“To Be a Good Mathematician, You Need Inner Voice” ”Огонёкъ” Met with Yakov Sinai, One of the World’S Most Renowned Mathematicians
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Tarjan Transcript Final with Timestamps
A.M. Turing Award Oral History Interview with Robert (Bob) Endre Tarjan by Roy Levin San Mateo, California July 12, 2017 Levin: My name is Roy Levin. Today is July 12th, 2017, and I’m in San Mateo, California at the home of Robert Tarjan, where I’ll be interviewing him for the ACM Turing Award Winners project. Good afternoon, Bob, and thanks for spending the time to talk to me today. Tarjan: You’re welcome. Levin: I’d like to start by talking about your early technical interests and where they came from. When do you first recall being interested in what we might call technical things? Tarjan: Well, the first thing I would say in that direction is my mom took me to the public library in Pomona, where I grew up, which opened up a huge world to me. I started reading science fiction books and stories. Originally, I wanted to be the first person on Mars, that was what I was thinking, and I got interested in astronomy, started reading a lot of science stuff. I got to junior high school and I had an amazing math teacher. His name was Mr. Wall. I had him two years, in the eighth and ninth grade. He was teaching the New Math to us before there was such a thing as “New Math.” He taught us Peano’s axioms and things like that. It was a wonderful thing for a kid like me who was really excited about science and mathematics and so on. The other thing that happened was I discovered Scientific American in the public library and started reading Martin Gardner’s columns on mathematical games and was completely fascinated. -
Information and Announcements Mathematics Prizes Awarded At
Information and Announcements Mathematics Prizes Awarded at ICM 2014 The International Congress of Mathematicians (ICM) is held once in four years under the auspices of the International Mathematical Union (IMU). The ICM is the largest, and the most prestigious, meeting of the mathematics community. During the ICM, the Fields Medal, the Nevanlinna Prize, the Gauss Prize, the Chern Medal and the Leelavati Prize are awarded. The Fields Medals are awarded to mathematicians under the age of 40 to recognize existing outstanding mathematical work and for the promise of future achievement. A maximum of four Fields Medals are awarded during an ICM. The Nevanlinna Prize is awarded for outstanding contributions to mathematical aspects of information sciences; this awardee is also under the age of 40. The Gauss Prize is given for mathematical research which has made a big impact outside mathematics – in industry or technology, etc. The Chern Medal is awarded to a person whose mathematical accomplishments deserve the highest level of recognition from the mathematical community. The Leelavati Prize is sponsored by Infosys and is a recognition of an individual’s extraordinary achievements in popularizing among the public at large, mathematics, as an intellectual pursuit which plays a crucial role in everyday life. The 27th ICM was held in Seoul, South Korea during August 13–21, 2014. Fields Medals The following four mathematicians were awarded the Fields Medal in 2014. 1. Artur Avila, “for his profound contributions to dynamical systems theory, which have changed the face of the field, using the powerful idea of renormalization as a unifying principle”. Work of Artur Avila (born 29th June 1979): Artur Avila’s outstanding work on dynamical systems, and analysis has made him a leader in the field. -
Excerpts from Kolmogorov's Diary
Asia Pacific Mathematics Newsletter Excerpts from Kolmogorov’s Diary Translated by Fedor Duzhin Introduction At the age of 40, Andrey Nikolaevich Kolmogorov (1903–1987) began a diary. He wrote on the title page: “Dedicated to myself when I turn 80 with the wish of retaining enough sense by then, at least to be able to understand the notes of this 40-year-old self and to judge them sympathetically but strictly”. The notes from 1943–1945 were published in Russian in 2003 on the 100th anniversary of the birth of Kolmogorov as part of the opus Kolmogorov — a three-volume collection of articles about him. The following are translations of a few selected records from the Kolmogorov’s diary (Volume 3, pages 27, 28, 36, 95). Sunday, 1 August 1943. New Moon 6:30 am. It is a little misty and yet a sunny morning. Pusya1 and Oleg2 have gone swimming while I stay home being not very well (though my condition is improving). Anya3 has to work today, so she will not come. I’m feeling annoyed and ill at ease because of that (for the second time our Sunday “readings” will be conducted without Anya). Why begin this notebook now? There are two reasonable explanations: 1) I have long been attracted to the idea of a diary as a disciplining force. To write down what has been done and what changes are needed in one’s life and to control their implementation is by no means a new idea, but it’s equally relevant whether one is 16 or 40 years old. -
Randomness and Computation
Randomness and Computation Rod Downey School of Mathematics and Statistics, Victoria University, PO Box 600, Wellington, New Zealand [email protected] Abstract This article examines work seeking to understand randomness using com- putational tools. The focus here will be how these studies interact with classical mathematics, and progress in the recent decade. A few representa- tive and easier proofs are given, but mainly we will refer to the literature. The article could be seen as a companion to, as well as focusing on develop- ments since, the paper “Calibrating Randomness” from 2006 which focused more on how randomness calibrations correlated to computational ones. 1 Introduction The great Russian mathematician Andrey Kolmogorov appears several times in this paper, First, around 1930, Kolmogorov and others founded the theory of probability, basing it on measure theory. Kolmogorov’s foundation does not seek to give any meaning to the notion of an individual object, such as a single real number or binary string, being random, but rather studies the expected values of random variables. As we learn at school, all strings of length n have the same probability of 2−n for a fair coin. A set consisting of a single real has probability zero. Thus there is no meaning we can ascribe to randomness of a single object. Yet we have a persistent intuition that certain strings of coin tosses are less random than others. The goal of the theory of algorithmic randomness is to give meaning to randomness content for individual objects. Quite aside from the intrinsic mathematical interest, the utility of this theory is that using such objects instead distributions might be significantly simpler and perhaps giving alternative insight into what randomness might mean in mathematics, and perhaps in nature. -
CURRICULUM VITAE November 2007 Hugo J
CURRICULUM VITAE November 2007 Hugo J. Woerdeman Professor and Department Head Office address: Home address: Department of Mathematics 362 Merion Road Drexel University Merion, PA 19066 Philadelphia, PA 19104 Phone: (610) 664-2344 Phone: (215) 895-2668 Fax: (215) 895-1582 E-mail: [email protected] Academic employment: 2005– Department of Mathematics, Drexel University Professor and Department Head (January 2005 – Present) 1989–2004 Department of Mathematics, College of William and Mary, Williamsburg, VA. Margaret L. Hamilton Professor of Mathematics (August 2003 – December 2004) Professor (July 2001 – December 2004) Associate Professor (September 1995 – July 2001) Assistant Professor (August 1989 – August 1995; on leave: ’89/90) 2002-03 Department of Mathematics, K. U. Leuven, Belgium, Visiting Professor Post-doctorate: 1989– 1990 University of California San Diego, Advisor: J. W. Helton. Education: Ph. D. degree in mathematics from Vrije Universiteit, Amsterdam, 1989. Thesis: ”Matrix and Operator Extensions”. Advisor: M. A. Kaashoek. Co-advisor: I. Gohberg. Doctoraal (equivalent of M. Sc.), Vrije Universiteit, Amsterdam, The Netherlands, 1985. Thesis: ”Resultant Operators and the Bezout Equation for Analytic Matrix Functions”. Advisor: L. Lerer Current Research Interests: Modern Analysis: Operator Theory, Matrix Analysis, Optimization, Signal and Image Processing, Control Theory, Quantum Information. Editorship: Associate Editor of SIAM Journal of Matrix Analysis and Applications. Guest Editor for a Special Issue of Linear Algebra and -
Your Project Title
Curriculum vitae Alfonso Sorrentino Curriculum Vitae • Personal Information Full Name: Alfonso Sorrentino. Citizenship: Italian. Researcher unique identifier (ORCID): 0000-0002-5680-2999. Contact Information: Address: Dipartimento di Matematica, Universit`adegli Studi di Roma \Tor Vergata" Via della Ricerca Scientifica 1, 00133 Rome (Italy). Phone: (+39) 06 72594663 Email: [email protected] Website: http://www.mat.uniroma2.it/∼sorrenti • Research Interests Hamiltonian and Lagrangian systems: Aubry-Mather-Ma~n´etheory, KAM theory, weak KAM theory, Integrable systems, geodesic flows, Stability and Instability. Twist maps and symplectic maps: low-dimensional (topological) dynamics, Aubry-Mather theory. Billiards: dynamics, integrability, spectral properties, rigidity phenomena. Dissipative systems: conformally symplectic Aubry-Mather theory. Hamilton-Jacobi equation: Homogenization, Symplectic Homogenization, Hamilton-Jacobi on net- works and ramified spaces. Symplectic and contact geometry/topology: general theory, Hofer and Viterbo geometries, applica- tions to dynamics. • Education 2004 - 2008: Ph.D. in Mathematics, Princeton University (USA). Thesis Title: On the structure of action-minimizing sets for Lagrangian systems. Advisor: Prof. John N. Mather. Degree Committee: John N. Mather (President), Elon Lindenstrauss,Yakov Sinai and Bo0az Klartag. 2003 - 2004: M.A. in Mathematics, Princeton University (USA). Exam Committee: John Mather (President), Alice Chang and J´anosKoll´ar. 1998 - 2003: Laurea degree in Mathematics, Universit`adegli Studi \Roma Tre". Thesis Title: On smooth quasi-periodic solutions of Hamiltonian Systems. Supervisor: Prof. Luigi Chierchia. Evaluation: 110/110 cum laude. • Academic Positions 2014 - present: Associate Professor in Mathematical Analysis (01/A3, MAT/05) (tenured position) at Dipartimento di Matematica, Universit`adegli Studi di Roma \Tor Vergata", Rome (Italy). 2012 - 2014: Researcher in Mathematical Analysis MAT/05 (tenured position) at Dipartimento di Matematica e Fisica, Universit`adegli Studi \Roma Tre", Rome (Italy). -
Ergodic Theory Plays a Key Role in Multiple Fields Steven Ashley Science Writer
CORE CONCEPTS Core Concept: Ergodic theory plays a key role in multiple fields Steven Ashley Science Writer Statistical mechanics is a powerful set of professor Tom Ward, reached a key milestone mathematical tools that uses probability the- in the early 1930s when American mathema- ory to bridge the enormous gap between the tician George D. Birkhoff and Austrian-Hun- unknowable behaviors of individual atoms garian (and later, American) mathematician and molecules and those of large aggregate sys- and physicist John von Neumann separately tems of them—a volume of gas, for example. reconsidered and reformulated Boltzmann’ser- Fundamental to statistical mechanics is godic hypothesis, leading to the pointwise and ergodic theory, which offers a mathematical mean ergodic theories, respectively (see ref. 1). means to study the long-term average behavior These results consider a dynamical sys- of complex systems, such as the behavior of tem—whetheranidealgasorothercomplex molecules in a gas or the interactions of vi- systems—in which some transformation func- brating atoms in a crystal. The landmark con- tion maps the phase state of the system into cepts and methods of ergodic theory continue its state one unit of time later. “Given a mea- to play an important role in statistical mechan- sure-preserving system, a probability space ics, physics, mathematics, and other fields. that is acted on by the transformation in Ergodicity was first introduced by the a way that models physical conservation laws, Austrian physicist Ludwig Boltzmann laid Austrian physicist Ludwig Boltzmann in the what properties might it have?” asks Ward, 1870s, following on the originator of statisti- who is managing editor of the journal Ergodic the foundation for modern-day ergodic the- cal mechanics, physicist James Clark Max- Theory and Dynamical Systems.Themeasure ory. -
Spring 2014 Fine Letters
Spring 2014 Issue 3 Department of Mathematics Department of Mathematics Princeton University Fine Hall, Washington Rd. Princeton, NJ 08544 Department Chair’s letter The department is continuing its period of Assistant to the Chair and to the Depart- transition and renewal. Although long- ment Manager, and Will Crow as Faculty The Wolf time faculty members John Conway and Assistant. The uniform opinion of the Ed Nelson became emeriti last July, we faculty and staff is that we made great Prize for look forward to many years of Ed being choices. Peter amongst us and for John continuing to hold Among major faculty honors Alice Chang Sarnak court in his “office” in the nook across from became a member of the Academia Sinica, Professor Peter Sarnak will be awarded this the common room. We are extremely Elliott Lieb became a Foreign Member of year’s Wolf Prize in Mathematics. delighted that Fernando Coda Marques and the Royal Society, John Mather won the The prize is awarded annually by the Wolf Assaf Naor (last Fall’s Minerva Lecturer) Brouwer Prize, Sophie Morel won the in- Foundation in the fields of agriculture, will be joining us as full professors in augural AWM-Microsoft Research prize in chemistry, mathematics, medicine, physics, Alumni , faculty, students, friends, connect with us, write to us at September. Algebra and Number Theory, Peter Sarnak and the arts. The award will be presented Our finishing graduate students did very won the Wolf Prize, and Yasha Sinai the by Israeli President Shimon Peres on June [email protected] well on the job market with four win- Abel Prize. -
Sinai Awarded 2014 Abel Prize
Sinai Awarded 2014 Abel Prize The Norwegian Academy of Sci- Sinai’s first remarkable contribution, inspired ence and Letters has awarded by Kolmogorov, was to develop an invariant of the Abel Prize for 2014 to dynamical systems. This invariant has become Yakov Sinai of Princeton Uni- known as the Kolmogorov-Sinai entropy, and it versity and the Landau Insti- has become a central notion for studying the com- tute for Theoretical Physics plexity of a system through a measure-theoretical of the Russian Academy of description of its trajectories. It has led to very Sciences “for his fundamen- important advances in the classification of dynami- tal contributions to dynamical cal systems. systems, ergodic theory, and Sinai has been at the forefront of ergodic theory. mathematical physics.” The He proved the first ergodicity theorems for scat- Photo courtesy of Princeton University Mathematics Department. Abel Prize recognizes contribu- tering billiards in the style of Boltzmann, work tions of extraordinary depth he continued with Bunimovich and Chernov. He Yakov Sinai and influence in the mathemat- constructed Markov partitions for systems defined ical sciences and has been awarded annually since by iterations of Anosov diffeomorphisms, which 2003. The prize carries a cash award of approxi- led to a series of outstanding works showing the mately US$1 million. Sinai received the Abel Prize power of symbolic dynamics to describe various at a ceremony in Oslo, Norway, on May 20, 2014. classes of mixing systems. With Ruelle and Bowen, Sinai discovered the Citation notion of SRB measures: a rather general and Ever since the time of Newton, differential equa- distinguished invariant measure for dissipative tions have been used by mathematicians, scientists, systems with chaotic behavior. -
Fundamental Theorems in Mathematics
SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 243 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were writ- ten down. Since [556] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context" we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The num- ber of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable" theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [193, 189, 29, 235, 254, 619, 412, 138], for history [217, 625, 376, 73, 46, 208, 379, 365, 690, 113, 618, 79, 259, 341], for popular, beautiful or elegant things [12, 529, 201, 182, 17, 672, 673, 44, 204, 190, 245, 446, 616, 303, 201, 2, 127, 146, 128, 502, 261, 172]. For comprehensive overviews in large parts of math- ematics, [74, 165, 166, 51, 593] or predictions on developments [47]. For reflections about mathematics in general [145, 455, 45, 306, 439, 99, 561]. Encyclopedic source examples are [188, 705, 670, 102, 192, 152, 221, 191, 111, 635]. -
A Modern History of Probability Theory
A Modern History of Probability Theory Kevin H. Knuth Depts. of Physics and Informatics University at Albany (SUNY) Albany NY USA 4/29/2016 Knuth - Bayes Forum 1 A Modern History of Probability Theory Kevin H. Knuth Depts. of Physics and Informatics University at Albany (SUNY) Albany NY USA 4/29/2016 Knuth - Bayes Forum 2 A Long History The History of Probability Theory, Anthony J.M. Garrett MaxEnt 1997, pp. 223-238. Hájek, Alan, "Interpretations of Probability", The Stanford Encyclopedia of Philosophy (Winter 2012 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/win2012/entries/probability-interpret/>. 4/29/2016 Knuth - Bayes Forum 3 … la théorie des probabilités n'est, au fond, que le bon sens réduit au calcul … … the theory of probabilities is basically just common sense reduced to calculation … Pierre Simon de Laplace Théorie Analytique des Probabilités 4/29/2016 Knuth - Bayes Forum 4 Taken from Harold Jeffreys “Theory of Probability” 4/29/2016 Knuth - Bayes Forum 5 The terms certain and probable describe the various degrees of rational belief about a proposition which different amounts of knowledge authorise us to entertain. All propositions are true or false, but the knowledge we have of them depends on our circumstances; and while it is often convenient to speak of propositions as certain or probable, this expresses strictly a relationship in which they stand to a corpus of knowledge, actual or hypothetical, and not a characteristic of the propositions in themselves. A proposition is capable at the same time of varying degrees of this relationship, depending upon the knowledge to which it is related, so that it is without significance to call a John Maynard Keynes proposition probable unless we specify the knowledge to which we are relating it. -
Public Recognition and Media Coverage of Mathematical Achievements
Journal of Humanistic Mathematics Volume 9 | Issue 2 July 2019 Public Recognition and Media Coverage of Mathematical Achievements Juan Matías Sepulcre University of Alicante Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the Arts and Humanities Commons, and the Mathematics Commons Recommended Citation Sepulcre, J. "Public Recognition and Media Coverage of Mathematical Achievements," Journal of Humanistic Mathematics, Volume 9 Issue 2 (July 2019), pages 93-129. DOI: 10.5642/ jhummath.201902.08 . Available at: https://scholarship.claremont.edu/jhm/vol9/iss2/8 ©2019 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. Public Recognition and Media Coverage of Mathematical Achievements Juan Matías Sepulcre Department of Mathematics, University of Alicante, Alicante, SPAIN [email protected] Synopsis This report aims to convince readers that there are clear indications that society is increasingly taking a greater interest in science and particularly in mathemat- ics, and thus society in general has come to recognise, through different awards, privileges, and distinctions, the work of many mathematicians.