Oslo 2004: the Abel Prize Celebrations
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Karen Uhlenbeck Awarded the 2019 Abel Prize
RESEARCH NEWS Karen Uhlenbeck While she was in Urbana-Champagne (Uni- versity of Illinois), Karen Uhlenbeck worked Awarded the 2019 Abel with a postdoctoral fellow, Jonathan Sacks, Prize∗ on singularities of harmonic maps on 2D sur- faces. This was the beginning of a long journey in geometric analysis. In gauge the- Rukmini Dey ory, Uhlenbeck, in her remarkable ‘removable singularity theorem’, proved the existence of smooth local solutions to Yang–Mills equa- tions. The Fields medallist Simon Donaldson was very much influenced by her work. Sem- inal results of Donaldson and Uhlenbeck–Yau (amongst others) helped in establishing gauge theory on a firm mathematical footing. Uhlen- beck’s work with Terng on integrable systems is also very influential in the field. Karen Uhlenbeck is a professor emeritus of mathematics at the University of Texas at Austin, where she holds Sid W. Richardson Foundation Chair (since 1988). She is cur- Karen Uhlenbeck (Source: Wikimedia) rently a visiting associate at the Institute for Advanced Study, Princeton and a visiting se- nior research scholar at Princeton University. The 2019 Abel prize for lifetime achievements She has enthused many young women to take in mathematics was awarded for the first time up mathematics and runs a mentorship pro- to a woman mathematician, Professor Karen gram for women in mathematics at Princeton. Uhlenbeck. She is famous for her work in ge- Karen loves gardening and nature hikes. Hav- ometry, analysis and gauge theory. She has ing known her personally, I found she is one of proved very important (and hard) theorems in the most kind-hearted mathematicians I have analysis and applied them to geometry and ever known. -
Programme 2009 the Abel Prize Ceremony 19 May 2009 Procession Accompanied by the “Abel Fanfare” Music: Klaus Sandvik
Programme 2009 The Abel Prize Ceremony 19 May 2009 Procession accompanied by the “Abel Fanfare” Music: Klaus Sandvik. Performed by three musicians from the Staff Band of the Norwegian Defence Forces Their Majesties King Harald and Queen Sonja enter the hall Soroban Arve Henriksen (trumpet) (Music: Arve Henriksen) Opening by Øyvind Østerud President of the Norwegian Academy of Science and Letters Eg veit i himmerik ei borg Trio Mediæval, Arve Henriksen (Norwegian folk tune from Hallingdal, arr. Linn A. Fuglseth) The Abel Prize Award Ceremony Professor Kristian Seip Chairman of the Abel Committee The Committee’s citation His Majesty King Harald presents the Abel Prize to Mikhail Leonidovich Gromov Acceptance speech by Mikhail Leonidovich Gromov Closing remarks by Professor Øyvind Østerud President of the Norwegian Academy of Science and Letters Till, till Tove Trio Mediæval, Arve Henriksen, Birger Mistereggen (percussion) (Norwegian folk tune from Vestfold, arr. Tone Krohn) Their Majesties King Harald and Queen Sonja leave the hall Procession leaves the hall Other guests leave the hall when the procession has left to a skilled mathematics teacher in the upper secondary school is called after Abel’s own Professor Øyvind Østerud teacher, Bernt Michael Holmboe. There is every reason to remember Holmboe, who was President of the Norwegian Academy of Science and Letters Abel’s mathematics teacher at Christiania Cathedral School from when Abel was 16. Holmboe discovered Abel’s talent, inspired him, encouraged him, and took the young pupil considerably further than the curriculum demanded. He pointed him to the professional literature, helped Your Majesties, Excellencies, dear friends, him with overseas contacts and stipends and became a lifelong colleague and friend. -
The Wrangler3.2
Issue No. 3, Autumn 2004 Leicester The Maths Wrangler From the mathematicians at the University of Leicester http://www.math.le.ac.uk/ email: [email protected] WELCOME TO The Wrangler This is the third issue of our maths newsletter from the University of Leicester’s Department of Mathematics. You can pick it up on-line and all the back issues at our new web address http://www.math.le.ac.uk/WRANGLER. If you would like to be added to our mailing list or have suggestions, just drop us a line at [email protected], we’ll be flattered! What do we have here in this new issue? You may wonder what wallpaper and frying pans have to do with each other. We will tell you a fascinating story how they come up in new interdisciplinary research linking geometry and physics. We portrait our chancellor Sir Michael Atiyah, who recently has received the Abel prize, the maths equivalent of the Nobel prize. Sir Michael Atiyah will also open the new building of the MMC, which will be named after him, with a public maths lecture. Everyone is very welcome! More info at our new homepage http://www.math.le.ac.uk/ Contents Welcome to The Wrangler Wallpaper and Frying Pans - Linking Geometry and Physics K-Theory, Geometry and Physics - Sir Michael Atiyah gets Abel Prize The GooglePlexor The Mathematical Modelling Centre MMC The chancellor of the University of Leicester and world famous mathematician Sir Michael Atiyah (middle) receives the Abel Prize of the year 2004 together with colleague Isadore Singer (left) during the prize ceremony with King Harald of Norway. -
Robert P. Langlands Receives the Abel Prize
Robert P. Langlands receives the Abel Prize The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2018 to Robert P. Langlands of the Institute for Advanced Study, Princeton, USA “for his visionary program connecting representation theory to number theory.” Robert P. Langlands has been awarded the Abel Prize project in modern mathematics has as wide a scope, has for his work dating back to January 1967. He was then produced so many deep results, and has so many people a 30-year-old associate professor at Princeton, working working on it. Its depth and breadth have grown and during the Christmas break. He wrote a 17-page letter the Langlands program is now frequently described as a to the great French mathematician André Weil, aged 60, grand unified theory of mathematics. outlining some of his new mathematical insights. The President of the Norwegian Academy of Science and “If you are willing to read it as pure speculation I would Letters, Ole M. Sejersted, announced the winner of the appreciate that,” he wrote. “If not – I am sure you have a 2018 Abel Prize at the Academy in Oslo today, 20 March. waste basket handy.” Biography Fortunately, the letter did not end up in a waste basket. His letter introduced a theory that created a completely Robert P. Langlands was born in New Westminster, new way of thinking about mathematics: it suggested British Columbia, in 1936. He graduated from the deep links between two areas, number theory and University of British Columbia with an undergraduate harmonic analysis, which had previously been considered degree in 1957 and an MSc in 1958, and from Yale as unrelated. -
Karen Keskulla Uhlenbeck
2019 The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2019 to Karen Keskulla Uhlenbeck University of Texas at Austin “for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” Karen Keskulla Uhlenbeck is a founder of modern by earlier work of Morse, guarantees existence of Geometric Analysis. Her perspective has permeated minimisers of geometric functionals and is successful the field and led to some of the most dramatic in the case of 1-dimensional domains, such as advances in mathematics in the last 40 years. closed geodesics. Geometric analysis is a field of mathematics where Uhlenbeck realised that the condition of Palais— techniques of analysis and differential equations are Smale fails in the case of surfaces due to topological interwoven with the study of geometrical and reasons. The papers of Uhlenbeck, co-authored with topological problems. Specifically, one studies Sacks, on the energy functional for maps of surfaces objects such as curves, surfaces, connections and into a Riemannian manifold, have been extremely fields which are critical points of functionals influential and describe in detail what happens when representing geometric quantities such as energy the Palais-Smale condition is violated. A minimising and volume. For example, minimal surfaces are sequence of mappings converges outside a finite set critical points of the area and harmonic maps are of singular points and by using rescaling arguments, critical points of the Dirichlet energy. Uhlenbeck’s they describe the behaviour near the singularities major contributions include foundational results on as bubbles or instantons, which are the standard minimal surfaces and harmonic maps, Yang-Mills solutions of the minimising map from the 2-sphere to theory, and integrable systems. -
The History of the Abel Prize and the Honorary Abel Prize the History of the Abel Prize
The History of the Abel Prize and the Honorary Abel Prize The History of the Abel Prize Arild Stubhaug On the bicentennial of Niels Henrik Abel’s birth in 2002, the Norwegian Govern- ment decided to establish a memorial fund of NOK 200 million. The chief purpose of the fund was to lay the financial groundwork for an annual international prize of NOK 6 million to one or more mathematicians for outstanding scientific work. The prize was awarded for the first time in 2003. That is the history in brief of the Abel Prize as we know it today. Behind this government decision to commemorate and honor the country’s great mathematician, however, lies a more than hundred year old wish and a short and intense period of activity. Volumes of Abel’s collected works were published in 1839 and 1881. The first was edited by Bernt Michael Holmboe (Abel’s teacher), the second by Sophus Lie and Ludvig Sylow. Both editions were paid for with public funds and published to honor the famous scientist. The first time that there was a discussion in a broader context about honoring Niels Henrik Abel’s memory, was at the meeting of Scan- dinavian natural scientists in Norway’s capital in 1886. These meetings of natural scientists, which were held alternately in each of the Scandinavian capitals (with the exception of the very first meeting in 1839, which took place in Gothenburg, Swe- den), were the most important fora for Scandinavian natural scientists. The meeting in 1886 in Oslo (called Christiania at the time) was the 13th in the series. -
All About Abel Dayanara Serges Niels Henrik Abel (August 5, 1802-April 6,1829) Was a Norwegian Mathematician Known for Numerous Contributions to Mathematics
All About Abel Dayanara Serges Niels Henrik Abel (August 5, 1802-April 6,1829) was a Norwegian mathematician known for numerous contributions to mathematics. Abel was born in Finnoy, Norway, as the second child of a dirt poor family of eight. Abels father was a poor Lutheran minister who moved his family to the parish of Gjerstad, near the town of Risr in southeast Norway, soon after Niels Henrik was born. In 1815 Niels entered the cathedral school in Oslo, where his mathematical talent was recognized in 1817 by his math teacher, Bernt Michael Holmboe, who introduced him to the classics in mathematical literature and proposed original problems for him to solve. Abel studied the mathematical works of the 17th-century Englishman Sir Isaac Newton, the 18th-century German Leonhard Euler, and his contemporaries the Frenchman Joseph-Louis Lagrange and the German Carl Friedrich Gauss in preparation for his own research. At the age of 16, Abel gave a proof of the Binomial Theorem valid for all numbers not only Rationals, extending Euler's result. Abels father died in 1820, leaving the family in straitened circumstances, but Holmboe and other professors contributed and raised funds that enabled Abel to enter the University of Christiania (Oslo) in 1821. Abels first papers, published in 1823, were on functional equations and integrals; he was the first person to formulate and solve an integral equation. He had also created a proof of the impossibility of solving algebraically the general equation of the fifth degree at the age of 19, which he hoped would bring him recognition. -
Éclat a Mathematics Journal
Éclat A Mathematics Journal Volume I 2010 Department of Mathematics Lady Shri Ram College For Women Éclat A Mathematics Journal Volume I 2010 To Our Beloved Teacher Mrs. Santosh Gupta for her 42 years of dedication Preface The revival of Terminus a quo into E´clat has been a memorable experience. Eclat´ , with its roots in french, means brilliance. The journey from the origin of Terminus a quo to the brilliance of E´clat is the journey we wish to undertake. In our attempt to present diverse concepts, we have divided the journal into four sections - History of Mathematics, Rigour in Mathematics, Extension of Course Contents and Interdisciplinary Aspects of Mathematics. The work contained here is not original but consists of the review articles contributed by both faculty and students. This journal aims at providing a platform for students who wish to publish their ideas and also other concepts they might have come across. Our entire department has been instrumental in the publishing of this journal. Its compilation has evolved after continuous research and discussion. Both the faculty and the students have been equally enthusiastic about this project and hope such participation continues. We hope that this journal would become a regular annual feature of the department and would encourage students to hone their skills in doing individual research and in writing academic papers. It is an opportunity to go beyond the prescribed limits of the text and to expand our knowledge of the subject. Dootika Vats Ilika Mohan Rangoli Jain Contents Topics Page 1) History of Mathematics 1 • Abelia - The Story of a Great Mathematician 2 • Geometry in Ancient Times 6 2) Rigour in Mathematics 10 • Lebesgue Measure and Integration 11 • Construction of the Real Number System 18 • Fuzzy Logic in Action 25 3) Extension of Course Contents 29 • Continuum Hypothesis 30 • Dihedral Groups 35 4) Inter-disciplinary Aspects of Mathematics 41 • Check Digits 42 • Batting Average 46 1 History of Mathematics The history behind various mathematical concepts and great mathemati- cians is intriguing. -
Karen Uhlenbeck Awarded Abel Prize
COMMUNICATION Karen Uhlenbeck Awarded Abel Prize The Norwegian Academy of Science and Letters has awarded the Abel Prize for 2019 to Karen Keskulla Uhlenbeck of the University of Texas at Austin, “for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” The Abel Prize recognizes contributions of extraordinary depth and influence in the mathematical sciences and has been awarded annually since 2003. It carries a cash award of six million Norwegian krone (approximately US$700,000). Citation detail what happens when the Palais–Smale condition is Karen Keskulla Uhlenbeck is a violated. A minimizing sequence of mappings converges founder of modern geometric outside a finite set of singular points, and, by using resca- analysis. Her perspective has ling arguments, they describe the behavior near the singu- permeated the field and led larities as bubbles or instantons, which are the standard to some of the most dramatic solutions of the minimizing map from the 2-sphere to the advances in mathematics in the target manifold. last forty years. In higher dimensions, Uhlenbeck in collaboration with Geometric analysis is a field Schoen wrote two foundational papers on minimizing of mathematics where tech- harmonic maps. They gave a profound understanding niques of analysis and differ- of singularities of solutions of nonlinear elliptic partial ential equations are interwoven differential equations. The singular set, which in the case Karen Keskulla Uhlenbeck with the study of geometrical of surfaces consists only of isolated points, is in higher and topological problems. -
Reposs #11: the Mathematics of Niels Henrik Abel: Continuation and New Approaches in Mathematics During the 1820S
RePoSS: Research Publications on Science Studies RePoSS #11: The Mathematics of Niels Henrik Abel: Continuation and New Approaches in Mathematics During the 1820s Henrik Kragh Sørensen October 2010 Centre for Science Studies, University of Aarhus, Denmark Research group: History and philosophy of science Please cite this work as: Henrik Kragh Sørensen (Oct. 2010). The Mathematics of Niels Henrik Abel: Continuation and New Approaches in Mathemat- ics During the 1820s. RePoSS: Research Publications on Science Studies 11. Aarhus: Centre for Science Studies, University of Aarhus. url: http://www.css.au.dk/reposs. Copyright c Henrik Kragh Sørensen, 2010 The Mathematics of NIELS HENRIK ABEL Continuation and New Approaches in Mathematics During the 1820s HENRIK KRAGH SØRENSEN For Mom and Dad who were always there for me when I abandoned all good manners, good friends, and common sense to pursue my dreams. The Mathematics of NIELS HENRIK ABEL Continuation and New Approaches in Mathematics During the 1820s HENRIK KRAGH SØRENSEN PhD dissertation March 2002 Electronic edition, October 2010 History of Science Department The Faculty of Science University of Aarhus, Denmark This dissertation was submitted to the Faculty of Science, University of Aarhus in March 2002 for the purpose of ob- taining the scientific PhD degree. It was defended in a public PhD defense on May 3, 2002. A second, only slightly revised edition was printed October, 2004. The PhD program was supervised by associate professor KIRSTI ANDERSEN, History of Science Department, Univer- sity of Aarhus. Professors UMBERTO BOTTAZZINI (University of Palermo, Italy), JEREMY J. GRAY (Open University, UK), and OLE KNUDSEN (History of Science Department, Aarhus) served on the committee for the defense. -
Science-Traditional-Knowledge
March 2002 SCIENCE AND TRADITIONAL KNOWLEDGE Report from the ICSU Study Group on Science and Traditional Knowledge Explanatory note The recommendations in this report are those of the authors and have not yet been ratified by the ICSU Executive Board and General Assembly. In setting out these recommendations for future ICSU activities, the authors have defined a number of possible actions and are fully aware that they may not all be implemented and, indeed, that alternative actions might eventually be considered more appropriate. The ICSU General Assembly will formally consider the report and its recommendations at its meeting in September 2002. March 2002 INTERNATIONAL COUNCIL FOR SCIENCE ICSU CONSEIL INTERNATIONAL POUR LA SCIENCE SCIENCE AND TRADITIONAL KNOWLEDGE Report from the ICSU Study Group on Science and Traditional Knowledge SECTION 1: BACKGROUND The World Conference on Science (WCS) was organized by UNESCO in cooperation with ICSU and took place in Budapest, Hungary, from 26 June to 1 July 1999. The objectives of the Conference were to help strengthen the commitment of ICSU and UNESCO's Member States and other major stakeholders to science education, research and development, and to define a strategy that would ensure that science responds better to society's needs and aspirations in the twenty-first century. The results of the Conference are embodied in two principal documents: (i) Declaration on Science and the Use of Scientific knowledge and (ii) Science Agenda - Framework for Action. The Declaration affirms that scientific knowledge has led to remarkable innovations that have been of great benefit to humankind. But it also notes at the same time the challenge to use this knowledge in a responsible manner to address human needs and aspirations. -
«Jeg Skjønner Hva Han Gjør, Men Ikke Hvordan Han Kommer På Å Gjøre Det»
«Jeg skjønner hva han gjør, men ikke hvordan han kommer på å gjøre det» En casestudie av R1-elevers forståelse av bevis Thomas Westly Eriksen Master i realfag Innlevert: mai 2015 Hovedveileder: Frode Rønning, MATH Norges teknisk-naturvitenskapelige universitet Institutt for matematiske fag Forord Denne masteroppgaven symboliserer slutten på en 5-årig lektorutdanning ved Norges teknisk- naturvitenskapelige universitet (NTNU). Det har vært 5 år fylt med mye læring, utfordringer, fortvilelse og mestring. Forelesninger, øvinger og eksamener har fylt opp ukene, og minnene er blitt mange. Jeg minnes Per Haag sine mxn-matriser, der jeg den dag i dag fremdeles sliter med skille mellom m-ene og n-ene i håndskriften hans. Jeg tenker tilbake på Marius Irgens billedlige beskrivelser av å se sammenhengene i matematikk, der jeg lærte at det var viktigere å se skogen enn trærne. Og så tenker jeg på Peter Lindquist sine humoristiske stikk til alle som ifølge ham ikke skjønte matematikk. Ingenting ville jeg vært foruten. I den forbindelse er det på sin plass å takke alle som har bidratt til 5 minneverdige år ved NTNU. Først vil jeg takke alle medstudenter, kommende lektorer og ikke minst vennene jeg har hatt og fått i løpet av disse årene. Dere har alle bidratt til at disse 5 årene har forsvunnet i en fei. Årene har vært fylt med mange gleder, festligheter og opplevelser. Sammen har vi gjennom oppturer og nedturer kjempet oss gjennom et utfordrende 5-årig lektorstudium, og er nå klare for sette våre kunnskaper og ideer ut i praksis. Jeg vil også benytte anledningen til å takke alle forelesere jeg har hatt på NTNU.