The BBC Series the Story of Math by Marcus Du Sautoy
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You and AI Conversations About AI Technologies and Their Implications for Society
You and AI Conversations about AI technologies and their implications for society SUPPORTED BY CONVERSATIONS ABOUT AI TECHNOLOGIES AND THEIR IMPLICATIONS FOR SOCIETY DeepMind1 2 CONVERSATIONS ABOUT AI TECHNOLOGIES AND THEIR IMPLICATIONS FOR SOCIETY You and AI Conversations about AI technologies and their implications for society Artificial Intelligence (AI) is the science of making computer systems smart, and an umbrella term for a range of technologies that carry out functions that typically require intelligence in humans. AI technologies already support many everyday products and services, and the power and reach of these technologies are advancing at pace. The Royal Society is working to support an environment of careful stewardship of AI technologies, so that their benefits can be brought into being safely and rapidly, and shared across society. In support of this aim, the Society’s You and AI series brought together leading AI researchers to contribute to a public conversation about advances in AI and their implications for society. CONVERSATIONS ABOUT AI TECHNOLOGIES AND THEIR IMPLICATIONS FOR SOCIETY 3 What AI can, and cannot, do The last decade has seen exciting developments in AI – and AI researchers are tackling some fundamental challenges to develop it further AI research seeks to understand what happens or inputs do not follow a standard intelligence is, and then recreate this through pattern, these systems cannot adapt their computer systems that can automatically rules or adjust their approach. perform tasks that require some level of reasoning or intelligence in humans. In the last decade, new methods that use learning algorithms have helped create In the past, AI research has concentrated computer systems that are more flexible on creating detailed rules for how to carry and adaptive, and Demis Hassabis FRS out a task and then developing computer (co-founder, DeepMind) has been at the systems that could carry out these rules; forefront of many of these developments. -
2011 Mathematics Newsletter
AUTUMN 2011 NEWSLETTER OF THE DEPARTMENT OF MATHEMATICS AT THE UNIVERSITY OF WASHINGTON Mathematics NEWS 1 DEPARTMENT OF MATHEMATICS NEWS MESSAGE FROM THE CHAIR It has been another exciting year The positive developments reported in this newsletter stand for our department. The work of in contrast to a backdrop of (global) financial and politi- the faculty has been recognized cal uncertainty. In the fourth year of the financial crisis, in a number of ways, includ- the end is not yet in sight. Repeated cuts in state support, ing the AMS Bôcher Prize and coupled with tuition increases, spell a fundamental shift the SIAM Kleinman Prize pre- in the funding of state universities. At the same time, the sented to Gunther Uhlmann, need to re-tool to pursue new career paths in a changing and the NSF CAREER award to economy, the return of soldiers from overseas deployments, Max Lieblich. As you will see on and the coming of age of the baby-boom echo generation page 15, the numbers of majors bring increasing numbers of students to our campus and to in the Mathematics program and the joint ACMS (Applied our department. and Computational Mathematical Sciences) program have Until the situation settles, new resources are generally made continued to rise, as have the numbers of degrees awarded. available to us in the form of temporary allocations instead In addition, these programs attract outstanding students of tenure-track faculty positions, which would require long- who continue to make us proud. For example, Math majors term financial commitments. This policy is understandable. -
What's Love Got to Do With
Aaron Brown What’s Love Got to Do With It? Edward Frenkel is writing a protracted Dear John letter to popular misconceptions about math and mathema- ticians… he great popular science and science fiction author Isaac Asimov told a story about a university committee meeting in which there was much laughter and joking about a student named “Milton” flunkingT English literature, but no one noticed when a student named “Gauss” was failing in mathematics. I wish I could find the reference to this, but I read it long ago in childhood, and some Internet searching proved fruitless. I may have the details wrong – especially the name of the student date are smaller than Asimov’s. They also have cians, and writers. With these people, screenwriters flunking English literature – but I remember the a different slant. Asimov tried to show every- often assume they must be tortured to be authentic. point. Asimov complained that a scientist would be one how mathematics and science could be fun. But there are plenty of exceptions – movies built thought a Philistine if he expressed no interest in Frenkel instead celebrates the passion and inten- around well-rounded, friendly, artistic genius- music or philosophy, but that an artist could boast sity of mathematics at the highest level. He has es. And, even when artists are a bit crazy, it is an about not knowing enough arithmetic to balance done this through lectures which are a sensation excess of passion, “agony and ecstasy,” not some his checkbook. on YouTube, an erotic film, and, most recently, a incomprehensible twisted obsession from another Edward Frenkel is one of the great mathema- book, Love and Math: The Heart of Hidden Reality. -
Popularising Mathematics
Popularising Mathematics Philipp Legner August 2013 Abstract Mathematics has countless applications in science, engineering and technology, yet school mathematics is one of the most unpopular subjects, perceived as difficult, boring and not useful in life. ‘Popularisation’ projects can help bridge this gap, by showing how exciting, applicable and beautiful mathematics is. Some popularisation projects focus on telling the wider public about mathematics, including its history, philosophy and applications; other projects encourage you to actively do mathematics and discover surprising relationships and beautiful results using mathematical reasoning and thinking. In this report I will develop a framework to classify and evaluate popularisation, and analyse a wide range of existing projects – ranging from competitions to websites, movies, exhibitions, books and workshops. I also reflect upon my personal experiences in designing popularisation activities. I would like to thank Professor Dave Pratt for his advise while writing this report. Table of Contents Introduction 1 Part 1: A Framework for Mathematics Popularisation The Value of Mathematics ........................................................................... 2 Defining Mathematics Popularisation ...................................................... 4 Designing Mathematics Popularisation ................................................... 8 Evaluating Popularisation Projects ............................................................ 11 Part 2: Case Studies of Popularisation Projects -
A Brief History of Numbers by Leo Corry
Reviews Osmo Pekonen, Editor A Brief History of Numbers by Leo Corry OXFORD: OXFORD UNIVERSITY PRESS, 2015, 336 PP., £24.99, ISBN: 9780198702597 REVIEWED BY JESPER LU¨TZEN he concept of number has an interesting and intriguing history and this is a highly recommendable TT book about it. When were irrational numbers (or negative numbers) introduced into mathematics? Such questions seem precise and simple, but they cannot be answered with a simple year. In fact, the years 2000 BC and AD 1872 and many years Feel like writing a review for The Mathematical in between could be a valid answer to the question about Intelligencer? Contact the column editor if you wish to irrational numbers, and many years between 1 and 1870 could be defended as an answer to the question about the submit an unsolicited review, or if you would welcome introduction of negative numbers. This is not just because modern mathematicians may consider pre-1870 notions of being assigned a book to review. numbers as nonrigorous but also because the historical actors were not in agreement about the nature and extent of the concept of number. Therefore the answer to the questions raised previously must necessarily be a long and contorted story. Many treatises and articles on the history of mathematics tell aspects of this story, and Corry’s book may be considered a synthesis of these more specialized works. Still, Corry also adds his own original viewpoints and results to the standard history. The last chapters of the book dealing with the modern foundations of the number system from the end of the 19th and the beginning of the 20th cen- turies obviously draw on Corry’s own research on the establishment of modern structural thinking that has con- tributed seminally to our understanding of the development of mathematics in this period. -
Career Pathway Tracker 35 Years of Supporting Early Career Research Fellows Contents
Career pathway tracker 35 years of supporting early career research fellows Contents President’s foreword 4 Introduction 6 Scientific achievements 8 Career achievements 14 Leadership 20 Commercialisation 24 Public engagement 28 Policy contribution 32 How have the fellowships supported our alumni? 36 Who have we supported? 40 Where are they now? 44 Research Fellowship to Fellow 48 Cover image: Graphene © Vertigo3d CAREER PATHWAY TRACKER 3 President’s foreword The Royal Society exists to encourage the development and use of Very strong themes emerge from the survey About this report science for the benefit of humanity. One of the main ways we do that about why alumni felt they benefited. The freedom they had to pursue the research they This report is based on the first is by investing in outstanding scientists, people who are pushing the wanted to do because of the independence Career Pathway Tracker of the alumni of University Research Fellowships boundaries of our understanding of ourselves and the world around the schemes afford is foremost in the minds of respondents. The stability of funding and and Dorothy Hodgkin Fellowships. This us and applying that understanding to improve lives. flexibility are also highly valued. study was commissioned by the Royal Society in 2017 and delivered by the Above Thirty-five years ago, the Royal Society The vast majority of alumni who responded The Royal Society has long believed in the Careers Research & Advisory Centre Venki Ramakrishnan, (CRAC), supported by the Institute for President of the introduced our University Research Fellowships to the survey – 95% of University Research importance of identifying and nurturing the Royal Society. -
Mathematics People
Mathematics People Ooguri Receives Chunichi Turaev and Virelizier Awarded Cultural Award Balaguer Prize Hirosi Ooguri of the California Vladimir Turaev of Indiana Uni- Institute of Technology has been versity and Alexis Virelizier of honored with the 2016 Chunichi Université Lille 1 have been awarded Cultural Award. The award carries the 2016 Ferran Sunyer i Balaguer a cash prize of 2 million yen (ap- Prize for their monograph Monoidal proximately US$20,000). Categories and Topological Field According to the prize citation, Theory. The monograph introduces Ooguri was honored for the “devel- monoidal categories and Penrose’s opment of innovative methods of graphical calculus; gives an alge- modern mathematics in high energy braic description of the center of Hirosi Ooguri theory.” His work involves “creating monoidal categories based on the Vladimir Turaev new theoretical tools in quantum theory of Hopf monads as devel- field theory and superstring theory.” He is especially oped by Virelizier and coauthors; known for his work on topological string theory, “which explains topological quantum field has had broad applications ranging from black hole phys- theories, including fundamental ics to algebraic geometry and knot theory in mathematics.” earlier work of Reshetihkin-Turaev Ooguri is a past recipient of the AMS Eisenbud Prize and Turaev-Viro; and shows how to (2008), a Humboldt Research Award (2008), the Nishina present ribbon graphs by diagrams Memorial Prize (2009), a Simons Investigator Award on skeletons of 3-manifolds and (2012), and the Kodansha Prize for Science Books of define graph topological quantum Japan (2014) for his popular science book, Introduction to field theories by means of state Superstring Theory. -
A Wealth of Numbers Reviewed by Andy R
Book Review A Wealth of Numbers Reviewed by Andy R. Magid to do with the quality, or even correctness, of their A Wealth of Numbers mathematical content. For example, consider the Benjamin Wardhaugh Amazon Best Sellers rankings of the following: Princeton University Press, April 2012 Constance Reid’s excellent From Zero to Infinity is Hardcover, 388 pages, US$45.00 number 907,624, only slightly better than Marilyn ISBN-13: 978-0691147758 vos Savant’s execrable The World’s Most Famous Math Problem, number 966,319, while Lancelot When it comes to mathematical exposition, we Hogben’s venerable (first published in 1937) and mathematicians are diligent consumers. We buy valuable Mathematics for the Million substantially non-textbook monographs, read Notices articles, outranks both at 153,398. For further comparison, and attend departmental colloquia, generally inde- John Allen Paulos’s 1980s classic Innumeracy ranks pendent of whether the exposition is high quality 16,221 (all ranks observed 16 November 2012). This (Notices), mixed (monographs), or low (most collo- highly unrepresentative sample of mathematics quia). Perhaps we are motivated by the hope that books for the general reader currently available ideas and methods from other fields will inspire consists of books this reviewer happened to read, our work in our own specialty, or perhaps we either as a general reader himself before becoming feel the duty to be informed about the world of a mathematician or, for the later ones, out of research mathematics in general. In any event, we curiosity when the books became newsworthy devote time and effort to consuming mathematical (Paulos) or notorious (vos Savant). -
Reference and Book List
Reference and Book List The Reference section of the Notices Upcoming Deadlines and for AMS scholarships. See http:// is intended to provide the reader with October 10, 2003: Applications for www.mccme.ru/mathinmoscow or frequently sought information in AWM Collaborative Research Grants contact Math in Moscow, P.O. Box 524, an easily accessible manner. New for Women. See the AWM website, Wynnewood, PA 19096; fax: +7095- information is printed as it becomes http://www.awm-math.org/news/ 291-65-01; email: [email protected]. For available and is referenced after the collab.html. information about and application first printing. As soon as information October 15, 2003: Proposals for NSA forms for the AMS scholarships, see is updated or otherwise changed, it Grant and Sabbatical Programs. See http://www.ams.org/careers-edu/ will be noted in this section. http://www.nsa.gov/programs/ mimoscow.html or contact Math in msp/grants.html. Moscow Program, Membership and Contacting the Notices October 15, 2003: Applications for Programs Department, American The preferred method for contacting spring semester of Math in Moscow Mathematical Society, 201 Charles the Notices is electronic mail. The editor is the person to whom to send Where to Find It articles and letters for consideration. A brief index to information that appears in this and previous issues. Articles include feature articles, AMS Bylaws—November 2003 p. 1283 memorial articles, communications, AMS Email Addresses—November 2003, p. 1266 opinion pieces, and book reviews. The AMS Ethical Guidelines—June/July 2002, p. 706 editor is also the person to whom to AMS Officers 2002 and 2003 (Council, Executive Committee, send news of unusual interest about Publications Committees, Board of Trustees)—May 2003, p. -
Marcus Du Sautoy Cutting an Impressive Figure
MARCUS DU SAUTOY CUTTING AN IMPRESSIVE FIGURE Mathematician Marcus du Sautoy is Science, for The Times. His books include The Music using his passion for the subject to of the Primes and Finding Moonshine. inspire a new generation of genius. And his own inspiration? “One of my heroes is Sir Christopher Zeeman. He’s a first rate mathematician He is an EPSRC senior media fellow and was but also a great communicator. I went to see the appointed University of Oxford’s Simonyi Professor Christmas Lecture he gave when I was 13 years for the Public Understanding of Science in 2008 – old and I came away saying ‘I want to be him when succeeding Professor Richard Dawkins. I grow up’.” “Maths is a way of understanding the way the world Thirty years later, du Sautoy is at the top of his field. works,” says du Sautoy. “It’s about seeing where you His career accolades range from the Berwick Prize are coming from and, more excitingly, predicting of the London Mathematical Society to being listed what happens next. It is the language of nature and as one of Esquire Magazine’s 100 most influential it is a way of unlocking the secrets of the universe.” men under 40. He recently wrote and presented BBC4’s The Story “Without EPSRC’s support there is no way I could of Maths, and has presented a number of Horizon have made the same impact,” he says. “The senior programmes. He is a regular contributor to media fellows scheme is so inspired that I am newspapers, including a weekly column, Sexy pushing for more positions to be created.” “IT IS ESSENTIAL THAT SCIENCE HAS AMBASSADORS TO COMMUNICATE THE EXCITEMENT AND IMPORTANCE OF SCIENCE IN SOCIETY.”. -
Beautiful Geometry by Eli Maor and Eugen Jost
blogs.lse.ac.uk http://blogs.lse.ac.uk/lsereviewofbooks/2014/03/03/book-review-beautiful-geometry-by-eli-maor-and-eugen-jost/ Book Review: Beautiful Geometry by Eli Maor and Eugen Jost How do art and mathematics cross over? Beautiful Geometry is an attractively designed coffee table book that has 51 short chapters, each consisting of an essay by the mathematical historian Eli Maor on a single topic, together with a colour plate by the artist Eugen Jost.The book achieves its aim to demonstrate that there is visual beauty in mathematics, finds Konrad Swanepoel. It is heartily recommended to mathematics students who want to broaden their horizons and to teachers of mathematics at school level. Beautiful Geometry. Eli Maor and Eugen Jost. Princeton University Press. January 2014. Find this book: Geometry has a history that goes back at least 3000 years, and under the ancient Greeks achieved a scientific level which even today survives all but the most exacting logical scrutiny. Having always been synonymous with Mathematics, in the 20th century Geometry has simultaneously specialised into a myriad subfields (algebraic geometry, differential geometry, discrete geometry, convex geometry, etc.) while losing its all-encompassing grip on Mathematics. At universities we are eager to teach our students Calculus and Linear Algebra instead of a course on Classical Geometry, now deemed old- fashioned. This book reminds us of what we are missing. This attractively designed coffee table book has 51 short chapters, each consisting of an essay by the mathematical historian Eli Maor on a single topic, together with a colour plate (occasionally two) by the artist Eugen Jost. -
S0002-9904-1957-10132-3.Pdf
2 POPULAR MATHEMATICS TITLES PEIRCE, FOSTER Short Table of Integrals, 4th Edition Classic text which includes additional definite inte grals, further information on Bessel, and other transcen dental functions. Expanded numerical tables. TAYLOR Advanced Calculus Thorough treatment emphasizing concepts and basic principles of analysis—those properties of the real num ber system which support the theory of limits and con tinuity. HOME OFFICE: Boston GINN AND COMPANY SALES OFFICES: New York 11 Chicago 6 Atlanta 3 Dallas 1 Columbus 16 Palo Alto Toronto 7 Recent MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY 22. R. S. PALAIS, A global formulation of the Lie theory of trans formation groups, 1957, iv, 123 pp. $2.20 23. D. G. DICKSON, Expansions in series of solutions of linear difference-differential and infinite order differential equations with constant coefficients, 1957, 72 pp. 1.70 24. ISAAC NAMIOKA, Partially ordered linear topological spaces, 1957, 50 pp. 1.60 25. A. ERDÉLYI and C. A. SWANSON, Asymptotic forms of Whit- taker's confluent hypergeometric functions, 1957, 49 pp. 1.40 26. WALTER STRODT, Principal solution of ordinary differential equations in the complex domain, 1957, 107 pp. 2.00 25% discount to members AMERICAN MATHEMATICAL SOCIETY 190 Hope Street, Providence, Rhode Island License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use PhD MATHEMATICIANS Our Systems Analysis Department has openings for PhD Mathematicians who have a lasting interest in some fields of Mathematics such as Algebra, Geometry, Measure Theory, Topology, Differential Equations, Numerical Analysis, or Statistics. Association will be with others with similar educa tional background engaged in the study of challenging problems vital to the nation's welfare.