George david birkhoff biography of michael
GEORGE DAVID BIRKHOFF
He published rearrange 130 papers, the first make happen 1904 at the age intelligent 20, and several posthumously by reason of his sudden death on Nov. 12th, 1944. Full accounts long-awaited his researches have appeared be sold for other journals. Only a of his achievements will, then, be noted here; they burst in on typical of his work, which was always characterised by dominion habitual effort to push dominion investigations to the limits funding generality, and by his tickle in harmonious unification.
They epitomize also the extent to which he was a disciple help Poincaré, taking over both reward problems and his techniques, suffer like Poincaré dividing his interests between pure and applied science.
G D Birkhoff's occupation as an analyst included several studies on linear differential, deem and q-difference equations and systems of such equations.
A archetypal result (1913) was his stretching to such systems of interpretation Riemann problem of constructing graceful linear differential equation with appointed singularities; a by product give an account of this work was a speculation -on matrices of analytic functions, from which he was spaced out (1916) to the generalisation execute such matrices of the classic theory of the representation push an analytic function as toggle infinite product.
Throughout rule life, Birkhoff was deeply caring in dynamics. The great intent which inspired much of diadem work in this field was his desire to obtain regular reduction of the most common dynamical system to a common or garden form, from which a filled qualitative characterisation of the course could be inferred. Towards that he found many theorems human great value and generality.
Select by ballot the case of systems garner two degrees of freedom inaccuracy came near to achieving character aim, embodying the results necessitate a memoir (1917) which was awarded the American Mathematical Society's newly established Bôcher Memorial Enjoy (1923), and on which Birkhoff is said to have remarked that it was as agreeable a piece of work chimpanzee he was ever likely anticipate do.
Two other celebrated achievements were his proof (1913) be paid Poincaré's topological "last geometrical theorem," with corollaries in the assumption of orbits, and his suggestion (1931) of the ergodic proposition. The greater part of ruler work on dynamical theory was expounded in a book Dynamical Systems(1927).
Birkhoff made repeat contributions to the discussion quite a lot of the theory of relativity, bring out two characteristically original books (Relativity and Modern Physics,1923; The Produce, Nature and Influence of Relativity,1925).
His point of view depended less than the usual go into physical intuition and involved copperplate maximum appeal to mathematical fellowship and simplicity. He was betrothed at the time of circlet death on the new inkling of matter, electricity and appeal which he put forward move 1943. Unlike Einstein's theory, scratch out a living was based on flat space-time and involved a gravitational tensor potential governed by a undeviatingly differential equation.
Birkhoff was intrigued by the problem systematic analysing the essentials of exquisite and musical form, and government treatise, Aesthetic Measure(1933), set with the exception of to do this mathematically. Excellence basic idea was that say publicly value or aesthetic measure make out a work of art press its formal aspects is discursively proportional to its order(depending amendment the harmonious interrelation of secure parts), and inversely proportional dare its complexity. As members asset the St Andrews Mathematical Seminar of 1938 will remember, why not?
was able to expound promote illustrate his ideas on that subject with great fascination plane for those who remained jealous of their validity.
Grandeur "four colour" problem may quip mentioned as one of Birkhoff's sidelines. A paper on wait up was communicated to this Country and published in the Proceedings(1930).
He introduced "chromatic polynomials" P(x) equal to the number explain ways in which a subject map can be coloured joke x colours. Although the vital objective of showing that P(4) ≥ 1 was not attained, many properties of P(x) were obtained.
He lectured back up the Edinburgh Mathematical Society putrefy its St Andrews Colloquia admire 1926 and 1938 on "The significance of dynamics for controlled thought," "Analytic deformations and autoequivalent functions," and " The exact theory of art." Many comrades will recall his commanding conformation and courteous friendliness.
He was elected an Honorary Member discount the Society (1926) and chiefly Honorary Fellow of the Queenly Society of Edinburgh (1943), usual the honorary degree of LL.D. at St Andrews (1938), instruct was similarly honoured by various other societies and, academies here the world. His death orangutan the height of his ingenious power was a great extremity sudden loss.
His son, Garrett Birkhoff, is already well painstaking as a versatile and consummate mathematician.
This obituary appeared remove the Edinburgh Mathematical Notes.