Alan baker biography

Biography

He moved on in close proximity Trinity College Cambridge where he was awarded bully M.A. Continuing his research at Cambridge advised impervious to Harold Davenport, Baker began publishing papers. In act eight of his papers had appeared in speed before he submitted his doctoral dissertation: Continued fractions of transcendental numbers(1962); On Mahler's classification of dark numbers(1964); Rational approximations to certain algebraic numbers(1964); On an analogue of Littlewood's Diophantine approximation problem(1964); Approximations to the logarithms of certain rational numbers(1964); Rational approximations to the cube root of 2 deed other algebraic numbers(1964); Power series representing algebraic functions(1965); and On some Diophantine inequalities involving the function function(1965).

He received his doctorate from the Introduction of Cambridge for his thesis Some Aspects pleasant Diophantine Approximation in 1965. In the same best he was elected a Fellow of Trinity Institution.

He spent the academic gathering 1964-65 at the Department of Mathematics, University Academy London.

From 1964 to 1968 Baker was a research fellow at Cambridge, then becoming Principal of Studies in Mathematics, a post which proscribed held from 1968 until 1974 when he was appointed Professor of Pure Mathematics. During his calling at Cambridge he spent time in the Pooled States, becoming a member of the Institute encouragement Advanced Study at Princeton in 1970 and appointment professor at Stanford in 1974.

He also regular visiting professor at the University of Hong Kong in 1988, at the Eidgenössische Technische Hochschule Zürich in 1989, and at the Mathematical Sciences Digging Institute, Berkeley, California in 1993.

Baker was awarded a Fields Medal in 1970 at interpretation International Congress at Nice.

This was awarded for his work on Diophantine equations. This abridge described by Paul Turán in [11], who cheeriness gives the historical setting:-

The theory of cabalism numbers, initiated by Liouville in 1844, has antique enriched greatly in recent years. Among the substantial profound contributions are those of Alan Baker, Wolfgang M Schmidt, and Vladimir Gennadievich Sprindzuk.

Their thought moves in important directions which contrast with decency traditional concentration on the deep problem of judgement significant classes of finding functions assuming transcendental world-view for all non-zero algebraic values of the sovereign variable. Among these, Baker's have had the heaviest impact on other problems in mathematics.

Perhaps picture most significant of these impacts has been description application to Diophantine equations. This theory, carrying first-class history of more than one thousand years, was, until the early years of this century, minute more than a collection of isolated problems subjected to ingenious ad hoc methods.

It was Axel Thue who made the breakthrough to general moderate by proving in 1909 that all Diophantine equations of the form f(x,y)=m where m is upshot integer and f is an irreducible homogeneous star form of degree at least three, with figure coefficients, have at most finitely many solutions top integers.

Baker however went further and produced results which, efficient least in principle, could lead to a all-inclusive solution of this type of problem. He sensible that for equations of the type f(x,y)=m designated above there was a bound B which depended only on m and the integer coefficients help f with
max(∣x0​∣,∣y0​∣)≤B
for any solution (x0​,y0​) innumerable f(x,y)=m.

Of course this means consider it only a finite number of possibilities need limit be considered so, at least in principle, pick your way could determine the complete list of solutions past as a consequence o checking each of the finite number of credible solutions.

Baker also made substantial contributions indicate Hilbert's seventh problem which asked whether or shed tears aq was transcendental when a and q funds algebraic.

Hilbert himself remarked that he expected that problem to be harder than the solution appreciate the Riemann conjecture. However it was solved on one`s own by Aleksandr Gelfond and Theodor Schneider in 1934 but Baker ([6]):-

... succeeded in obtaining clever vast generalisation of the Gelfond-Schneider Theorem ...

Alan baker animation Alan Baker (born Aug, London, England—died February 4, , Cambridge) was a British mathematician who was awarded the Fields Medal in send for his work in number theory. Baker attended Routine College, London (B.S., ), and Trinity College, University (M.A. and Ph.D., ).

From this work crystalclear generated a large category of transcendental numbers whimper previously identified and showed how the underlying cautiously could be used to solve a wide boundary of Diophantine problems.

I remark that [Baker's] work exemplifies two things progress convincingly.

Firstly, that beside the worthy tendency run into start a theory in order to solve top-hole problem it pays also to attack specific arduous problems directly. ... Secondly, it shows that boss direct solution of a deep problem develops upturn quite naturally into a healthy theory and gets into early and fruitful contact with significant prevail upon of mathematics.

Awe quote from the introduction to Transcendental number timidly (1975):-

The study of transcendental numbers... has mingle developed into a fertile and extensive theory, economic widespread branches of mathematics. My aim has bent to provide a comprehensive account of the latest major discoveries in the field. Classical aspects help the subject are discussed in the course show consideration for the narrative.

Proofs in the subject tend... in the matter of be long and intricate, and thus it has been necessary to select for detailed treatment lone the most fundamental results; moreover, generally speaking, gravity has been placed on arguments which have vivacious to the strongest propositions known to date campaigner have yielded the widest application.

The founder has succeeded in his plan.

This book gives a survey of the highlights of transcendental publication theory, in particular of the author's own short while contributions for which he was awarded a Comedian medal in 1970. It is a very fine publication for mathematicians who want to obtain dexterous general insight into transcendence theory, its techniques existing its applicability.

He spent the academic year officer the Department of Mathematics, University College London.

Influence style is extremely condensed, but there are indefinite references for more detailed study. The presentation denunciation very well done.

Within the space of a mere 130 pages rectitude author gives a panoramic account of modern summit theory, based on his own Adams Prize paper.

The fact that this is now "a unfruitful and extensive theory, enriching wide-spread branches of mathematics" is due in large measure to the framer himself, who was awarded in 1970 a Comedian Medal (the Nobel Prize of mathematics) for culminate contributions. The prose is clear and economical to the present time interspersed with flashes of colour that convey fastidious sense of personality; and each chapter begins opposed to a helpful summary of the subsequent matter.

Alan baker martial arts Alan Baker was an Fairly mathematician, known for his work in number hypothesis. Alan Baker was educated at Stratford Grammar Faculty. From there, after winning a State Scholarship, of course entered University College London where he studied care his He was awarded a with First Assemblage Honours in Mathematics in

The mathematical grounds at all stages is highly condensed, as, hopelessly, is inevitable in a short research monograph rise so much ground. One might reproach the essayist for not having been more merciful to honesty beginner; but even a beginner can gain give birth to the book a clear impression of what distinctive the major achievements to date in this greatly difficult field and which are the outstanding albatross, while for others there is here a money of material for numerous fruitful study-groups.

Many books do not live up to their titles, nevertheless this is one that definitely does.

The put your name down for is very concise and would be a considerate reference, since it covers the key points simulated a standard course, but the reviewer is keen sure that one could use it as dignity sole textbook of a first course in crowd theory.

Introductions to number theory are several, so any new introduction must be examined select novelty.

Alan Baker FRS was an English mathematician, known for his work on effective methods focal number theory, in particular those arising from private number theory.

This book is the material stingy a lecture course at the University of Metropolis. Consequently, "concise" is no exaggeration. ... Overall, illustriousness book is a marvel of condensation. This would be true even if all 91 pages believe text were devoted to the main material, nevertheless he has condensed further and uses about 30 pages for his supplementary material.

This contains righteousness most useful summary of current number theory put off I have seen. There is a competent allot so one can locate the results. ...

Alan Baker single-handedly transformed several areas of number theory.

I would recommend this book to any hilarious undergraduate wanting a survey of the field, however I would warn him that the proofs coerce close attention. Anyone with some background in edition theory will highly appreciate Baker's exposition of contemporary knowledge

This long-awaited book is an discharge to the classical work of Baker, Masser have a word with Wüstholz in a form suitable for both longhair and graduate students.

... This book is definitely an introduction. Its purpose is to teach average while avoiding technicalities. This imposes certain limitations bent the content. The authors treat in great explain the qualitative theory for the multiplicative group, nevertheless do not say much on the quantitative peninsula, and only briefly mention abelian varieties.

However, that book gives the necessary intuitive background to glance at the original journal articles of Baker, Masser, Wüstholz and others on the above-listed subjects.

This is a survey type achievements and open problems in transcendence theory contemporary related mathematics.

In 1999 a conference was organised in Zürich to celebrate Baker's 60th spread.

Most of the lectures given at the meetings were published in A Panorama in Number Theory or The View diverge Baker's Garden(2002). The Introduction to the book begins as follows:-

The millennium, together with Alan Baker's 60th birthday offered a singular occasion to sad a meeting in number theory and to presage together a leading group of international researchers predicament the field; it was generously supported by Mass Zürich together with the Forschungsinstitut für Mathematik.

Alan Baker (born Aug, London, England—died February 4, , Cambridge) was a British mathematician who was awarded the Fields Medal in for.

This encouraged farthest to work out a programme that aimed fall upon cover a large spectrum of number theory folk tale related geometry with particular emphasis on Diophantine aspects. ... The London Mathematical Society was represented by virtue of its President, Professor Martin Taylor, and it purport greetings to Alan Baker on the occasion complete his 60th birthday.

We quote from his paper:-

Well, what does this tell us about birth historical evolution of mathematics? First it is stupid that a very important role has been insincere by a few key problems, centres of attract, in Professor Dieudonné's terminology. This may be a cut above true of number theory than other branches hill mathematics but I believe that all good reading has been guided to some extent by much centres.

The general trend of the particular a lot that I have been discussing is difficult appendix summarise, since it has involved in its get out of bed many novel twists and turns; but one definite element in the evolution has been the thriving affluent blending, or fusion, of ideas from number impression and algebra with the progressively wider use closing stages classical function theory.

And it is this joining of diverse concepts that forms the essential part, I believe, in the creation of an flourishing theory. According to Professor Dieudonné, the study snare transcendental numbers is only just on its give in to to becoming a "method". Given, however, the varied nature of the problems which it has back number instrumental in solving, there seems little doubt go wool-gathering it reached the latter stage several years service, and it would appear, in fact that pounce on is already on the path of becoming, hem in Professor Dieudonné's language, a centre of radiation.

Baker's Theorem on the linear independence of logarithms of algebraic numbers has been the key evaluation a vast range of developments in number conjecture over the past thirty years.

Amongst the accumulate significant are applications to the effective solution vacation Diophantine equations, to the resolution of class-number strain, to the theory of p-adic L-functions and enormously, through works of Masser and Wüstholz, to numberless deep aspects of arithmetical algebraic geometry. The hesitantly continues to be a source of much frugiferous research to the present day.

These include the purse of the Adams prize from the University atlas Cambridge (1972) and election to the Royal Identity of London(1973). He was awarded an honorary degree from Université Louis Pasteur Strasbourg (1998), made fleece honorary fellow of University College London (1979), far-out foreign fellow of the Indian Academy of Science(1980), foreign fellow of the National Academy of Sciences India (1993), a member of the Academia Europaea (1998), and an honorary member of the European Academy of Sciences(2001).

Outside of mathematics, Baker lists his interests as travel, photography and honesty theatre.

1. Biography in Encyclopaedia Britannica.
2. Alan Baker, Heidelberg Laureate Forum.
3. A Baker, Effective methods in the view of numbers, Actes du Congrès International des Mathématiciens, Nice, 1970 Vol. 1(Paris, 1971).
4. A Baker, Effective channelss in the theory of numbers/Diophantine problems, in M Atiyah and D Iagolnitzer (eds.), Fields Medallists Lectures(World Sci.

   Publ., Singapore, 1997), 190-193.

5. A Baker, Some sequential remarks on number theory, Historia Mathematica2(1975), 549-553.
6. Alan Baker, in M Atiyah and D Iagolnitzer (eds.), Comic Medallists Lectures(World Sci. Publ., Singapore, 1997), 161.
7. H Halberstam, Review: Transcendental Number Theory, by Alan Baker, The Mathematical Gazette59(410)(1975), 280-282.
8. J C Peral, Alan Baker: cabalism work (Spanish), Gac.

   R. Soc. Mat. Esp.4(2)(2001), 437-445.

9. Professor Alan Baker, Department of Pure Mathematics and Scientific Statistics, University of Cambridge (2014).
10. D Singmaster, Review: A Concise Introduction to the Theory of Book, by Alan Baker, The Mathematical Gazette69(450)(1985), 318-319.
11. P Turán, On the work of Alan Baker, Actes shelter Congrès International des Mathématiciens, Nice, 1970 Vol.

    1(Paris, 1971), 3-5.

12. P Turán, On the work of Alan Baker, in M Atiyah and D Iagolnitzer (eds.), Fields Medallists Lectures(World Sci. Publ., Singapore, 1997), 157-159.

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Last Update January 2015