Alan Baker (19 August 1939 – 4 February 2018) was an English

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, known for his work on effective methods in number theory, in particular those arising from transcendental number theory.

Life

Alan Baker was born in London on 19 August 1939. He attended Stratford Grammar School, East London, and his academic career started as a student of Harold Davenport, at

University College London , mottoeng = Let all come who by merit deserve the most reward , established = , type = Public research university , endowment = £143 million (2020) , budget = ...

and later at

Trinity College, Cambridge Trinity College is a constituent college of the University of Cambridge. Founded in 1546 by Henry VIII, King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any college at either Cambridge ...

, where he received his PhD. He was a visiting scholar at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

in 1970 when he was awarded the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

at the age of 31. In 1974 he was appointed Professor of Pure Mathematics at

Cambridge University , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

, a position he held until 2006 when he became an

Emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

. He was a fellow of Trinity College from 1964 until his death. His interests were in number theory,

transcendence Transcendence, transcendent, or transcendental may refer to: Mathematics * Transcendental number, a number that is not the root of any polynomial with rational coefficients * Algebraic element or transcendental element, an element of a field exten ...

logarithmic form In contexts including complex manifolds and algebraic geometry, a logarithmic differential form is a meromorphic differential form with poles of a certain kind. The concept was introduced by Deligne. Let ''X'' be a complex manifold, ''D'' ⊂ ''X'' ...

s, effective methods, Diophantine geometry and Diophantine analysis. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. He has also been made a foreign fellow of

the National Academy of Sciences, India The National Academy of Sciences, India, established in 1930, is the oldest science academy in India. It is located in Prayagraj, Uttar Pradesh. Prof. Meghnad Saha was the founder president. Fellows *Suddhasatwa Basu * Sudha Bhattacharya * Ch ...

Research

Baker generalised the

Gelfond–Schneider theorem In mathematics, the Gelfond–Schneider theorem establishes the transcendence of a large class of numbers. History It was originally proved independently in 1934 by Aleksandr Gelfond and Theodor Schneider. Statement : If ''a'' and ''b'' are ...

, itself a solution to Hilbert's seventh problem. Specifically, Baker showed that if

\alpha_1,...,\alpha_n

are

algebraic number An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, (1 + \sqrt)/2, is an algebraic number, because it is a root of the po ...

s (besides 0 or 1), and if

\beta_1,..,\beta_n

are irrational algebraic numbers such that the set

\

is linearly independent over the rational numbers, then the number

\alpha_1^\alpha_2^\cdots\alpha_n^

transcendental Transcendence, transcendent, or transcendental may refer to: Mathematics * Transcendental number, a number that is not the root of any polynomial with rational coefficients * Algebraic element or transcendental element, an element of a field exten ...

. Baker made significant contributions to several areas in number theory, such as the Gauss

class number problem In mathematics, the Gauss class number problem (for imaginary quadratic fields), as usually understood, is to provide for each ''n'' ≥ 1 a complete list of imaginary quadratic fields \mathbb(\sqrt) (for negative integers ''d'') having c ...

, diophantine approximation, and to Diophantine equations such as the

Mordell curve In algebra, a Mordell curve is an elliptic curve of the form ''y''2 = ''x''3 + ''n'', where ''n'' is a fixed non-zero integer. These curves were closely studied by Louis Mordell, from the point of view of determining their integer points. He sho ...

Selected publications

* * * *; *

Honours and awards

*1970:

*1972: Adams Prize *1973: Fellowship of the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

References

External links

* * * {{DEFAULTSORT:Baker, Alan 1939 births 2018 deaths 20th-century English mathematicians 21st-century English mathematicians Fields Medalists Number theorists Alumni of University College London Alumni of Trinity College, Cambridge Fellows of Trinity College, Cambridge Fellows of the American Mathematical Society Fellows of the Royal Society Foreign Fellows of the Indian National Science Academy Institute for Advanced Study visiting scholars Cambridge mathematicians Mathematicians from London