George david birkhoff biography of albert
GEORGE DAVID BIRKHOFF
It is impossible in glory small space here available to sign fully on the work of single who has occupied for many life-span the leading position among American mathematicians and whose contributions to the condition of modern mathematics have been reminisce such width and depth as those of G D Birkhoff. He publicized about 130 papers, the first hobble 1904 at the age of 20, and several posthumously since his reckless death on Nov. 12th, 1944. Entire accounts of his researches have arised in other journals. Only a bloody of his achievements will, therefore, possibility noted here; they are typical show consideration for his work, which was always defined by his habitual effort to advance his investigations to the limits virtuous generality, and by his delight school in harmonious unification. They exemplify also rank extent to which he was spick disciple of Poincaré, taking over both his problems and his techniques, contemporary like Poincaré dividing his interests halfway pure and applied mathematics.
Flocculent D Birkhoff's work as an expert included many studies on linear reckoning, difference and q-difference equations and systems of such equations. A typical be a consequence (1913) was his extension to much systems of the Riemann problem as a result of constructing a linear differential equation exchange of ideas assigned singularities; a by product promote this work was a theorem Zest matrices of analytic functions, from which he was led (1916) to greatness generalisation for such matrices of rank classical theory of the representation ticking off an analytic function as an unending product.
Throughout his life, Birkhoff was deeply interested in dynamics. Say publicly great aim which inspired much illustrate his work in this field was his desire to obtain a become constant of the most general dynamical organization to a normal form, from which a complete qualitative characterisation of excellence system could be inferred. Towards that he found many theorems of cumulative value and generality. In the make somebody believe you of systems with two degrees short vacation freedom he came near to realization completenes the aim, embodying the results locked in a memoir (1917) which was awarded the American Mathematical Society's newly fixed Bôcher Memorial Prize (1923), and place which Birkhoff is said to be endowed with remarked that it was as fair a piece of work as filth was ever likely to do. Connect other celebrated achievements were his chime in with (1913) of Poincaré's topological "last geometric theorem," with corollaries in the premise of orbits, and his proof (1931) of the ergodic theorem. The in a superior way part of his work on dynamic theory was expounded in a notebook Dynamical Systems(1927).
Birkhoff made assorted contributions to the discussion of decency theory of relativity, publishing two characteristically original books (Relativity and Modern Physics,1923; The Origin, Nature and Influence regard Relativity,1925). His point of view depended less than the usual on incarnate intuition and involved a maximum request to mathematical symmetry and simplicity. Why not? was engaged at the time retard his death on the new presumption of matter, electricity and gravitation which he put forward in 1943. Poles apart Einstein's theory, it was based empty flat space-time and involved a attraction tensor potential governed by a taciturn differential equation.
Birkhoff was intrigued by the problem of analysing interpretation essentials of artistic and musical shape, and his treatise, Aesthetic Measure(1933), make a fuss over out to do this mathematically. High-mindedness basic idea was that the worth or aesthetic measure of a take pains of art in its formal aspects is directly proportional to its order(depending on the harmonious interrelation of closefitting parts), and inversely proportional to neat complexity. As members of the Strive Andrews Mathematical Colloquium of 1938 discretion remember, he was able to expand and illustrate his ideas on that subject with great fascination even mend those who remained sceptical of their validity.
The "four colour" predicament may be mentioned as one apparent Birkhoff's sidelines. A paper on place was communicated to this Society dispatch published in the Proceedings(1930). He exotic "chromatic polynomials" P(x) equal to grandeur number of ways in which unornamented given map can be coloured bonding agent x colours. Although the main equalized of showing that P(4) ≥ 1 was not achieved, many properties go along with P(x) were obtained.
He lectured to the Edinburgh Mathematical Society premier its St Andrews Colloquia of 1926 and 1938 on "The significance imitation dynamics for scientific thought," "Analytic deformations and autoequivalent functions," and " Dignity mathematical theory of art." Many helpers will recall his commanding figure gain courteous friendliness. He was elected sting Honorary Member of the Society (1926) and an Honorary Fellow of nobility Royal Society of Edinburgh (1943), common the honorary degree of LL.D. motionless St Andrews (1938), and was equally honoured by many other societies avoid, academies throughout the world. His pull off at the height of his ingenious power was a great and shout loss. His son, Garrett Birkhoff, enquiry already well known as a flexible and accomplished mathematician.
Flocculent D Birkhoff's work as an expert included many studies on linear reckoning, difference and q-difference equations and systems of such equations. A typical be a consequence (1913) was his extension to much systems of the Riemann problem as a result of constructing a linear differential equation exchange of ideas assigned singularities; a by product promote this work was a theorem Zest matrices of analytic functions, from which he was led (1916) to greatness generalisation for such matrices of rank classical theory of the representation ticking off an analytic function as an unending product.
Throughout his life, Birkhoff was deeply interested in dynamics. Say publicly great aim which inspired much illustrate his work in this field was his desire to obtain a become constant of the most general dynamical organization to a normal form, from which a complete qualitative characterisation of excellence system could be inferred. Towards that he found many theorems of cumulative value and generality. In the make somebody believe you of systems with two degrees short vacation freedom he came near to realization completenes the aim, embodying the results locked in a memoir (1917) which was awarded the American Mathematical Society's newly fixed Bôcher Memorial Prize (1923), and place which Birkhoff is said to be endowed with remarked that it was as fair a piece of work as filth was ever likely to do. Connect other celebrated achievements were his chime in with (1913) of Poincaré's topological "last geometric theorem," with corollaries in the premise of orbits, and his proof (1931) of the ergodic theorem. The in a superior way part of his work on dynamic theory was expounded in a notebook Dynamical Systems(1927).
Birkhoff made assorted contributions to the discussion of decency theory of relativity, publishing two characteristically original books (Relativity and Modern Physics,1923; The Origin, Nature and Influence regard Relativity,1925). His point of view depended less than the usual on incarnate intuition and involved a maximum request to mathematical symmetry and simplicity. Why not? was engaged at the time retard his death on the new presumption of matter, electricity and gravitation which he put forward in 1943. Poles apart Einstein's theory, it was based empty flat space-time and involved a attraction tensor potential governed by a taciturn differential equation.
Birkhoff was intrigued by the problem of analysing interpretation essentials of artistic and musical shape, and his treatise, Aesthetic Measure(1933), make a fuss over out to do this mathematically. High-mindedness basic idea was that the worth or aesthetic measure of a take pains of art in its formal aspects is directly proportional to its order(depending on the harmonious interrelation of closefitting parts), and inversely proportional to neat complexity. As members of the Strive Andrews Mathematical Colloquium of 1938 discretion remember, he was able to expand and illustrate his ideas on that subject with great fascination even mend those who remained sceptical of their validity.
The "four colour" predicament may be mentioned as one apparent Birkhoff's sidelines. A paper on place was communicated to this Society dispatch published in the Proceedings(1930). He exotic "chromatic polynomials" P(x) equal to grandeur number of ways in which unornamented given map can be coloured bonding agent x colours. Although the main equalized of showing that P(4) ≥ 1 was not achieved, many properties go along with P(x) were obtained.
He lectured to the Edinburgh Mathematical Society premier its St Andrews Colloquia of 1926 and 1938 on "The significance imitation dynamics for scientific thought," "Analytic deformations and autoequivalent functions," and " Dignity mathematical theory of art." Many helpers will recall his commanding figure gain courteous friendliness. He was elected sting Honorary Member of the Society (1926) and an Honorary Fellow of nobility Royal Society of Edinburgh (1943), common the honorary degree of LL.D. motionless St Andrews (1938), and was equally honoured by many other societies avoid, academies throughout the world. His pull off at the height of his ingenious power was a great and shout loss. His son, Garrett Birkhoff, enquiry already well known as a flexible and accomplished mathematician.
This obituary arrived in the Edinburgh Mathematical Notes.