Why Should Historical Truth Matter to Teachers of Mathematics? Dispelling Myths while Promoting Maths Judith V. Grabiner

Why Should Historical Truth Matter to Teachers of Mathematics? Dispelling Myths while Promoting Maths Judith V. Grabiner

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## Why Should Historical Truth Matter to Teachers of Mathematics? Dispelling Myths while Promoting Maths Judith V. Grabiner

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**Why Should Historical Truth Matter to Teachers of**Mathematics? Dispelling Myths while Promoting Maths Judith V. Grabiner Pitzer College, Claremont, California jgrabiner@pitzer.edu**1. First Myth: The social history of mathematics is easy;**just determine what nation or group your mathematician comes from and generalize**2. All modern mathematics comes from Christian men in the**Graeco-European tradition.**Notable mathematicians of the past who are**included on the 2009 MAA Poster, “Women of Mathematics” Hypatia of Alexandria (ca. 355-415) Gabrielle du Châtelet (1706-1749) Maria Gaetana Agnesi (1718-1799) Caroline Herschel (1750-1848) Marie-Sophie Germain (1776-1831) Ada Lovelace (1815-1852) Florence Nightingale (1820-1910) Christine Ladd-Franklin (1847-1930)**Sofia Kovalevskaia (1850-1890)**Charlotte Angas Scott (1858-1931) Grace Chisolm Young (1868-1944) Emmy Noether (1882-1935) Ann Johnson Pell Wheeler (1883-1966) Dame Mary Cartwright (1900-1998) Mina Rees (1902-1997) Ruth Moufang (1905-1977) Olga Taussky-Todd (1906-1995)**Grace Hopper (1906-1992)**Emma Lehmer (1906-2007) Cora Ratto de Sadosky (1912-1981) Hanna Neumann (1914-1971) Julia Bowman Robinson (1919-1985) Olga Ladyzhenskaya (1922-2004) Olga Arsen’enva Oleinik (1925-2001) Etta Zubner Falconer (1933-2002) Over 30% of all U. S. Ph. Ds. in math now are women. Biological change? Oh, sure.**You can still buy the colorful MAA “Women of Math”**poster • http://www.maa.org/pubs/posterW.pdf**Muhammad ibn Musa al-Khwarizmi**(c. 780 – 850) Name Latinized as Algorismus Name then confused with Arithmos Name & method became “Algorithm” _________________________________ His book: Al-kitab al-muhtasar fi hisab al-jabr wa’l’muqabala became“Algebra”**The picture illustrates a bow and bowstring, or cord, or**(Greek) “chord”**Since the sine is the half-chord:**Sanskrit: jya - ardha (chord –half) Shortened into jya or jiva Transliterated into Arabic as: jiba RD WTHT VWLS: jaib = bay, inlet, cavity Translated into Latin as: Sinus**3. There wasn’t any real mathematics in the European**Middle Ages. After the decline of Greek mathematics, nothing important happened mathematically in Europe until the Renaissance.**Merton mean-speed theorem**If the velocity is changing uniformly, Distance covered in time t = distance covered by average speed (Vmax+ Vmin)/2 in the same time Stated by William of Heytesbury, 1335, at Merton College, Oxford**Diagram is first drawn by Nicole Oresme, 1350Area under**velocity graph= distance covered in time t= distance covered by average speed (Vmax+ Vmin)/2in the same time**Galileo’s diagram, from**his epoch-making book Two New Sciences, 1633**1/2 + 2/4 + 3/8 + 4/16 + 5/32 + …k/2k+ … Sum?**1/2 + 1/4 + 1/8 + 1/16 + 1/32 +…= 1 + 1/4 + 1/8 + 1/16 + 1/32 +…= 1/2 + 1/8 + 1/16 + 1/32 +…= 1/4 + 1/16 + 1/32 +…= 1/8 + 1/32 +…= 1/16, etc. Right column adds up to2 So the sum is 2. This solution is due to Richard Swineshead (Suiseth), 14th century, nicknamed “Calculator.”**Proof that the harmonic series diverges:Nicole Oresme, 14th**Century 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 +… = 1/2 + (1/3 + 1/4) + (1/5 + 1/6 + 1/7 + 1/8) +… ≥ 1/2 + (1/ 4 + 1/ 4) + (1/8 + 1/8 + 1/8 + 1/8) + … = 1/2 + 1/2 + 1/ 2 + . .. which exceeds any given quantity.**4. Newton invented the calculus just so he could do his**physics.**D. T. Whiteside, ed., The Mathematical Papers of Isaac**Newton, 8 volumes, Cambridge University Press, 1967 – 1981 The papers on the discovery of the calculus are in Volume I, covering 1664 – 1666 (in Latin – sorry!)**5. Serious statistical thinking in the sciences begins in**the natural sciences; the social sciences learned this from natural science and copied it so they’d look scientific.**Quetelet, heights of French conscripts, early 19th century**(dip in graph greatly exaggerated)1.57 meters N = 100,000. < 1.57 m, 2275 more than predictedBetween 1.570 and 1.624 m, 2114 fewer than predicted**Augustin-Louis Cauchy (1789 - 1857)**• Auguste Comte (1798 - 1857)**Check it out!**Victor J. Katz, A History of Mathematics: An Introduction (a 950-page Introduction) Best is the Third Edition, Addison-Wesley, 2009**“Convergence”: Using historical materials to teach**mathematics http://mathdl.maa.org/mathDL/46/ History and Pedagogy of Mathematics Newsletter: http://www.clab.edc.uoc.gr/hpm/NewsLetters.htm**Let’s ask again: Why should historical truth matter to**teachers of mathematics? • Examples • Mathematical practice • In general, truth matters. • Mathematics evolves.