DOCSLIB.ORG

Chen Jingrun, China's Famous Mathematician

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Chen Jingrun, China's Famous Mathematician NEUROSURGICAL FOCUS Neurosurg Focus 41 (1):E11, 2016 Chen Jingrun, China’s famous mathematician: devastated by brain injuries on the doorstep to solving a fundamental mathematical puzzle Ting Lei, MD,1 Evgenii Belykh, MD,1 Alexander B. Dru, BA,2 Kaan Yagmurlu, MD,1 Ali M. Elhadi, MD,1 Peter Nakaji, MD,1 and Mark C. Preul, MD1 1Department of Neurosurgery, Barrow Neurological Institute, St. Joseph’s Hospital and Medical Center, Phoenix; and 2University of Arizona College of Medicine, Tucson, Arizona Chen Jingrun (1933–1996), perhaps the most prodigious mathematician of his time, focused on the field of analytical number theory. His work on Waring’s problem, Legendre’s conjecture, and Goldbach’s conjecture led to progress in ana- lytical number theory in the form of “Chen’s Theorem,” which he published in 1966 and 1973. His early life was ravaged by the Second Sino-Japanese War and the Chinese Cultural Revolution. On the verge of solving Goldbach’s conjecture in 1984, Chen was struck by a bicyclist while also bicycling and suffered severe brain trauma. During his hospitalization, he was also found to have Parkinson’s disease. Chen suffered another serious brain concussion after a fall only a few months after recovering from the bicycle crash. With significant deficits, he remained hospitalized for several years with- out making progress while receiving modern Western medical therapies. In 1988 traditional Chinese medicine experts were called in to assist with his treatment. After a year of acupuncture and oxygen therapy, Chen could control his basic bowel and bladder functions, he could walk slowly, and his swallowing and speech improved. When Chen was unable to produce complex work or finish his final work on Goldbach’s conjecture, his mathematical pursuits were taken up vigor- ously by his dedicated students. He was able to publish Youth Math, a mathematics book that became an inspiration in Chinese education. Although he died in 1996 at the age of 63 after surviving brutal political repression, being deprived of neurological function at the very peak of his genius, and having to be supported by his wife, Chen ironically became a symbol of dedication, perseverance, and motivation to his students and associates, to Chinese youth, to a nation, and to mathematicians and scientists worldwide. http://thejns.org/doi/abs/10.3171/2016.2.FOCUS1595 Key WORds brain trauma; Chen Jingrun; Chinese Cultural Revolution; Goldbach’s conjecture; history of neurosurgery; Parkinson’s disease HEN Jingrun (Fig. 1), one of the world’s greatest ed next announcement to the scientific and mathematics mathematicians, focused on the field of analytical communities was to be a full solution of Goldbach’s con- number theory. Although he made significant ad- jecture, but an unfortunate series of brain injuries altered vancementsC on Waring’s problem (Edward Waring, 1736– his life and substantially affected the science of mathemat- 1798) and Legendre’s conjecture (Adrien-Marie Legen- ics and Chinese education. dre, 1752–1833), he is best known for “Chen’s Theorem,” a significant step in his work on the search for a solution to Goldbach’s conjecture, posited by the German (Prussian) Chen’s Early Life mathematician Christian Goldbach (1690–1764). In 1966 Chen Jingrun was born on May 22, 1933, in Fuzhou, and 1973, Chen published two papers to explain that every Fujian Province, China, during a period of Chinese civil sufficiently large even integer can be written as the sum war. His father, Chen Yuanjun, was a post office clerk and of a prime and a semiprime.7,8 Chen’s work proved to be his mother cared for the family. Chen’s family consisted a milestone in the study of Goldbach’s conjecture, one of of 12 children, only 6 of whom currently survive. Chen the oldest unsolved mathematical problems, and in num- was the third child of his family, which lived on a meager ber progression theory in general. Chen’s anxiously await- income. Although poor, Chen’s parents sought to provide SUBMITTED February 27, 2015. ACCEPTED February 23, 2016. INCLUDE WHEN CITING DOI: 10.3171/2016.2.FOCUS1595. ©AANS, 2016 Neurosurg Focus Volume 41 • July 2016 1 Unauthenticated | Downloaded 10/08/21 03:20 AM UTC T. Lei et al. him significant traumatic emotional stress; Chen often spoke of being plagued by lifelong panic attacks and flash- backs to these events. It was not until September 9, 1945, that the Japanese troops in China (excluding Manchuria) formally stopped their military actions in the region. Chen’s childhood continued to be a struggle, even in the relative sanctuary of elementary school. He was fre- quently bullied and beaten by classmates who picked on him because of his thin, weak stature. As if life was not hard enough, Chen lost his mother in 1947 to tuberculosis when he was 13 years old. Chen began to find solace in his studies, particularly mathematics, where he was happiest when working on tedious algebraic equations. After the occupation ended, Chen returned to Fuzhou with his family and started his formal education at Sanyi Middle School. In 1948, Chen was admitted to Fuzhou Ying hua High School. Here, he met his mathematics teach- er, Shen Yuan, who also was a director of the Aviation De- partment of Tsinghua University. Shen was a knowledge- able and passionate teacher known to mix his teachings with concrete applications to foster interest and apprecia- tion for the esoteric topics covered in his class. One day, Shen lectured on a famous number theory problem in his class called Goldbach’s conjecture. Chen recounted his teacher’s vivid description of the significance of the prob- lem: “Mathematics is the science of the queen, number theory is the crown of mathematics, and Goldbach’s con- jecture is the pearl on the crown.” Playfully, Shen told his students that he dreamt that one of them would prove the conjecture. Everyone laughed except Chen. On December 18, 1989, Chen published a memoir for The Daily Worker FIG. 1. Chen Jingrun (May 22, 1933–March 19, 1996) during his early newspaper and stated, “I did not laugh, did not dare to academic years. laugh. I was worried my classmates would know my vi- sion. But I never forgot this lesson to always remember the pearl on the crown and to never forget my aspirations or and instill the traditional strong tenets of perseverance in ideals.”22 all aspects of life, as they struggled to send their children Goldbach’s conjecture, one of the oldest and most fa- to school and obtain even basic health care.9 mous unsolved problems in number theory and mathemat- On July 7, 1937, war erupted with the Chinese War of ics, was created by Goldbach, and proposed in a series of Resistance against Japan, also known as the Second Sino- letters in June 1742 to Leonhard Euler (Fig. 2). The Gold- Japanese War. By October 26, 1937, the invading Japanese bach conjecture states simply that all positive even inte- army had advanced to occupy the Golden Gate after mov- gers of 4 or more can be expressed as the sum of 2 primes. ing across the Strait of Taiwan in a prelude to the inva- The set of integers are numbers that can be written with- sion of Fujian. At that time, Chen’s father, Chen Yuanjun, out a fractional component, consisting of zero, the natural was deployed to be a director of the Sanyuan County post numbers, and the additive inverses of natural numbers. A office, which was set up in an old temple in the nearby prime number is a natural number greater than 1 that has mountains. no positive divisors other than 1 and itself. For example, 3 The next 8 years in Fuzhou were marked by the hor- is a prime number because its only positive divisors are 1 rors of unrelenting conflicts and foreign military occupa- and 3; 4 is not a prime number because 4 has 1, 2, and 4 as tion. On April 21, 1941, and September 27, 1944, Japan positive divisors, not just 1 and 4. made aggressive moves in the Fujian Province that were On June 7, 1742, Goldbach wrote to Euler proposing characterized by multiple bombing campaigns that rav- that every integer that can be written as the sum of 2 aged the civilian populace. These raids also resulted in primes can also be written as the sum of as many primes vast destruction of public and personal property and the as one wishes, until all terms are units. Goldbach then pro- enslavement of survivors. Natives who could escape the posed a second conjecture in the margin of his letter, that concentration camps established for survivors fled to the every integer greater than 2 can be written as the sum of 3 mountains where Chen lived. Thousands of refugees were primes. He considered 1 to be a prime number, a conven- quickly followed by the Japanese soldiers, and this haven tion subsequently abandoned. The 2 conjectures are now was soon taken over by the Japanese, who interrogated and known to be equivalent, but this did not seem to be an is- tortured most of the inhabitants. The horrific memories sue at the time. A modern version of Goldbach’s marginal and sights that Chen experienced as a young child caused conjecture states that every integer greater than 5 can be 2 Neurosurg Focus Volume 41 • July 2016 Unauthenticated | Downloaded 10/08/21 03:20 AM UTC China’s famous mathematician Chen Jingrun Chen’s Academic Life In 1949, Chen (Fig. 3 left) was admitted to the Math- ematical Physics Department of Xiamen University.
Load more

Recommended publications
  • A MATHEMATICIAN's SURVIVAL GUIDE 1. an Algebra Teacher I
    A MATHEMATICIAN’S SURVIVAL GUIDE PETER G. CASAZZA 1. An Algebra Teacher I could Understand Emmy award-winning journalist and bestselling author Cokie Roberts once said: As long as algebra is taught in school, there will be prayer in school. 1.1. An Object of Pride. Mathematician’s relationship with the general public most closely resembles “bipolar” disorder - at the same time they admire us and hate us. Almost everyone has had at least one bad experience with mathematics during some part of their education. Get into any taxi and tell the driver you are a mathematician and the response is predictable. First, there is silence while the driver relives his greatest nightmare - taking algebra. Next, you will hear the immortal words: “I was never any good at mathematics.” My response is: “I was never any good at being a taxi driver so I went into mathematics.” You can learn a lot from taxi drivers if you just don’t tell them you are a mathematician. Why get started on the wrong foot? The mathematician David Mumford put it: “I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate.” 1.2. A Balancing Act. The other most common response we get from the public is: “I can’t even balance my checkbook.” This reflects the fact that the public thinks that mathematics is basically just adding numbers. They have no idea what we really do. Because of the textbooks they studied, they think that all needed mathematics has already been discovered.
    [Show full text]
  • The "Greatest European Mathematician of the Middle Ages"
    Who was Fibonacci? The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in Italian since he was born in Pisa (Italy), the city with the famous Leaning Tower, about 1175 AD. Pisa was an important commercial town in its day and had links with many Mediterranean ports. Leonardo's father, Guglielmo Bonacci, was a kind of customs officer in the North African town of Bugia now called Bougie where wax candles were exported to France. They are still called "bougies" in French, but the town is a ruin today says D E Smith (see below). So Leonardo grew up with a North African education under the Moors and later travelled extensively around the Mediterranean coast. He would have met with many merchants and learned of their systems of doing arithmetic. He soon realised the many advantages of the "Hindu-Arabic" system over all the others. D E Smith points out that another famous Italian - St Francis of Assisi (a nearby Italian town) - was also alive at the same time as Fibonacci: St Francis was born about 1182 (after Fibonacci's around 1175) and died in 1226 (before Fibonacci's death commonly assumed to be around 1250). By the way, don't confuse Leonardo of Pisa with Leonardo da Vinci! Vinci was just a few miles from Pisa on the way to Florence, but Leonardo da Vinci was born in Vinci in 1452, about 200 years after the death of Leonardo of Pisa (Fibonacci). His names Fibonacci Leonardo of Pisa is now known as Fibonacci [pronounced fib-on-arch-ee] short for filius Bonacci.
    [Show full text]
  • The Astronomers Tycho Brahe and Johannes Kepler
    Ice Core Records – From Volcanoes to Supernovas The Astronomers Tycho Brahe and Johannes Kepler Tycho Brahe (1546-1601, shown at left) was a nobleman from Denmark who made astronomy his life's work because he was so impressed when, as a boy, he saw an eclipse of the Sun take place at exactly the time it was predicted. Tycho's life's work in astronomy consisted of measuring the positions of the stars, planets, Moon, and Sun, every night and day possible, and carefully recording these measurements, year after year. Johannes Kepler (1571-1630, below right) came from a poor German family. He did not have it easy growing Tycho Brahe up. His father was a soldier, who was killed in a war, and his mother (who was once accused of witchcraft) did not treat him well. Kepler was taken out of school when he was a boy so that he could make money for the family by working as a waiter in an inn. As a young man Kepler studied theology and science, and discovered that he liked science better. He became an accomplished mathematician and a persistent and determined calculator. He was driven to find an explanation for order in the universe. He was convinced that the order of the planets and their movement through the sky could be explained through mathematical calculation and careful thinking. Johannes Kepler Tycho wanted to study science so that he could learn how to predict eclipses. He studied mathematics and astronomy in Germany. Then, in 1571, when he was 25, Tycho built his own observatory on an island (the King of Denmark gave him the island and some additional money just for that purpose).
    [Show full text]
  • Newton.Indd | Sander Pinkse Boekproductie | 16-11-12 / 14:45 | Pag
    omslag Newton.indd | Sander Pinkse Boekproductie | 16-11-12 / 14:45 | Pag. 1 e Dutch Republic proved ‘A new light on several to be extremely receptive to major gures involved in the groundbreaking ideas of Newton Isaac Newton (–). the reception of Newton’s Dutch scholars such as Willem work.’ and the Netherlands Jacob ’s Gravesande and Petrus Prof. Bert Theunissen, Newton the Netherlands and van Musschenbroek played a Utrecht University crucial role in the adaption and How Isaac Newton was Fashioned dissemination of Newton’s work, ‘is book provides an in the Dutch Republic not only in the Netherlands important contribution to but also in the rest of Europe. EDITED BY ERIC JORINK In the course of the eighteenth the study of the European AND AD MAAS century, Newton’s ideas (in Enlightenment with new dierent guises and interpre- insights in the circulation tations) became a veritable hype in Dutch society. In Newton of knowledge.’ and the Netherlands Newton’s Prof. Frans van Lunteren, sudden success is analyzed in Leiden University great depth and put into a new perspective. Ad Maas is curator at the Museum Boerhaave, Leiden, the Netherlands. Eric Jorink is researcher at the Huygens Institute for Netherlands History (Royal Dutch Academy of Arts and Sciences). / www.lup.nl LUP Newton and the Netherlands.indd | Sander Pinkse Boekproductie | 16-11-12 / 16:47 | Pag. 1 Newton and the Netherlands Newton and the Netherlands.indd | Sander Pinkse Boekproductie | 16-11-12 / 16:47 | Pag. 2 Newton and the Netherlands.indd | Sander Pinkse Boekproductie | 16-11-12 / 16:47 | Pag.
    [Show full text]
  • Famous Mathematicians Key
    Infinite Secrets AIRING SEPTEMBER 30, 2003 Learning More Dzielska, Maria. Famous Mathematicians Hypatia of Alexandria. Cambridge, MA: Harvard University The history of mathematics spans thousands of years and touches all parts of the Press, 1996. world. Likewise, the notable mathematicians of the past and present are equally Provides a biography of Hypatia based diverse.The following are brief biographies of three mathematicians who stand out on several sources,including the letters for their contributions to the fields of geometry and calculus. of Hypatia’s student Synesius. Hypatia of Alexandria Bhaskara wrote numerous papers and Biographies of Women Mathematicians books on such topics as plane and spherical (c. A.D. 370–415 ) www.agnesscott.edu/lriddle/women/ Born in Alexandria, trigonometry, algebra, and the mathematics women.htm of planetary motion. His most famous work, Contains biographical essays and Egypt, around A.D. 370, Siddhanta Siromani, was written in A.D. comments on woman mathematicians, Hypatia was the first 1150. It is divided into four parts: “Lilavati” including Hypatia. Also includes documented female (arithmetic), “Bijaganita” (algebra), resources for further study. mathematician. She was ✷ ✷ ✷ the daughter of Theon, “Goladhyaya” (celestial globe), and a mathematician who “Grahaganita” (mathematics of the planets). Patwardhan, K. S., S. A. Naimpally, taught at the school at the Alexandrine Like Archimedes, Bhaskara discovered and S. L. Singh. Library. She studied astronomy, astrology, several principles of what is now calculus Lilavati of Bhaskaracharya. centuries before it was invented. Also like Delhi, India:Motilal Banarsidass, 2001. and mathematics under the guidance of her Archimedes, Bhaskara was fascinated by the Explains the definitions, formulae, father.She became head of the Platonist concepts of infinity and square roots.
    [Show full text]
  • Chen Prime Liczby Pierwsze Chena
    Chen Prime Liczby pierwsze Chena Chen Jingrun • Data urodzenia: 22 maj 1933 • Data śmierci: 19 marzec 1996 Pochodzi z wielodzietnej rodziny z Fuzhou, Fujian, Chiny. W 1953 roku skończył wydział matematyki na Uniwersytecie w Xiamen. Jego prace nad przypuszczeniem o bliźniaczych liczbach pierwszych oraz hipotezą Goldbacha doprowadziły do postępu analitycznej teorii liczb. Największym jego osiągnięciem było tzw. twierdzenie Chena stanowiące słabszą wersję słynnej hipotezy Goldbacha. Nazwiskiem Chen Jingruna została nazwana planetoida 7681 Chenjingrun odkryta w 1996 roku Hipoteza Goldbacha • jeden z najstarszych nierozwiązanych problemów w teorii liczb, liczy sobie ponad 250 lat • W 1742 roku, w liście do Leonharda Eulera, Christian Goldbach postawił hipotezę: każda liczba naturalna większa niż 2 może być przedstawiona w postaci sumy trzech liczb pierwszych (ta sama liczba pierwsza może być użyta dwukrotnie) Euler po otrzymaniu listu stwierdził iż hipotezę Goldbacha można uprościć i przedstawić ją w następujący sposób: każda liczba naturalna parzysta większa od 2 jest sumą dwóch liczb pierwszych Powyższą hipotezę do dzisiaj nazywaną "hipotezą Goldbacha" sformułował w rezultacie Euler, jednak nazwa nie została zmieniona. Oto kilka prostych przykładów: 4=2+2 6=3+3 8=3+5 10=3+7=5+5 … 100=53+47… Dzięki użyciu komputerów udało się pokazać, że hipoteza Goldbacha jest prawdziwa dla liczb naturalnych mniejszych niż 4 × 1017 (przez przedstawienie każdej z tych liczb w postaci sumy dwóch liczb pierwszych). Co więcej, większość współczesnych matematyków
    [Show full text]
  • Professor Shiing Shen CHERN Citation
    ~~____~__~~Doctor_~______ of Science honoris cau5a _-___ ____ Professor Shiing Shen CHERN Citation “Not willing to yield to the saints of ancient mathematics. In his own words, his objective is and modem times / He alone ascends the towering to bring about a situation in which “Chinese height.” This verse, written by Professor Wu-zhi mathematics is placed on a par with Western Yang, the father of Nobel Laureate in Physics mathematics and is independent of the latter. That Professor Chen-Ning Yang, to Professor Shiing Shen is, Chinese mathematics must be on the same level CHERN, fully reflects the high achievements as its Western counterpart, though not necessarily attained by Professor Chern during a career that bending its efforts in the same direction.” has spanned over 70 years. Professor Chern was born in Jiaxing, Zhejiang Professor Chern has dedicated his life to the Province in 1911, and displayed considerable study of mathematics. In his early thirties, he mathematical talent even as a child. In 1930, after realized the importance of fiber bundle structure. graduating from the Department of Mathematics From an entirely new perspective, he provided a at Nankai University, he was admitted to the simple intrinsic proof of the Gauss-Bonnet Formula graduate school of Tsinghua University. In 1934, 24 and constructed the “Chern Characteristic Classes”, he received funding to study in Hamburg under thus laying a solid foundation for the study of global the great master of geometry Professor W Blaschke, differential geometry as a whole. and completed his doctoral dissertation in less than a year.
    [Show full text]
  • An Outstanding Mathematician Sergei Ivanovich Adian Passed Away on May 5, 2020 in Moscow at the Age of 89
    An outstanding mathematician Sergei Ivanovich Adian passed away on May 5, 2020 in Moscow at the age of 89. He was the head of the Department of Mathematical Logic at Steklov Mathematical Institute of the Russian Academy of Sciences (since 1975) and Professor of the Department of Mathematical Logic and Theory of Algorithms at the Mathematics and Mechanics Faculty of Moscow M.V. Lomonosov State University (since 1965). Sergei Adian is famous for his work in the area of computational problems in algebra and mathematical logic. Among his numerous contributions two major results stand out. The first one is the Adian—Rabin Theorem (1955) on algorithmic unrecognizability of a wide class of group-theoretic properties when the group is given by finitely many generators and relators. Natural properties covered by this theorem include those of a group being trivial, finite, periodic, and many others. A simpler proof of the same result was obtained by Michael Rabin in 1958. Another seminal contribution of Sergei Adian is his solution, together with his teacher Petr Novikov, of the famous Burnside problem on periodic groups posed in 1902. The deluding simplicity of its formulation fascinated and attracted minds of mathematicians for decades. Is every finitely generated periodic group of a fixed exponent n necessarily finite? Novikov—Adian Theorem (1968) states that for sufficiently large odd numbers n this is not the case. By a heroic effort, in 1968 Sergei Adian finished the solution of Burnside problem initiated by his teacher Novikov, having overcome in its course exceptional technical difficulties. Their proof was arguably one of the most difficult proofs in the whole history of Mathematics.
    [Show full text]
  • Goldbach, Christian
    CHRISTIAN GOLDBACH (March 18, 1690 – November 20, 1764) by HEINZ KLAUS STRICK, Germany One of the most famous, still unproven conjectures of number theory is: • Every even number greater than 2 can be represented as the sum of two prime numbers. The scholar CHRISTIAN GOLDBACH made this simple mathematical statement to his pen pal LEONHARD EULER in 1742 as an assumption. (In the original version it said: Every natural number greater than 2 can be represented as the sum of three prime numbers, since at that time the number 1 was still considered a prime number.) All attempts to prove this theorem have so far failed. Even the offer of a prize of one million dollars hardly led to any progress. CHEN JINGRUN (1933-1996, Chinese stamp on the left), student of HUA LUOGENG (1910-1985, stamp on the right), the most important Chinese mathematician of the 20th century, succeeded in 1966 in making the "best approximation" to GOLDBACH's conjecture. CHEN JINGRUN was able to prove that any sufficiently large even number can be represented as the sum of a prime number and another number that has at most two prime factors. Among the first even numbers are those that have only one GOLDBACH decomposition: 4 = 2 + 2; 6 = 3 + 3; 8 = 3 + 5; 12 = 5 + 7. For larger even numbers one finds a "tendency" to increase the number of possibilities, but even then there is always a number that has only a few decompositions, such as 98 = 19 + 79 = 31 + 67 = 37 + 61. See the graph below and The On-Line Encyclopedia of Integer Sequences A045917.
    [Show full text]
  • Conjecture of Twin Primes (Still Unsolved Problem in Number Theory) an Expository Essay
    Surveys in Mathematics and its Applications ISSN 1842-6298 (electronic), 1843-7265 (print) Volume 12 (2017), 229 { 252 CONJECTURE OF TWIN PRIMES (STILL UNSOLVED PROBLEM IN NUMBER THEORY) AN EXPOSITORY ESSAY Hayat Rezgui Abstract. The purpose of this paper is to gather as much results of advances, recent and previous works as possible concerning the oldest outstanding still unsolved problem in Number Theory (and the most elusive open problem in prime numbers) called "Twin primes conjecture" (8th problem of David Hilbert, stated in 1900) which has eluded many gifted mathematicians. This conjecture has been circulating for decades, even with the progress of contemporary technology that puts the whole world within our reach. So, simple to state, yet so hard to prove. Basic Concepts, many and varied topics regarding the Twin prime conjecture will be cover. Petronas towers (Twin towers) Kuala Lumpur, Malaysia 2010 Mathematics Subject Classification: 11A41; 97Fxx; 11Yxx. Keywords: Twin primes; Brun's constant; Zhang's discovery; Polymath project. ****************************************************************************** http://www.utgjiu.ro/math/sma 230 H. Rezgui Contents 1 Introduction 230 2 History and some interesting deep results 231 2.1 Yitang Zhang's discovery (April 17, 2013)............... 236 2.2 "Polymath project"........................... 236 2.2.1 Computational successes (June 4, July 27, 2013)....... 237 2.2.2 Spectacular progress (November 19, 2013)........... 237 3 Some of largest (titanic & gigantic) known twin primes 238 4 Properties 240 5 First twin primes less than 3002 241 6 Rarefaction of twin prime numbers 244 7 Conclusion 246 1 Introduction The prime numbers's study is the foundation and basic part of the oldest branches of mathematics so called "Arithmetic" which supposes the establishment of theorems.
    [Show full text]
  • Gottfried Wilhelm Leibniz Papers, 1646-1716
    http://oac.cdlib.org/findaid/ark:/13030/kt2779p48t No online items Finding Aid for the Gottfried Wilhelm Leibniz Papers, 1646-1716 Processed by David MacGill; machine-readable finding aid created by Caroline Cubé © 2003 The Regents of the University of California. All rights reserved. Finding Aid for the Gottfried 503 1 Wilhelm Leibniz Papers, 1646-1716 Finding Aid for the Gottfried Wilhelm Leibniz Papers, 1646-1716 Collection number: 503 UCLA Library, Department of Special Collections Manuscripts Division Los Angeles, CA Processed by: David MacGill, November 1992 Encoded by: Caroline Cubé Online finding aid edited by: Josh Fiala, October 2003 © 2003 The Regents of the University of California. All rights reserved. Descriptive Summary Title: Gottfried Wilhelm Leibniz Papers, Date (inclusive): 1646-1716 Collection number: 503 Creator: Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716 Extent: 6 oversize boxes Repository: University of California, Los Angeles. Library. Dept. of Special Collections. Los Angeles, California 90095-1575 Abstract: Leibniz (1646-1716) was a philosopher, mathematician, and political advisor. He invented differential and integral calculus. His major writings include New physical hypothesis (1671), Discourse on metaphysics (1686), On the ultimate origin of things (1697), and On nature itself (1698). The collection consists of 35 reels of positive microfilm of more than 100,000 handwritten pages of manuscripts and letters. Physical location: Stored off-site at SRLF. Advance notice is required for access to the collection. Please contact the UCLA Library, Department of Special Collections Reference Desk for paging information. Language: English. Restrictions on Use and Reproduction Property rights to the physical object belong to the UCLA Library, Department of Special Collections.
    [Show full text]
  • A Mathematician's Lament
    A Mathematician’s Lament by Paul Lockhart musician wakes from a terrible nightmare. In his dream he finds himself in a society where A music education has been made mandatory. “We are helping our students become more competitive in an increasingly sound-filled world.” Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made— all without the advice or participation of a single working musician or composer. Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the “language of music.” It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school. As for the primary and secondary schools, their mission is to train students to use this language— to jiggle symbols around according to a fixed set of rules: “Music class is where we take out our staff paper, our teacher puts some notes on the board, and we copy them or transpose them into a different key. We have to make sure to get the clefs and key signatures right, and our teacher is very picky about making sure we fill in our quarter-notes completely.
    [Show full text]