DOCSLIB.ORG

Mersenne Primes

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Mersenne Primes OC TM Mersenne Primes Joseph Fryer and Casey Detro, Miami University Marin Mersenne’s mathematical contributions helped paved the way for advances in mathematics. In this article, his life is not only depicted but his mathematical intellect is highlighted through his achievements. Since his time, technology has helped further the fi nding of Mersenne primes. Prime numbers are large concepts for students to learn in school. Mersenne primes further examine the study of prime numbers. Introduction Prime numbers have intrigued the minds of mathematicians throughout history. Prime numbers are characterized by only having two factors: 1 and itself. Th e development of these numbers was a major advancement in number theory. Whether mathematicians studied these numbers in their free time Many people or they studied them to make advances in only know of number theory, many positive contributions Mersenne for have come from such investigations. One his famous such mathematician who made a great advance in the study of prime numbers was conjecture for Marin Mersenne. He is most widely known which numbers for a certain kind of prime number, Mersenne (Image Courtesy of http://fr.academic.ru/dic.nsf/frwiki/1240555 are named for prime numbers. Fig 1 Marin Mersenne (1588-1648) him; however, Mersenne primes are a special type of prime number. Th ey have distinct characteristics in shrewd thinker, a brilliant experimentalist, he was also comparison to “regular” prime numbers. Th e an inferior mathematician” while some even an important mathematical concept of Mersenne primes believe he needed psychiatric evaluation infl uence was developed in the search for perfect (Buske & Keith, 2000). Although, many on young numbers. A perfect number is a number in people only know of Mersenne for his which the sum of its proper factors equals the famous conjecture for which numbers are mathematicians original number. named for him, he was also an important infl uence on young mathematicians. He For example, 6 is a perfect number. The factors became a mentor to young researchers in the of 6 are: 1,2,3,6. When we add the factors fi elds of mathematics and science. Mersenne together that are less than 6 we get: 1+2+3=6 was discouraged because these fi elds were in decline, unable to attract a suffi cient number History of scholars. He created a research center in Marin Mersenne was born in 1588 in Europe and used it to keep in contact with France. He studied at the Jesuit Collége other mathematicians and scientists and du Mains of La Fléche (Wanko, 2005) notify them of any recent discoveries in their and became an ordained priest in 1614. fi elds. He was a mentor to a young Pascal. Mersenne is described in many diff erent Without such mentoring, it is hard to say ways by historians. Some believe he was “a if we would have the same theorems we do Ohio Journal of School Mathematics | No. 64 • Fall, 2011 Page 19 OC TM today. Mersenne was friends with other a challenge to fi nd more perfect numbers. famous mathematicians such as Descartes Euclid wrote a series of books entitled and Fermat. Unlike Mersenne, they did not Elements. In Proposition 36 of book IX of enjoy reading the works of other scholars the Elements, Euclid states a formula to fi nd because they feared they would be overly perfect numbers. infl uenced by their discoveries. “Mersenne Euclid’s formula stated: felt that much more could be accomplished If 2k − 1 is prime for k>1, then through shared ideas and communication n =2k − 1(2k − 1) is a perfect number. and thus took it upon himself to correspond For example if k =2 then 22 − 1=3 with young mathematicians and scientists and (which is prime). Now we can plug 3 into provide them with detail of others’ fi ndings” Euclid’s equation. n =22− 1(3) = 6, (Wanko, 2005). After Mersenne had passed which is a perfect number. away in 1648, it was determined that he had seventy eight diff erent correspondents all How does Euclid’s formula for perfect across Europe (Wanko, 2005). Mersenne’s numbers relate to the primes that Mersenne discovered? “If Euclid’s theorem were During famous conjecture came in 1644, only four years prior to his death. true, the problem of fi nding larger perfect his time, numbers could be boiled down to fi nding 2k − 1 Mersenne Brief explanation of primes values for k where the expression had to Before we delve further into Mersenne is prime,” (Wanko, 2005). Th is is when Marin Mersenne stepped in and formed his compute all primes, it is helpful to fi rst provide a brief overview of prime numbers. Recall that a conjecture. He was also interested in fi nding calculations more perfect numbers, so he took it on himself prime number only has two factors: one k to fi nd values of to satisfy Euclid’s formula. by hand. and the number itself. For example, fi ve is a 2k − 1 Mersenne was aware that in order for He spent prime number because it only has 2 factors, 1 k and 5. If a number has more than these two to be prime, itself must also be prime. In countless 1644, he claimed that he had found all the factors it is said to be composite. Primes are 2k − 1 hours trying considered a building block in mathematics. prime numbers that make prime. to fi nd As the Fundamental Th eorem of Algebra His conjecture consisted of the numbers: 2, values of k. indicates, all integers may be represented as a 3, 5, 7, 13, 17, 19, 31, 67, 127, and 257. unique product of primes. Prime numbers are Th ese numbers then became known as the Mersenne Primes. important in mathematics, and it is crucial k for students to learn about them while in Mersenne’s list of possible values for was middle school. questioned by some in regards to his degree of accuracy. During his time, Mersenne had Mersenne Primes to compute all calculations by hand. He spent countless hours trying to fi nd values of Th e discovery of Mersenne primes can be k attributed to contributions made by Euclid, . Since they were all worked out by hand, the Pythagoreans, and Marin Mersenne there were probably some computational himself. Th e history begins with an increasing errors. “It wasn’t until 1947p that all of the interest in fi nding perfect numbers. possible Mersenne primes ( ) were checked During Mersenne’s time, the Pythagoreans using computers,” (Wanko, 2005). Much had only found four perfect numbers: 6, to the surprise of many mathematicians, 28, 496, and 8128. Th e fact that only four his conjecture was correct (although not perfect numbers had been found presented complete). Page 20 Ohio Journal of School Mathematics | No. 64 • Fall, 2011 OC TM Mersenne’s original conjecture: from all the people participating. Anyone can M =2k − 1 is prime for k = 2, 3, 5, 7, 13, help participate in the search if they have the 17, 19, 31, 67, 127, and 257. right type of computer. Monetary rewards are even being off ered to whoever fi nds the Actual Primes (Wanko, 2005): With k ≤ 257, k fi rst ten-million-digit prime number. In M =2 − 1 is prime for k = 2, 3, 5, 7, 13, 1999, the search found its then record high 26972593 − 1. 17, 19, 31, 67, 127, and 257. prime It was found by Nayan Hajratwala of Michigan using the GIMPS One may notice that this list of primes software that he downloaded on his computer starts out by listing the prime numbers in 11 (Buske & Keith, 2000).Th is number is over order, but isn’t also a prime number? two million digits long and could fi ll over Mersenne noticed that not every prime seven miles of digits and commas (Buske & number satisfi ed the equation. For instance, 11 211 − 1 = 2048. Keith, 2000). Th en, in 2004, another prime if we try to use we get: 2048 became the largest known world prime, We know that can’t be prime because it 224036583 − 1, 2 consisting of over seven is divisible by (2 × 1024). Now, with the aid of technology, people continue to search for larger and larger prime and Mersenne (Image Courtesy of gilchrist.ca/jeff/MprimeDigits/index.html) Fig 2 Beware of false generalizations! Fig 3 Mersenne digits calculator prime numbers. Mersenne Primes and Technology million digits (Wanko, 2005). At the time In the seventeenth century, when Mersenne of this writing, the largest known Mersenne 43112609 made his famous conjecture, the only method prime is 2 − 1. To date there are 47 mathematicians had for fi nding large numbers known Mersenne primes and the search is was by hand. Now, with the aid of technology, still ongoing and it is surprising at how large people continue to search for larger and larger these numbers can be. prime and Mersenne prime numbers. “In 1996, George Woltman, using networking software Conclusion by Scott Kurowski, created the database In conclusion, Marin Mersenne made a GIMPS (Great Internet Mersenne Prime signifi cant contribution to mathematics. His Search), which coordinates the eff orts of more intellect and mathematical curiosity about than 8,000 computer users internationally in perfect numbers helped to pave the way a practice known as distributed internet data for his conjecture. Today, with the help of processing” (Buske & Keith, 2000). Th e main computers, mathematicians have found the server then distributes and collects information largest prime number to date through the Ohio Journal of School Mathematics | No.
Load more

Recommended publications
  • ACT Resources for Arts A/V Technology
    Career Cluster: Arts, A/V Technology, & Communications Mathematics in Digital Arts and Design III – Addresses standard 11 Question A graphic designer at a bottling company is tasked with designing efficient packaging for soda cans. Two options are being considered. Which of the two arrangements has less unused space in the package and how does the arrangement compare with the alternative? The radius of a soda can is approximately 3.2 cm. Package A Package B A. Package A; Package A has 16.7% less unused space than Package B. B. Package B; Package B has 16.7% less unused space than Package A. C. Package B; Package B has 8.3% less unused space than Package A. D. Neither; The two packages have equal unused space. Source: Adapted from Zordak, S. E. (n.d.). Soda Cans. Retrieved February 24, 2016, from http://illuminations.nctm.org/Lesson.aspx?id=2363 Office of Career and Technical Education • 710 James Robertson Parkway • Nashville, TN 37243 1 | March 2016 Tel: (615) 532-2830 • tn.gov/education/cte Career Cluster: Arts, A/V Technology, & Communications Science in A/V Production I – Addresses Standard 15 Passage I Natural Science: This passage is adapted from the chapter “The Wave Theory of Sound” in Acoustics: An Introduction to Its Physical Principles and Applications by Allan Pierce. (Acoustical Society of America). Acoustics is the science of sound, including 20 ability, of communication via sound, along with the its production, transmission, and effects. In variety of psychological influences sound has on present usage, the term sound implies not only those who hear it.
    [Show full text]
  • Marin Mersenne English Version
    MARIN MERSENNE (September 8, 1588 – September 1, 1648) by HEINZ KLAUS STRICK, Germany Although no stamp with a portrait of the French mathematician MARIN MERSENNE has yet been issued, the postal administration of the Principality of Liechtenstein took the discovery of the 39th MERSENNE prime number = 13,466,917 − M13,466,9 17 2 1 as an opportunity to select this number as the motif for a stamp of a series on science (the graphic on the stamp below shows a logarithmic spiral). (drawings © Andreas Strick) EUCLID had already dealt with numbers of the type 2n −1 and, among other things, proved the theorem: If 2n −1 is a prime number, then 2n1- ⋅ (2 n − 1) is a perfect number. th Until the end of the 16 century it was believed that all numbers of the type 2n −1 were prime numbers if the exponent n was a prime number. In 1603, the Italian mathematician PIETRO CATALDI, who was also the first to write a treatise on continued fractions, proved the following: If the exponent n is not a prime number, i.e. if it can be represented as the product of n a⋅ b= with a b∈ , IN , then 2n −1 is not a prime number either; because then the number can be broken down into at least two factors: ⋅ − ⋅ 2a b − 12112 =( a −) ⋅( +a + 22 a + 23 a + ...2 + (b 1) a ). He also showed by systematic trial and error with all prime divisors up to the root of the number in question that 217 −1 and 219 −1 are prime numbers.
    [Show full text]
  • 1 Mersenne Primes and Perfect Numbers
    1 Mersenne Primes and Perfect Numbers Basic idea: try to construct primes of the form an − 1; a, n ≥ 1. e.g., 21 − 1 = 3 but 24 − 1=3· 5 23 − 1=7 25 − 1=31 26 − 1=63=32 · 7 27 − 1 = 127 211 − 1 = 2047 = (23)(89) 213 − 1 = 8191 Lemma: xn − 1=(x − 1)(xn−1 + xn−2 + ···+ x +1) Corollary:(x − 1)|(xn − 1) So for an − 1tobeprime,weneeda =2. Moreover, if n = md, we can apply the lemma with x = ad.Then (ad − 1)|(an − 1) So we get the following Lemma If an − 1 is a prime, then a =2andn is prime. Definition:AMersenne prime is a prime of the form q =2p − 1,pprime. Question: are they infinitely many Mersenne primes? Best known: The 37th Mersenne prime q is associated to p = 3021377, and this was done in 1998. One expects that p = 6972593 will give the next Mersenne prime; this is close to being proved, but not all the details have been checked. Definition: A positive integer n is perfect iff it equals the sum of all its (positive) divisors <n. Definition: σ(n)= d|n d (divisor function) So u is perfect if n = σ(u) − n, i.e. if σ(u)=2n. Well known example: n =6=1+2+3 Properties of σ: 1. σ(1) = 1 1 2. n is a prime iff σ(n)=n +1 p σ pj p ··· pj pj+1−1 3. If is a prime, ( )=1+ + + = p−1 4. (Exercise) If (n1,n2)=1thenσ(n1)σ(n2)=σ(n1n2) “multiplicativity”.
    [Show full text]
  • An Analysis of Primality Testing and Its Use in Cryptographic Applications
    An Analysis of Primality Testing and Its Use in Cryptographic Applications Jake Massimo Thesis submitted to the University of London for the degree of Doctor of Philosophy Information Security Group Department of Information Security Royal Holloway, University of London 2020 Declaration These doctoral studies were conducted under the supervision of Prof. Kenneth G. Paterson. The work presented in this thesis is the result of original research carried out by myself, in collaboration with others, whilst enrolled in the Department of Mathe- matics as a candidate for the degree of Doctor of Philosophy. This work has not been submitted for any other degree or award in any other university or educational establishment. Jake Massimo April, 2020 2 Abstract Due to their fundamental utility within cryptography, prime numbers must be easy to both recognise and generate. For this, we depend upon primality testing. Both used as a tool to validate prime parameters, or as part of the algorithm used to generate random prime numbers, primality tests are found near universally within a cryptographer's tool-kit. In this thesis, we study in depth primality tests and their use in cryptographic applications. We first provide a systematic analysis of the implementation landscape of primality testing within cryptographic libraries and mathematical software. We then demon- strate how these tests perform under adversarial conditions, where the numbers being tested are not generated randomly, but instead by a possibly malicious party. We show that many of the libraries studied provide primality tests that are not pre- pared for testing on adversarial input, and therefore can declare composite numbers as being prime with a high probability.
    [Show full text]
  • Mersenne and Fermat Numbers 2, 3, 5, 7, 13, 17, 19, 31
    MERSENNE AND FERMAT NUMBERS RAPHAEL M. ROBINSON 1. Mersenne numbers. The Mersenne numbers are of the form 2n — 1. As a result of the computation described below, it can now be stated that the first seventeen primes of this form correspond to the following values of ra: 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281. The first seventeen even perfect numbers are therefore obtained by substituting these values of ra in the expression 2n_1(2n —1). The first twelve of the Mersenne primes have been known since 1914; the twelfth, 2127—1, was indeed found by Lucas as early as 1876, and for the next seventy-five years was the largest known prime. More details on the history of the Mersenne numbers may be found in Archibald [l]; see also Kraitchik [4]. The next five Mersenne primes were found in 1952; they are at present the five largest known primes of any form. They were announced in Lehmer [7] and discussed by Uhler [13]. It is clear that 2" —1 can be factored algebraically if ra is composite; hence 2n —1 cannot be prime unless w is prime. Fermat's theorem yields a factor of 2n —1 only when ra + 1 is prime, and hence does not determine any additional cases in which 2"-1 is known to be com- posite. On the other hand, it follows from Euler's criterion that if ra = 0, 3 (mod 4) and 2ra + l is prime, then 2ra + l is a factor of 2n— 1.
    [Show full text]
  • Founding a Family of Fiddles
    The four members of the violin family have changed very little In hundreds of years. Recently, a group of musi- cians and scientists have constructed a "new" string family. 16 Founding a Family of Fiddles Carleen M. Hutchins An article from Physics Today, 1967. New measmement techniques combined with recent acoustics research enable us to make vioUn-type instruments in all frequency ranges with the properties built into the vioHn itself by the masters of three centuries ago. Thus for the first time we have a whole family of instruments made according to a consistent acoustical theory. Beyond a doubt they are musically successful by Carleen Maley Hutchins For three or folti centuries string stacles have stood in the way of practi- quartets as well as orchestras both cal accomplishment. That we can large and small, ha\e used violins, now routinely make fine violins in a violas, cellos and contrabasses of clas- variety of frequency ranges is the re- sical design. These wooden instru- siJt of a fortuitous combination: ments were brought to near perfec- violin acoustics research—showing a tion by violin makers of the 17th and resurgence after a lapse of 100 years— 18th centuries. Only recendy, though, and the new testing equipment capa- has testing equipment been good ble of responding to the sensitivities of enough to find out just how they work, wooden instruments. and only recently have scientific meth- As is shown in figure 1, oiu new in- ods of manufactiu-e been good enough struments are tuned in alternate inter- to produce consistently instruments vals of a musical fourth and fifth over with the qualities one wants to design the range of the piano keyboard.
    [Show full text]
  • Primes and Primality Testing
    Primes and Primality Testing A Technological/Historical Perspective Jennifer Ellis Department of Mathematics and Computer Science What is a prime number? A number p greater than one is prime if and only if the only divisors of p are 1 and p. Examples: 2, 3, 5, and 7 A few larger examples: 71887 524287 65537 2127 1 Primality Testing: Origins Eratosthenes: Developed “sieve” method 276-194 B.C. Nicknamed Beta – “second place” in many different academic disciplines Also made contributions to www-history.mcs.st- geometry, approximation of andrews.ac.uk/PictDisplay/Eratosthenes.html the Earth’s circumference Sieve of Eratosthenes 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Sieve of Eratosthenes We only need to “sieve” the multiples of numbers less than 10. Why? (10)(10)=100 (p)(q)<=100 Consider pq where p>10. Then for pq <=100, q must be less than 10. By sieving all the multiples of numbers less than 10 (here, multiples of q), we have removed all composite numbers less than 100.
    [Show full text]
  • Mersenne and Mixed Mathematics
    Mersenne and Mixed Mathematics Antoni Malet Daniele Cozzoli Pompeu Fabra University One of the most fascinating intellectual ªgures of the seventeenth century, Marin Mersenne (1588–1648) is well known for his relationships with many outstanding contemporary scholars as well as for his friendship with Descartes. Moreover, his own contributions to natural philosophy have an interest of their own. Mersenne worked on the main scientiªc questions debated in his time, such as the law of free fall, the principles of Galileo’s mechanics, the law of refraction, the propagation of light, the vacuum problem, the hydrostatic paradox, and the Copernican hypothesis. In his Traité de l’Harmonie Universelle (1627), Mersenne listed and de- scribed the mathematical disciplines: Geometry looks at continuous quantity, pure and deprived from matter and from everything which falls upon the senses; arithmetic contemplates discrete quantities, i.e. numbers; music concerns har- monic numbers, i.e. those numbers which are useful to the sound; cosmography contemplates the continuous quantity of the whole world; optics looks at it jointly with light rays; chronology talks about successive continuous quantity, i.e. past time; and mechanics concerns that quantity which is useful to machines, to the making of instruments and to anything that belongs to our works. Some also adds judiciary astrology. However, proofs of this discipline are The papers collected here were presented at the Workshop, “Mersenne and Mixed Mathe- matics,” we organized at the Universitat Pompeu Fabra (Barcelona), 26 May 2006. We are grateful to the Spanish Ministry of Education and the Catalan Department of Universities for their ªnancial support through projects Hum2005-05107/FISO and 2005SGR-00929.
    [Show full text]
  • Appendix a Tables of Fermat Numbers and Their Prime Factors
    Appendix A Tables of Fermat Numbers and Their Prime Factors The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. Carl Friedrich Gauss Disquisitiones arithmeticae, Sec. 329 Fermat Numbers Fo =3, FI =5, F2 =17, F3 =257, F4 =65537, F5 =4294967297, F6 =18446744073709551617, F7 =340282366920938463463374607431768211457, Fs =115792089237316195423570985008687907853 269984665640564039457584007913129639937, Fg =134078079299425970995740249982058461274 793658205923933777235614437217640300735 469768018742981669034276900318581864860 50853753882811946569946433649006084097, FlO =179769313486231590772930519078902473361 797697894230657273430081157732675805500 963132708477322407536021120113879871393 357658789768814416622492847430639474124 377767893424865485276302219601246094119 453082952085005768838150682342462881473 913110540827237163350510684586298239947 245938479716304835356329624224137217. The only known Fermat primes are Fo, ... , F4 • 208 17 lectures on Fermat numbers Completely Factored Composite Fermat Numbers m prime factor year discoverer 5 641 1732 Euler 5 6700417 1732 Euler 6 274177 1855 Clausen 6 67280421310721* 1855 Clausen 7 59649589127497217 1970 Morrison, Brillhart 7 5704689200685129054721 1970 Morrison, Brillhart 8 1238926361552897 1980 Brent, Pollard 8 p**62 1980 Brent, Pollard 9 2424833 1903 Western 9 P49 1990 Lenstra, Lenstra, Jr., Manasse, Pollard 9 p***99 1990 Lenstra, Lenstra, Jr., Manasse, Pollard
    [Show full text]
  • UNIVERSITY of CALIFORNIA, SAN DIEGO Non-Contact
    UNIVERSITY OF CALIFORNIA, SAN DIEGO Non-contact Ultrasonic Guided Wave Inspection of Rails: Next Generation Approach A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Structural Engineering by Stefano Mariani Committee in Charge: Professor Francesco Lanza di Scalea, Chair Professor David J. Benson Professor Michael J. Buckingham Professor William S. Hodgkiss Professor Chia-Ming Uang 2015 Copyright, Stefano Mariani, 2015 All rights reserved. The dissertation of Stefano Mariani is approved, and it is acceptable in quality and form for publication on microfilm and electronically: ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ Chair University of California, San Diego 2015 iii DEDICATION To Bob iv TABLE OF CONTENTS Signature Page iii Dedication iv Table of Contents v List of Abbreviations ix List of Figures xi List of Tables xxii Acknowledgments xxiv Vita xvii Abstract of the Dissertation xxix 1 Introduction ................................................................................................................... 1 1.1 Non Destructive Evaluation of railroad tracks. Introductory discussions and motivations for the research ............................................................................................ 1 1.2
    [Show full text]
  • MATH 404: ARITHMETIC 1. Divisibility and Factorization After Learning To
    MATH 404: ARITHMETIC S. PAUL SMITH 1. Divisibility and Factorization After learning to count, add, and subtract, children learn to multiply and divide. The notion of division makes sense in any ring and much of the initial impetus for the development of abstract algebra arose from problems of division√ and factoriza- tion, especially in rings closely related to the integers such as Z[ d]. In the next several chapters we will follow this historical development by studying arithmetic in these and similar rings. √ To see that there are some serious issues to be addressed notice that in Z[ −5] the number 6 factorizes as a product of irreducibles in two different ways, namely √ √ 6 = 2.3 = (1 + −5)(1 − −5). 1 It isn’t hard to show these factors are irreducible but we postpone√ that for now . The key point for the moment is to note that this implies that Z[ −5] is not a unique factorization domain. This is in stark contrast to the integers. Since our teenage years we have taken for granted the fact that every integer can be written as a product of primes, which in Z are the same things as irreducibles, in a unique way. To emphasize the fact that there are questions to be understood, let us mention that Z[i] is a UFD. Even so, there is the question which primes in Z remain prime in Z[i]? This is a question with a long history: Fermat proved in ??? that a prime p in Z remains prime in Z[i] if and only if it is ≡ 3(mod 4).√ It is then natural to ask for each integer d, which primes in Z remain prime in Z[ d]? These and closely related questions lie behind much of the material we cover in the next 30 or so pages.
    [Show full text]
  • Music and Science from Leonardo to Galileo International Conference 13-15 November 2020 Organized by Centro Studi Opera Omnia Luigi Boccherini, Lucca
    MUSIC AND SCIENCE FROM LEONARDO TO GALILEO International Conference 13-15 November 2020 Organized by Centro Studi Opera Omnia Luigi Boccherini, Lucca Keynote Speakers: VICTOR COELHO (Boston University) RUDOLF RASCH (Utrecht University) The present conference has been made possibile with the friendly support of the CENTRO STUDI OPERA OMNIA LUIGI BOCCHERINI www.luigiboccherini.org INTERNATIONAL CONFERENCE MUSIC AND SCIENCE FROM LEONARDO TO GALILEO Organized by Centro Studi Opera Omnia Luigi Boccherini, Lucca Virtual conference 13-15 November 2020 Programme Committee: VICTOR COELHO (Boston University) ROBERTO ILLIANO (Centro Studi Opera Omnia Luigi Boccherini) FULVIA MORABITO (Centro Studi Opera Omnia Luigi Boccherini) RUDOLF RASCH (Utrecht University) MASSIMILIANO SALA (Centro Studi Opera Omnia Luigi Boccherini) ef Keynote Speakers: VICTOR COELHO (Boston University) RUDOLF RASCH (Utrecht University) FRIDAY 13 NOVEMBER 14.45-15.00 Opening • FULVIA MORABITO (Centro Studi Opera Omnia Luigi Boccherini) 15.00-16.00 Keynote Speaker 1: • VICTOR COELHO (Boston University), In the Name of the Father: Vincenzo Galilei as Historian and Critic ef 16.15-18.15 The Galileo Family (Chair: Victor Coelho, Boston University) • ADAM FIX (University of Minnesota), «Esperienza», Teacher of All Things: Vincenzo Galilei’s Music as Artisanal Epistemology • ROBERTA VIDIC (Hochschule für Musik und Theater Hamburg), Galilei and the ‘Radicalization’ of the Italian and German Music Theory • DANIEL MARTÍN SÁEZ (Universidad Autónoma de Madrid), The Galileo Affair through
    [Show full text]