Roots Of Mathematics

• Authors: Duda Roman
• Languages of publication: EN

Abstracts

EN

To understand the origin of mathematics it seems reasonable to turn our attention to its deep anthropological roots and thus to consider the role of the central nervous system; the evolution of the faculties of thinking, speaking, and understanding symbols; the emergence of mythology, magic and rites; and early geometrical and arithmetical conceptions and their initial development. The article offers a survey of our knowledge on these roots, based upon archaeology, ethnology, psychology, linguistics, cognitive sciences, and it underlines the enormous amount of work done in elaborating primary mathematical ideas in prehistoric times.

Keywords

EN

central nervous system; thinking; speaking; symbols; mythology; primary geometry; primary arithmetic

• Publisher: Instytut Historii Nauki Polskiej Akademii Nauk
• Journal: Organon
• Year: 2017
• Volume: 49
• Pages: 5-27

Contributors

author

Duda Roman

• University of Wroclaw

References

• Aristotle, Parts of Animals, transl. W. Ogle in: The Complete Works of Aris- totle, vol. 1, (ed.) J. Barnes, Princeton University Press, Princeton 1984.
• Asher M., Ethnomathematics. A Multicultural View of Mathematical Ideas, Books/Coel, Pacific Grove CA 1991.
• Atkinson R. J. C., Stonehenge, Penguin Books, Harmondsworth 1990.
• Burl A., Stone Circles of the British Isles, Yale University Press, New Haven 1977.
• Burl A., The recumbent stone circles of Scotland in: Scientific American 6/1981 (245), pp. 66–72.
• Butterworth B., The Mathematical Brain, Macmillan, London 1999.
• Carey S., The Origins of Concepts, Oxford University Press, Oxford 2011.
• Chrisomalis S., Numerical Notation: A Comparative Study, Cambridge University Press, New York 2010.
• Crump Th., The Anthropology of Numbers, Cambridge University Press, Cambridge 1992.
• Damerow P. & Hoyrup J. (eds.), Changing View on Ancient Near Eastern Mathematics, Berlinear Aufträge zum Vordern Orient Bd. 19, Berlin 2001.
• Dehaene S. & Brannon E. (eds.), Space, Time and Number in the Brain. Searching for the Foundations of Mathematical Thought, Academic Press, Amsterdam 2011.
• Dehaene S., Izard V., Pica P. & Spelke E., Core knowledge of geometry in an Amazonian indigene group in: Science 311 (5759), 2006, pp. 381–384.
• Dehaene S., Spelke E., Pinel P. & Stanescu R., Sources of mathematical thinking: behavioral and brain–imaging evidence in: Science 284 (5416), 1999, pp. 970–974.
• Dehaene S., Izard V., Lemer C. & Pica P., Quels sont les liens entre arithmétique et langage? Une étude en Amazonie in: J. Bricmont & J. J. Franck (eds.), Cahiers de l’Herne Chomsky, 2007, pp. 188–196.
• Donaldson M., Children’s minds, Fontana, Glasgow 1978.
• Duroselle J.–B., L’Europe. Histoire de ses peuples, Hachette, Paris 1998.
• Eliade M., A History of Religious Ideas, vol. 1: From the Stone Age to the Eleusian Mysteries, transl. W. R. Trask, The University of Chicago Press, Chicago 1978.
• [Euclid], The Thirteen Books of Euclid’s Elements, transl. Th. L. Heath, Dover Publications, Inc., New York 1956.
• Everett D., Don’t Sleep, There are Snakes: Life and Language in the Amazonian Jungle, Vintage Books, New York 2008.
• Fraser G., The Golden Bough, Part 1: The Magic Art and the Evolution of Kings, vol. 1, MacMillan & Co Ltd, London 1955.
• Freiberg J., Methods and traditions of Babylonian mathematics. Plimpton 922, Pythagorean triples, and the Babylonian triangle parameter equations in: Historia Mathematica 8, 1981, pp. 277–318.
• Freiberg J., Numbers and Measures in the Earliest Written Records in: Scientific American 2/1984 (250), pp. 110–118.
• Frolov B. A., Czisła v grafikie paleolita [Numbers in the Graphics of Paleolith], Izdatelstvo “Nauka”, Novosibirsk 1974.
• Gelman R. & Butterworth B., Number and language: how are they related? in: Trends in Cognitive Sciences 9, 1/2005, pp. 6–10.
• Gericke H., Mathematik in Antike und Orient, Springer–Verlag, Berlin 1984.
• Hawkings G. S., Beyond Stonehenge, Hutchinson, London 1973.
• Heggie D. C., Megalithic Science: Ancient Mathematic and Astronomy in Northwest Europe, Thames and Hudson, London 1981.
• Hersh R., What Mathematics Is, Really?, Oxford University Press, Oxford 1997.
• Homer, The Odyssey, transl. A. T. Murray, William Heinemann, London 1919.
• Hoyle F., On Stonehenge, Heinemann Educational, London 1977.
• Hurford J. R., The Linguistic Theory of Numerals, Cambridge University Press, Cambridge 2011.
• Izard V., Interactions entre les représentations numériques verbales et non–verbales: étude théorique et expérimentale, PhD Thesis, Paris 6, 2006.
• Izard V., Pica P., Dehaene S., Hinchey D. & Spelke E., Geometry as a Uni- versal Mental Construction in: S. Dehaene & E. Brannon (eds.), Space, Time and Number in the Brain. Searching for the Foundations of Mathematical Thought, Academic Press, Amsterdam 2011, pp. 319–332.
• Izard V., Pica P., Spelke E. & Dehaene S., Flexible intuitions of Euclidean geometry in an Amazonian indigene group in: Proceedins of the National Academy of Sciences of the United States of America 108, 2011, pp. 9782–9787.
• Lakoff G. & Nuñez R., Where Mathematics Come From. How the Embodied Human Mind Brings Mathematics into Being, Basic Books, New York 2000.
• Leach E., Claude Lévi–Strauss, The University of Chicago Press, Chicago 1970.
• Lévi–Strauss C., Le totémisme aujourd’hui, PUF, Paris 1962.
• Lévy–Bruhl L., Fonctions mentales dans les sociétés inférieures, Félix Alcan, Paris 1910.
• Lovell K., The Growth of Basic Mathematical and Scientific Concepts in Children, University of London Press, London 1961.
• MacKie E., The Megalith Builders, Phaidon, Oxford 1977.
• MacKie E., Science and Society in Prehistoric Britain, Paul Elek, London 1977.
• Malinowski B., Myth in primitive psychology [1926] in: B. Malinowski, Magic, Science and Religion and Other Essays, Beacon Press, Boston 1948, pp. 72–124.
• Marshack A., The Roots of Civilization: The Cognitive Beginnings of Man’s First Art, Symbol and Notation, McGraw–Hill, New York 1972.
• Marshack A., Exploring the Mind of Ice Age Man in: National Geographic, Jan. 1975, pp. 64–89.
• Moffat M., The Origins, Doubleday and Co., New York 1977 [vol. 1 of The Ages of Mathematics].
• Overmann K., The Role of Materiality in Numerical Cognition in: Quarternary International 405, 2016, pp. 42–51.
• Parker Pearson M., Stonehenge. Exploring the Greatest Stone Age Mystery, Simon & Schuster, London 2012.
• Penrose R., The Road to Reality. A Complete Guide to the Laws of Universe, Alfred A. Knopf, New York 2004.
• Piaget J., Genetic Epistemology, transl. E. Duckworth, W. W. Norton, New York 1971.
• Piaget J., The Language and Thought of the Child, transl. M. & R. Gabain, Routledge & Kegan Paul, London 1926.
• Piaget J. & Inhelder B., La psychologie de l’enfant, PUF, Paris 1966.
• Pica P., Lemer C., Izard V. & Dehaene S., Exact and approximate arithmetic in an Amazonian indigene group in: Science 306 (5695), Oct. 2004, pp. 499–503.
• Poincaré H., Science and Method, transl. F. Maitland, Thomas Nelson and Sons, London 1914.
• Pólya G., The Teaching of Mathematics and the Biogenetic Law in: I. J. Good (ed.), The Scientist Speculates, Heinemann, London 1962, pp. 352–356.
• Raglan F. R. S., How Came Civilization, Methuen, London 1939.
• Rips L. J., The psychology of Proof: Deduction in Human Thinking, The MIT Press, Cambridge MA 1994.
• Saussure de F., Course in General Linguistics, transl. R. Harris, Open Court, La Salle IL 1983.
• Saxe G., Cultural Development of Mathematical Ideas: Papua New Guinea Studies, Cambridge University Press, New York 2012.
• Schmandt–Besserat D., The Earliest Precursor of Writing in: Scientific Ameri- can 6/1977 (238), pp. 50–58.
• Schmandt–Besserat D., Before Writing, vol. 1: From Counting to Cuneiform, University of Texas Press, Austin 1992.
• Seidenberg A., The ritual origin of geometry in: Archive for History of Exact Sciences 1, 5/1961, pp. 488–527.
• Seidenberg A., The ritual origin of counting in: Archive for History of Exact Sciences 2, 1/1962, pp. 1–40.
• Seidenberg A., The origin of mathematics in: Archive for History of Exact Sciences 18, 4/1978, pp. 301–342.
• Shafarevitsh I. R., Über einige Tendenzen in der Entwicklung der Mathematik in: Jahrbuch der Akademie der Wissenschaften in Göttingen 1973, pp. 31–36.
• Spelke E., Differences in Intrinsic Aptitude for Mathematics and Science? in: American Psychologist 60, 9/2005, pp. 950–958.
• Thom A., Megalithic Sites in Britain, Clarendon Press, Oxford 1967.
• Thom R., De l’icône au symbole. Esquisse d’une théorie du symbolisme in: Cahiers Internationaux de Symbolisme 22–23, 1973, pp. 85–106.
• Thom R., Les mathématiques et l’intelligible in: Dialectica 29, 1975, pp. 71–80.
• Urton G., Signs of the Inka Khipu: Binary Coding in the Andean Knotted–String Records, University of Texas Press, Austin 2003.
• Vygotsky L., Thought and language, transl. E. Hanfmann & G. Vakar, The MIT Press, Cambridge MA 1962.
• Waerden van der B. L., Erwachende Wissenschaft, Birkhäuser Verlag, Basel – Stuttgart 1966.
• Waerden van de B. L., Geometry and Algebra in Ancient Civilizations, Sprin- ger–Verlag, Berlin 1983.
• Washburn S. L., The Evolution of Man in: Scientific American 3/1978 (239), pp. 194–206.
• Washburn S. L. & McCrown E. R. (eds.), Human Evolution: Biosocial Perspectives, Benjamin & Cummings, Menlo Park CA 1978.
• Wiese H., Zahl und Numerals. Eine Untersuchung zur Korrellation konzeptueller und sprachlicher Strukturen, De Gruyter, Berlin 1997.