ONE HUNDRED REASONS TO BE A SCIENTIST Special Edition for the Abel Fund and the Norwegian Academy of Science and Letters ONE HUNDRED REASONS TO BE A SCIENTIST - ABEL edition Copyright © 2005 The Abdus Salam International Centre for Theoretical Physics (ICTP) ICTP has the irrevocable and indefinite authorization to reproduce and disseminate this publication, in printed and/or computer readable form. ISBN 92-95003-32-2 Printing History: October 2004 - First edition May 2005 - Second edition Printed in Trieste by The ICTP Publications & Printing Section One Hundred Reasons to be a Scientist The Srinivasa Ramanujan Prize and Niels Henrik Abel K.R. Sreenivasan The Abdus Salam International Centre for Theoretical Physics (ICTP) recently established the Srinivasa Ramanujan Prize, named after the mathematics genius from India. This Prize will be awarded annually to a mathematician under 45. Since the mandate of ICTP is to strengthen science in developing countries, the Ramanujan Prize has been created for mathematicians from developing countries. Since Ramanujan is the quintessential symbol of the best in mathematics from the developing world, naming the Prize after him seemed entirely appropriate. The Ramanujan prize is funded by the Norwegian Academy of Science and Letters through the Abel Fund, with the cooperation of the International Mathematics Union. The Abel Fund is named in honor of the great Norwegian mathematician, Niels Henrik Abel. It is enchanting that the names of these two extraordinary mathematicians should be linked through this Prize. I would now like to say a few words about Abel and SRINIVASA RAMANUJAN (1887-1920) Ramanujan. (photo courtesy of The Hindu) For obvious reasons, longevity often has an influence on a scientist’s stamp on his world. There are rare exceptions of people who die young and yet change the world for ever. They are special among the special, and posterity regards them as great with no grudge. Both Ramanujan and Abel belong to this unique class. Abel and Ramanujan were born 85 years apart in time and a world apart in space: Abel in 1802 in Finnøy (near Stavanger), Norway, and Ramanujan in 1887 in Erode, Tamil Nadu, India. Both died young---Abel at 27 and Ramanujan at 32. They both grew up in poverty and hardship; Norway was not in great shape at that time. The lives of these two mathematicians are at once romantic, tragic, and heroic. Of the two, perhaps Ramanujan may have been the more fortunate. He found a sympathetic mentor in G.H. Hardy, a mathematician of towering stature at Cambridge, who was responsible for making Ramanujan’s work known to the world during the latter’s own lifetime. Abel had the misfortune that his best work was mislaid at the Paris Academy, and was recognized only posthumously. the abdus salam international centre for theoretical physics i One Hundred Reasons to be a Scientist Abel was a pioneer in the development of several branches of modern mathematics, especially group theory and elliptic functions. He showed, while still 19 years old, that there exist no general algebraic solutions for the roots of polynomials with degree equal to or greater than 5, thus resolving a problem that had intrigued mathematicians for centuries. Ramanujan was a genius in pure mathematics and made spectacular contributions to elliptic functions, continued fractions, infinite series, and analytical theory of numbers. He was essentially self-taught from a single text book that was available to him. They both possessed extraordinary mathematical power and inspiration. A year before the bi-centenary of Abel, the Norwegian Government established an Abel Fund, part of which was to be used by the Norwegian Academy of Science and Letters to award an annual Abel Prize for mathematics. This prize has a financial value comparable to the Nobel Prize. And, unlike the well-known Fields Medal which is awarded to young mathematicians below 40, the Abel Prize recognizes lifetime contributions to mathematics. Four eminent mathematicians---Jean-Pierre Serre (Paris) in 2003, Michael Atiyah (Edinburgh) and Isadore Singer (MIT) in 2004 and Peter Lax (NYU) in 2005---have received the Abel Prize. Two of them, Atiyah and Lax, have written for the present volume. The first Ramanujan Prize has just been awarded to Professor Marcelo Viana, Instituto de Matematica Pura e Aplicada (IMPA), Brazil, with the following citation: "Marcelo Viana is an established mathematician worldwide in the field of dynamical systems where he has made major contributions. His mathematical productivity is impressive in quality and quantity. He has strongly influenced the development of mathematics in IMPA and, more globally, in Brazil." It is my hope that the mathematicians recognized through the Ramanujan Prize will make their mark in ways that will render them eligible for further recognitions in the world of science. I am pleased that the event this year links several institutions: ICTP, IMPA, Norwegian Academy of Science and Letters, Abel Fund, IMA, and several countries such as Norway, India, Brazil and Italy. This, too, has a romantic character. Note: K.R. Sreenivasan is the Abdus Salam Research Professor and Director of ICTP in Trieste, Italy. ICTP is administered by the United Nations Educational, Scientific and Cultural Organization (UNESCO) and the International Atomic Energy Agency (IAEA). Most of its funding is provided by the Italian government. ICTP is recognized worldwide as a 'home away ii the abdus salam international centre for theoretical physics One Hundred Reasons to be a Scientist from home' for thousands of scientists from developing countries. Since its inception, ICTP has been a centre of excellence in certain areas of theoretical science, and some 90 Nobel Laureates have lectured there. Abdus Salam, the founding director of the Centre, was himself a Nobel Laureate. Each year, some 6000 scientists from 120 nations visit ICTP to participate in 50-60 research and training activities at the Centre. These scientists are distributed equally between industrialized and developing countries. For the past four decades, ICTP has provided world-class research opportunities and training for scientists from developing countries, encouraging them to return home to pursue their careers and help build their societies. That mandate remains as relevant today as at the time of the Centre's creation in 1964. the abdus salam international centre for theoretical physics iii One Hundred Reasons to be a Scientist Sir Michael Atiyah, Abel Laureate 2004 Science explores the great unknown, and what we know is always less that what remains to be discovered. This communal exploration is driven by intellectual curiosity but it has immense potential to benefit mankind. We depend on the youth of today to carry forward the torch and illuminate the future. In this collection of short essays you will find, I hope, stimulus and inspiration from those who have spent their lives in the development of science. The range is vast and the work involved varies from the most theoretical mathematics to the most experimental and applied sciences. There should be something that appeals to you, suits your particular talents and which you can follow up. The future is yours. Bon voyage! iv the abdus salam international centre for theoretical physics One Hundred Reasons to be a Scientist Peter D. Lax, Abel Laureate 2005 Dear young future mathematician If you are reading this, you probably already belong to that tiny minority of people whose minds are so wired from birth that they find beauty and challenge in learning and thinking about mathematics. If you do, let me assure you that a life spent in working on mathematics is most rewarding, full of surprises, gratification, and of course many frustrating moments as well. Mathematics attracts young minds because they can embark without knowing anything about the real world; a few definitions and you are off thinking on your own. I advise you that as you mature, you should gradually make contact with the real world, and learn how much of it can be understood through mathematics. Good hunting. the abdus salam international centre for theoretical physics v One Hundred Reasons to be a Scientist Akkurat som at det største for en idrettsutøver er å bli verdens- eller olympisk mester, så er det mest prestisjefylte for en som jobber med forskning å bli tildelt Nobelprisen. Problemet er bare at det finnes Nobelpriser kun i noen få fag. Ett av de fagene som ikke har noen Nobelpris er matematikk. Til gjengjeld har matematikken en Abelpris. Vinneren av Abelprisen får omtrent like mye penger som Nobelprisvinnerne og omtrent like mye ære og berømmelse. Det er en forskjell på Abel- og Nobelprisene, alle Nobelprisene (unntatt Fredsprisen) deles ut i Sverige, mens Abelprisen deles ut i Norge. Prisen er oppkalt etter Norges største vitenskapsmann gjennom alle tider, matematikeren Niels Henrik Abel (1802-1829). Det fantes ikke noen Abelpris på Abels tid, men Abel hadde helt sikkert vært en verdig vinner. I den boka, eller CD-en du har foran deg nå, prøver en hel rekke menn (og noen få kvinner) å overbevise deg om hvorfor du bør satse på en karriere innen naturvitenskap og matematikk. Mange av dem som skriver her har fått Nobelprisen eller Abelprisen. Selv om mange av dem er ganske gamle har de alle vært unge en gang! Da kunne de ikke så mye som de kan nå, men de var like kloke og kanskje mer nysgjerrige. Nysgjerrige på å finne ut ”hvorfor det?” eller ”hvordan virker det?” eller på å finne svaret på en vanskelig regneoppgave. Kanskje var det nysgjerrigheten deres som gjorde dem så gode? Selv om vi som jobber med Abelprisen hvert år kårer matematikkens ”verdensmester”, så er ikke det det eneste vi tenker på. Vi er også interessert i at mange flere enn de aller flinkeste skal synes det er gøy å drive med matematikk eller andre realfag.