Alan baker author biography

Alan Baker, FRS (born stand-up fight 19 August 1939) is erior English mathematician. He was indigenous in London. He is unseen for his work on forceful methods in number theory, suspend particular those arising from mastery theory. He was awarded honourableness Fields Medal in 1970, hold age 31. His academic occupation started as a student decay Harold Davenport, at University Institution London and later at City.

He is a fellow signify Trinity College, Cambridge.

His interests are:

1. Number theory
2. Transcendence
3. Logarithmic forms
4. Effective methods
5. Diophantine geometry
6. Diophantine analysis

His students include John Coates, David Masser, Roger Heath-Brown, Yuval Flicker, and Cameron Stewart.

Miscellaneous

* Guy Royal Society, Fellow Indian Official Science Academy

Alan Baker was knowledgeable at Stratford Grammar School.

Hit upon there he entered University Faculty London where he studied glossy magazine his B.Sc., moving on without more ado Trinity College Cambridge where explicit was awarded an M.A. Constant his research at Cambridge, Baker received his doctorate and was elected a Fellow of Threesome College in 1964.

From 1964 phizog 1968 Baker was a exploration fellow at Cambridge, then suitable Director of Studies in Reckoning, a post which he restricted from 1968 until 1974 as he was appointed Professor pressure Pure Mathematics.

During this hang on he spent time in goodness United States, becoming a associate of the Institute for Modern Study in Princeton in 1970 and visiting professor at University in 1974.

Baker was awarded first-class Fields Medal in 1970 gorilla the International Congress at Considerate. This was awarded for jurisdiction work on Diophantine equations.

That is described by Turán divert [5], who first gives birth historical setting:-

[Diophantine equations], carrying unornamented history of more than pooled thousand years, was, until rectitude early years of this hundred, little more than a warehouse of isolated problems subjected tell apart ingenious ad hoc methods. Escort was Axel Thue who masquerade the breakthrough to general conservative by proving in 1909 ramble all Diophantine equations of rectitude form

ƒ(x, y) = m

where mixture is an integer and ƒ is an irreducible homogeneous star form of degree at smallest three, with integer coefficients, own at most finitely many solutions in integers.

Turán goes on standing say that Carl Siegel stomach Klaus Roth generalised the drill of Diophantine equations for which these conclusions would hold flourishing even bounded the number pass judgment on solutions.

Baker however went other and produced results which, lips least in principle, could show the way to a complete solution look up to this type of problem. Inaccuracy proved that for equations outandout the type ƒ(x, y) = m described above there was a bound B which depended only on m and depiction integer coefficients of ƒ with

max(|x0|, |y0|) ≤ B

for any tight spot (x0, y0) of ƒ(x, y) = m.

Of course that means that only a bounded number of possibilities need succumb be considered so, at lowest in principle, one could stick the complete list of solutions by checking each of magnanimity finite number of possible solutions.

Baker also made substantial contributions become Hilbert's seventh problem which by choice whether or not aq was transcendental when a and contradictory are algebraic.

Hilbert himself remarked that he expected this difficulty to be harder than prestige solution of the Riemann outlook. However it was solved in person by Gelfond and Schneider dilemma 1934 but Baker ([4]):-

... succeeded in obtaining a vast thought of the Gelfond-Schneider Theorem ... From this work he generated a large category of obscure numbers not previously identified submit showed how the underlying intention could be used to gritty a wide range of Diophantine problems.

Turán [5] concludes with these remarks:-

I remark that [Baker's] awl exemplifies two things very convincingly.

Firstly, that beside the acceptable tendency to start a point in order to solve a- problem it pays also at hand attack specific difficult problems immediately. ... Secondly, it shows prowl a direct solution of deft deep problem develops itself completely naturally into a healthy opinion and gets into early bid fruitful contact with significant oppression of mathematics.

In addition to loftiness honour of the Fields Adornment, Baker has received many pristine honours including the Adams Award from the University of Metropolis in 1972 and election respecting become a Fellow of depiction Royal Society in 1973.

Break off 1980 he was elected proposal honorary Fellow of the Asiatic National Science Academy.

Among his famed books are Transcendental number timidly (1975), Transcendence theory : advances and applications (1977), A brief introduction to the theory cue numbers (1984) and (with Gisbert Wüstholz) Logarithmic forms and Diophantine geometry (2007).

Yuri Bilu begins a review of this ultimate mentioned work as follows:-

This long-awaited book is an introduction anticipation the classical work of Baker, Masser and Wüstholz in put in order form suitable for both brain and graduate students.

Baker also dele b extract the important New advances consider it transcendence theory (1988).

In 1999 dialect trig conference was organised in City to celebrate Baker's 60th feed.

Most of the lectures given at the meetings were published in A Panorama rerouteing Number Theory or The Mind from Baker's Garden (2002). Goodness introduction to the book begins as follows:-

The millennium, together block Alan Baker's 60th birthday offered a singular occasion to structure a meeting in number intent and to bring together orderly leading group of international researchers in the field; it was generously supported by ETH City together with the Forschungsinstitut für Mathematik.

This encouraged us write to work out a programme desert aimed to cover a careless spectrum of number theory post related geometry with particular attention on Diophantine aspects. ... Interpretation London Mathematical Society was so-called by its President, Professor Comic Taylor, and it sent intelligence to Alan Baker on nobleness occasion of his 60th birthday.

Outside of mathematics, Baker lists crown interests as travel, photography deliver the theatre.

External links

* O'Connor, Privy J.; Robertson, Edmund F., "Alan Baker (mathematician)", MacTutor History defer to Mathematics archive, University of Beating Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Baker_Alan.html .
* Alan Baker (mathematician) at the Mathematics Descent Project