 Problems (1900).
Fascinated by Kepler’s famous conjecture, Princeton University scientists Paul Chaikin, Salvatore Torquato, and colleagues studied the packing of M&M chocolate candies. They discovered that the candies had a packing density of about 68 percent, or 4 percent greater than for randomly packed spheres.
Notes and Further Reading
c. 18,000 BCE, Ishango Bone
Bogoshi, J., Naidoo, K., Webb, J., Math. Gazette, 71:294; 1987.
Teresi, D., Lost Discoveries, Simon & Schuster, 2002.
c. 11,000 BCE, Wheat: The Staff of Life
Kirby, E. J. M., Food and Agricultural Organization of the United Nations—Botany of the Wheat Plant.
c. 10,000 BCE, Agriculture
Denison, R. F., Darwinian Agriculture: How Understanding Evolution Can Improve Agriculture. Princeton, NJ: Princeton University Press, 2012.
c. 10,000 BCE, Domestication of Animals
Manning, A., et al., Animals and Human Society: Changing Perspectives. New York: Routledge, 1994.
c. 7000 BCE, Rice Cultivation
Tsunoda, S. (ed.), Biology of Rice. New York: Elsevier Science (1984).
c. 5000 BCE, Birth of Cosmology
According to an official NASA definition, cosmology is the study of the structure and changes in the present universe, whereas the study of the origin and evolution of the early universe is technically called cosmogony.
c. 3300 BCE, Bronze
Ekserdjian, D., ed. Bronze. London: Royal Academy of Arts, 2012.
Radivojevíc et al. “Tainted Ores and the Rise of Tin Bronzes in Eurasia.” Antiquity 87 (2013): 1030.
Sherby, O. D., and J. Wadsworth. “Ancient Blacksmiths, the Iron Age, Damascus Steels, and Modern Metallurgy.” U.S. Department of Energy, September 11, 2011, https://e-reports-ext.llnl.gov/pdf/238547.pdf.
c. 3000 BCE, Dice
Hayes, B., Am. Scient. 89:300;2001.
3000 BCE, Sutures
Kirkup, J. The Evolution of Surgical Instruments, Novato, CA: Norman, 2006.
c. 2500 BCE, Egyptian Astronomy
The author remembers reading an early edition of E.C. Krupp’s Echoes of the Ancient Skies: The Astronomy of Lost Civilizations (Mineola, NY: Dover Publications, 2003) when he was young and being fascinated by how much the objects and motions of the sky meant to our distant ancestors.
c. 1650 BCE, Rhind Papyrus
Eves, H., Great Moments in Mathematics (Before 1650), The Mathematical Association of America, Washington, D.C., 1983.
Robins, G., Shute, C., The Rhind Mathematical Papyrus, Dover Publications, NY, 1990.
c. 1300 BCE, Iron Smelting
Hosford, W. G. Iron and Steel. New York: Cambridge Univ. Press, 2012.
Sherby, O. D., and J. Wadsworth. “Ancient Blacksmiths, the Iron Age, Damascus Steels, and Modern Metallurgy.” U.S. Department of Energy, September 11, 2011, https://e-reports-ext.llnl.gov/pdf/238547.pdf.
c. 1000 BCE, Olmec Compass
Carlson, J., Science, 189: 753; 1975.
c. 600 BCE, Pythagorean Theorem and Triangles
Loomis, E., Pythagorean Proposition, Washington, D.C.: Natl. Council of Teachers of Math., 1972.
Maor, E., The Pythagorean Theorem, Princeton University Press, 2007.
c. 600 BCE, Sewage Systems
IN.gov, tinyurl.com/482p73f.
c. 350 BCE, Aristotle’s Organon
SparkNotes, tinyurl.com/5qhble.
c. 350 BCE, Platonic Solids
Platonic solids are convex polyhedrons. A polyhedron is convex if for every pair of points that belong to the shape, the shape contains the whole straight line segment connecting the two points. Some astrophysicists have suggested that our entire universe may be in the form of a dodecahedron.
c. 300 BCE Euclid’s Elements
Boyer, C., Merzbach, U., A History of Mathematics, John Wiley & Sons, 1991.
c. 240 BCE, Eratosthenes Measures the Earth
Hubbard, D., How to Measure Anything, Hoboken, NJ, 2007.
c. 230 BCE, Pulley
Haven, K., 100 Greatest Science Inventions of All Time, Westport, CT: Libraries Unlimited, 2005.
c. 125 BCE, Antikythera Mechanism
Marchant, J., tinyurl.com/ca8ory.
c. 126 CE, Roman Concrete
Brandon, C. J., et. al. Building for Eternity. Oxford: Oxbow Books, 2014.
Pruitt, S. “The Secret of Ancient Roman Concrete.” History in the Headlines (blog), June 21, 2013, www.history.com/news/the-secrets-of-ancient-roman-concrete.
c. 650, Zero
Arsham, http://tinyurl.com/y7rcvhen.
c. 850, Gunpowder
Kelly, J. Gunpowder: Alchemy, Bombards, and Pyrotechnics. New York: Basic Books, 2004.
Partington, J. R. A History of Greek Fire and Gunpowder. Cambridge: W. Heffer, 1960.
1202, Fibonacci’s Liber Abaci
Today, many authors begin the Fibonacci sequence with a 0, as in 0, 1, 1, 2, 3. . . . Note that the number of columns in mammalian microtubule is typically a Fibonacci number.
1284, Eyeglasses
In 1268, R. Bacon used scientific principles to show that lenses could be used to correct vision.
Magner, L., A History of the Life Sciences, NY: Marcel Dekker, 1979.
c. 1500, Early Calculus
The figure is adapted from Ramasubramanian, K., et al., “Modification of the Earlier Indian Planetary Theory by the Kerala Astronomers (c. 1500) and the Implied Heliocentric Picture of Planetary Motion” (Current Science, vol. 66, 784–790, 1994).
1509, Golden Ratio
The origin of the term golden ratio is disputed but appears to have emerged in the twelfth century. Although the recent history of the golden ratio was triggered by Luca Pacioli’s Divina Proportione (1509), ancient Greek mathematicians studied the ratio much earlier because it frequently appeared in geometrical studies. Note that the artistic figure for this entry depicts a Fibonacci spiral, based on consecutive terms of a Fibonacci sequence. Because the ratios of consecutive terms in the Fibonacci series approach ø, the two spirals are quite similar in appearance.
1543, De Humani Corporis Fabrica
Adler, R., Medical Firsts, Hoboken, NJ: John Wiley & Sons, 2004.
Saunders, J., O’Malley, C., The Illustrations from the Works of Andreas Vesalius of Brussels, NY: Dover Publications, NY, 1973.
1543, Sun-Centered Universe
O’Connor, J., Robertson, http://tinyurl.com/pkglrpa.
1545, Paré’s “Rational Surgery”
Keynes, G., The Apologie and Treatise of Ambroise Paré, London: Falcon, 1951.
1608, Telescope
Lang, K., tinyurl.com/yad22mv.
Brockman, J., ed., The Greatest Inventions of the Past 2000 Years, NY: Simon & Schuster, 2000.
1609, Kepler’s Laws of Planetary Motion
Gingerich, O., Dictionary of Scientific Biography, Gillispie, C., ed., NY: Scribner, 1970.
1614, Logarithms
Gibson, G., “Napier and the Invention of Logarithms,” in Handbook of the Napier Tercentenary Celebration, E. M. Horsburgh, ed., Los Angeles: Tomash Publishers, 1982.
Tallack, P., The Science Book, Weidenfeld & Nicholson, 2003.
1620, Scientific Method
Beveridge, W. I. B., The Art of Scientific Investigation. Caldwell, NJ: Blackburn, 2004.
Wilson, Jr., E. B., An Introduction to Scientific Research. Mineola, NY: Dover Publications, 1991.
1621, Slide Rule
F. Cajori writes, “It is by no means clear that Delamain [the student] stole the invention from Oughtred; Delamain was probably an independent inventor.”
Cajori, F., William Oughtred, Chicago: Open Court, 1916.
Oughtred Society, oughtred.org.
Stoll, C., Sci. Am. 294:81; 2006.
1628, Circulatory System
The hearts of cold-blooded animals, such as eels, were useful to Harvey because
their hearts beat more slowly than mammalian hearts and allowed more careful observation. Harvey also showed that the pulse was caused not directly by the motion of the arteries but rather by a passive response from pressures caused by heart contractions. Other researchers also theorized about blood circulation, including M. Servetus, R. Columbus (also Colombo), and A. Cesalpino.
Adler, R., Medical Firsts, Hoboken, NJ: John Wiley & Sons, 2004.
1637, Descartes’ La Géométrie
Boyer, C., Merzbach, U., A History of Mathematics, John Wiley & Sons, 1991.
Grabiner, J., Math. Mag. 68:83, 1995.
Gullberg, J., Mathematics, W.W. Norton & Company, 1997.
1638, Acceleration of Falling Objects
Other earlier researchers into the acceleration of falling bodies include Nicole Oresme and Domingo de Soto.
1639, Projective Geometry
Other prominent people of the fifteenth and early sixteenth centuries who advanced the mathematical theory of perspective were P. Francesca, L. da Vinci, and A. Dürer.
1654, Pascal’s Triangle
Gordon, J. et al., Phys. Rev. Lett. 56:2280;1986.
1660, Von Guericke’s Electrostatic Generator
Brockman, J., ed., The Greatest Inventions of the Past 2000 Years. New York: Simon & Schuster, 2000.
Gurstelle, W., Adventures from the Technology Underground. New York: Three Rivers Press, 2006.
1665, Development of Modern Calculus
In 1671, Newton wrote On the Methods of Series and Fluxions. (Fluxion was Newton’s term for derivative in the field of calculus.) This work, although circulated in a manuscript to several peers in 1671, did not appear in print until 1736.
1665, Micrographia
Westfall, R., Dictionary of Scientific Biography, Gillispie, C., ed., NY: Scribner, 1970.
1668, Refuting Spontaneous Generation
Farley, J., The Spontaneous Generation Controversy from Descartes to Oparin. Baltimore: The Johns Hopkins Press, 1977.
1672, Measuring the Solar System
Haven, K., 100 Greatest Science Inventions of All Time. Westport, CT: Libraries Unlimited, 2005.
1672, Newton’s Prism
Douma, M., http://tinyurl.com/ybu2k7j.
1678, Discovery of Sperm
Some religious people wondered why God would be so wasteful of the homunculi, with so many preformed humans dying.
1687, Newton as Inspiration
Cropper, W., Great Physicists, NY: Oxford University Press, 2001.
Gleick, J., Isaac Newton, NY: Vintage, 2004.
Koch, R., Smith, C., New Scientist, 190: 25; 2006.
Hawking, S., Black Holes and Baby Universes, NY: Bantam, 1993.
1727, Euler’s Number, e
The mathematical constant e is special for many reasons, e.g., f(x)=ex is its own derivative.
Darling, D., The Universal Book of Mathematics, John Wiley & Sons, 2004.
Kasner, E., Newman, J., Mathematics and the Imagination, Dover Publications, NY, 2001.
Maor, Eli, e: The Story of a Number, Princeton University Press, 1998.
1733, Normal Distribution Curve
Galton, F., Natural Inheritance, London: Macmillan, 1889.
1735, Linnaean Classification of Species
Blunt, W., et al., Linnaeus: The Compleat Naturalist. Princeton, NJ: Princeton University Press, 2002.
1760, Artificial Selection (Selective Breeding)
Wood, R. J., et al., Genetic Prehistory in Selective Breeding: A Prelude to Mendel. New York: Oxford University Press, 2001.
1761, Bayes’ Theorem
Some historians feel that English mathematician Nicholas Saunderson may have discovered Bayes’ theorem before Bayes.
1761, Causes of Cancer
Bloom, J., Texas Monthly 6:175; 1978.
1761, Morgagni’s “Cries of Suffering Organs”
Simmons, J., Doctors & Discoveries, Boston: Houghton Mifflin, 2002.
1783, Black Holes
Quantum physics suggests that short-lived pairs of particles are created in space, and these pairs flicker in and out of existence in very short time scales. The process by which a black hole emits particles involves the creation of virtual particle pairs right on the edge of the black hole’s horizon. The black hole’s tidal gravity pulls the pair of virtual photons apart, thereby feeding energy into them. One member of the pair is swallowed by the black hole, and the leftover particle scoots away out into the universe
1797, Fundamental Theorem of Algebra
Dunham, W., College Math. J. 22:282;1991.
1798, Smallpox Vaccination
Despite his success, Jenner did not know of the cellular mechanism of immunity, which involves white blood cells. Initially, his work was attacked and ridiculed.
Mulcahy, R., Diseases, Minneapolis, MN: Oliver Press, 1996.
Riedel, S., Proc. Bayl. Univ. Med. Cent. 18:21; 2005.
1800, Battery
Brain, M., Bryant, C., tinyurl.com/a2vpe.
Guillen, M., Five Equations that Changed the World, NY: Hyperion, 1995.
1800, High-Pressure Steam Engine
Kirby, R., Engineering in History, Mineola, NY: Dover Publications, 1990.
1801, Wave Nature of Light
Tallack, P., ed., The Science Book, London: Weidenfeld & Nicolson, 2001.
Moring, G., The Complete Idiot’s Guide to Understanding Einstein, NY: Alpha, 2004.
1807, Fourier Series
Jeans, J., Science and Music, Dover Publications, NY, 1968.
Ravetz, J., Grattan-Guinness, I., “Fourier,” in Dictionary of Scientific Biography, Gillispie, C., ed., NY: Scribner, 1970.
1812, Laplace’s Théorie Analytique des Probabilités
Hawking, S., God Created the Integers, Running Press, 2005.
Richeson, A., Natl. Math. Mag. 17:73; 1942.
1822, Babbage Mechanical Computer
Norman, J., From Gutenberg to the Internet, Novato, CA: Historyofscience.com, 2005.
Swade, D., Sci. Am. 268:86; 1993.
1824, Greenhouse Effect
Friedman, T., Hot, Flat, and Crowded, NY: Farrar, Straus and Giroux, 2008.
Gonzalez, J., Werthman, T., Sherer, T., The Complete Idiot’s Guide to Geography, NY: Alpha, 2007.
Sagan, C., Billions and Billions, NY: Ballantine, 1998.
Tallack, P., ed., The Science Book, London: Weidenfeld & Nicolson, 2001.
1827, Brownian Motion
Other early researchers who worked in the area of Brownian motion include T. N. Thiele, L. Bachelier, and J. Ingenhousz.
1828, Germ-Layer Theory of Development
Gilbert, S., Developmental Biology. Sunderland, MA: Sinauer Associates, 2013.
McGeady, T. A., et al., Veterinary Embryology. Oxford, UK: Blackwell, 2006.
1829, Blood Transfusion
Hurt, R., The History of Cardiothoracic Surgery, Pearl River, NY: Parthenon, 1996.
1829, Non-Euclidean Geometry
Tallack, P., The Science Book, Weidenfeld & Nicholson, 2003.
1831, Cell Nucleus
Misteli, T. et al., The Nucleus. Cold Spring Harbor, NY: Cold Spring Harbor Laboratory Press, 2010.
1831, Darwin and the Voyages of the Beagle
Darwin, C., The Voyage of the Beagle (many editions)
Moorehead, A., Darwin and the Beagle: Charles Darwin as Naturalist on the HMS Beagle Voyage. New York: Harper & Row, 1970.
1836, Fossil Record and Evolution
Switek, B., Written in Stone: Evolution, the Fossil Record, and Our Place in Nature. New York: Bellevue Literary Press, 2010.
Taylor, T. N, et al., Paleobotany: The Biology and Evolution of Fossil Plants. New York: Academic Press, 2008.
1837, Nitrogen Cycle and Plant Chemistry
Stevenson, F. J., et al., Cycles of Soil: Carbon, Nitrogen, Phosphorus, Sulfur, Micronutrients. New York: John Wiley & Sons, 1999.
1837, Telegraph System
Connected Earth, http://tinyurl.com/lgntn64.
; 1839, Daguerreotype
Daguerreian Society. “About the Daguerreian Society,” daguerre.org/index.php.
Wooters, D., and T. Mulligan, eds. A History of Photography: The George Eastman House Collection. London: Taschen, 2005.
1839, Rubber
Goodyear Tire & Rubber Company. “The Charles Goodyear Story,” www.goodyear.com/corporate/history/history_story.html.
Korman, R. The Goodyear Story. San Francisco: Encounter Books, 2002.
1842, General Anesthesia
In 1842, a student, W. Clarke, used ether to assist in a tooth extraction. The precise molecular effect of anesthesia is still a subject of research, and it appears that anesthetics affect the spinal cord and brain.
1843, Conservation of Energy
Angier, N., The Canon, NY: Houghton Mifflin, 2007.
Trefil, J., The Nature of Science, NY: Houghton Mifflin, 2003.
1847, Semmelweis’s Hand Washing
The lethal Streptococcus bacteria of septicemia could invade the uterus, which was made vulnerable and exposed by childbirth. Semmelweis referred to the cause as cadaverous particles. American physician O. W. Holmes Sr. also argued that puerperal fever spread from patient to patient via physician contact, and he suggested that physicians clean their instruments.
Carter, K., Carter, B., Childbed Fever, New Brunswick, NJ: Transaction Publishers, 2005.
1850, Second Law of Thermodynamics
French physicist S. Carnot in 1824 realized that the efficiency of converting heat to mechanical work depended on the difference of temperature between hot and cold objects. Other scientists, such as C. Shannon and R. Landauer, have shown how the Second Law and the notion of entropy also apply to communications and information theory. In 2010, scientists from the University of Twente conducted an experiment by bouncing beads against the vanes of a windmill-like device. One side of each vane was softer than the other, and a net windmill movement occurred. Of course, the machine does not violate the Second Law—most of the beads’ energy is lost through heat and sound.
1855, Bessemer Process
Ponting, C., World History, A New Perspective, New York: Pimlico, 2000.
1855, Cell Division
R. Remak also discovered that new cells are formed by the division of preexisting cells. F. Raspail coined the phrase omnis cellula e cellula.
Simmons, J., The Scientific 100, NY: Kensington, 1996.
1856, Plastic
Dreher, Carl, http://tinyurl.com/k8hsxtk.
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