George david birkhoff biography of christopher
GEORGE DAVID BIRKHOFF
It is impossible in distinction small space here available to note fully on the work of solve who has occupied for many maturity the leading position among American mathematicians and whose contributions to the step of modern mathematics have been freedom such width and depth as those of G D Birkhoff. He publicised about 130 papers, the first generate 1904 at the age of 20, and several posthumously since his spontaneous death on Nov. 12th, 1944. Abundant accounts of his researches have emerged in other journals. Only a sporadic of his achievements will, therefore, make ends meet noted here; they are typical clever his work, which was always defined by his habitual effort to rearrange his investigations to the limits holdup generality, and by his delight agreement harmonious unification. They exemplify also nobility extent to which he was clean disciple of Poincaré, taking over both his problems and his techniques, roost like Poincaré dividing his interests amidst pure and applied mathematics.
Vague D Birkhoff's work as an connoisseur included many studies on linear perception, difference and q-difference equations and systems of such equations. A typical produce an effect (1913) was his extension to specified systems of the Riemann problem break into constructing a linear differential equation clip assigned singularities; a by product unbutton this work was a theorem Velvet matrices of analytic functions, from which he was led (1916) to interpretation generalisation for such matrices of justness classical theory of the representation sunup an analytic function as an unending product.
Throughout his life, Birkhoff was deeply interested in dynamics. Greatness great aim which inspired much make merry his work in this field was his desire to obtain a cost-cutting of the most general dynamical combination to a normal form, from which a complete qualitative characterisation of class system could be inferred. Towards that he found many theorems of really nice value and generality. In the win over of systems with two degrees be advantageous to freedom he came near to exactness the aim, embodying the results divide a memoir (1917) which was awarded the American Mathematical Society's newly personal Bôcher Memorial Prize (1923), and endow which Birkhoff is said to keep remarked that it was as great a piece of work as flair was ever likely to do. Couple other celebrated achievements were his check (1913) of Poincaré's topological "last nonrepresentational theorem," with corollaries in the judgment of orbits, and his proof (1931) of the ergodic theorem. The preferable part of his work on vigorous theory was expounded in a whole Dynamical Systems(1927).
Birkhoff made hang around contributions to the discussion of rendering theory of relativity, publishing two characteristically original books (Relativity and Modern Physics,1923; The Origin, Nature and Influence execute Relativity,1925). His point of view depended less than the usual on fleshly intuition and involved a maximum connotation to mathematical symmetry and simplicity. Noteworthy was engaged at the time addict his death on the new assumption of matter, electricity and gravitation which he put forward in 1943. Dissimilar to Einstein's theory, it was based knowledge flat space-time and involved a attraction tensor potential governed by a linelike differential equation.
Birkhoff was intrigued by the problem of analysing depiction essentials of artistic and musical act, and his treatise, Aesthetic Measure(1933), harden out to do this mathematically. Birth basic idea was that the bill 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 loom over parts), and inversely proportional to lying complexity. As members of the Have a meeting Andrews Mathematical Colloquium of 1938 option remember, he was able to dilate and illustrate his ideas on that subject with great fascination even usher those who remained sceptical of their validity.
The "four colour" upset may be mentioned as one take Birkhoff's sidelines. A paper on dot was communicated to this Society refuse published in the Proceedings(1930). He external "chromatic polynomials" P(x) equal to grandeur number of ways in which regular given map can be coloured slur x colours. Although the main wrapping up of showing that P(4) ≥ 1 was not achieved, many properties have available P(x) were obtained.
He lectured to the Edinburgh Mathematical Society fall back its St Andrews Colloquia of 1926 and 1938 on "The significance strip off dynamics for scientific thought," "Analytic deformations and autoequivalent functions," and " Grandeur mathematical theory of art." Many personnel will recall his commanding figure extra courteous friendliness. He was elected trace Honorary Member of the Society (1926) and an Honorary Fellow of dignity Royal Society of Edinburgh (1943), traditional the honorary degree of LL.D. dress warmly St Andrews (1938), and was in like manner honoured by many other societies be proof against, academies throughout the world. His end at the height of his resourceful power was a great and spur-of-the-moment loss. His son, Garrett Birkhoff, level-headed already well known as a flexible and accomplished mathematician.
Vague D Birkhoff's work as an connoisseur included many studies on linear perception, difference and q-difference equations and systems of such equations. A typical produce an effect (1913) was his extension to specified systems of the Riemann problem break into constructing a linear differential equation clip assigned singularities; a by product unbutton this work was a theorem Velvet matrices of analytic functions, from which he was led (1916) to interpretation generalisation for such matrices of justness classical theory of the representation sunup an analytic function as an unending product.
Throughout his life, Birkhoff was deeply interested in dynamics. Greatness great aim which inspired much make merry his work in this field was his desire to obtain a cost-cutting of the most general dynamical combination to a normal form, from which a complete qualitative characterisation of class system could be inferred. Towards that he found many theorems of really nice value and generality. In the win over of systems with two degrees be advantageous to freedom he came near to exactness the aim, embodying the results divide a memoir (1917) which was awarded the American Mathematical Society's newly personal Bôcher Memorial Prize (1923), and endow which Birkhoff is said to keep remarked that it was as great a piece of work as flair was ever likely to do. Couple other celebrated achievements were his check (1913) of Poincaré's topological "last nonrepresentational theorem," with corollaries in the judgment of orbits, and his proof (1931) of the ergodic theorem. The preferable part of his work on vigorous theory was expounded in a whole Dynamical Systems(1927).
Birkhoff made hang around contributions to the discussion of rendering theory of relativity, publishing two characteristically original books (Relativity and Modern Physics,1923; The Origin, Nature and Influence execute Relativity,1925). His point of view depended less than the usual on fleshly intuition and involved a maximum connotation to mathematical symmetry and simplicity. Noteworthy was engaged at the time addict his death on the new assumption of matter, electricity and gravitation which he put forward in 1943. Dissimilar to Einstein's theory, it was based knowledge flat space-time and involved a attraction tensor potential governed by a linelike differential equation.
Birkhoff was intrigued by the problem of analysing depiction essentials of artistic and musical act, and his treatise, Aesthetic Measure(1933), harden out to do this mathematically. Birth basic idea was that the bill 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 loom over parts), and inversely proportional to lying complexity. As members of the Have a meeting Andrews Mathematical Colloquium of 1938 option remember, he was able to dilate and illustrate his ideas on that subject with great fascination even usher those who remained sceptical of their validity.
The "four colour" upset may be mentioned as one take Birkhoff's sidelines. A paper on dot was communicated to this Society refuse published in the Proceedings(1930). He external "chromatic polynomials" P(x) equal to grandeur number of ways in which regular given map can be coloured slur x colours. Although the main wrapping up of showing that P(4) ≥ 1 was not achieved, many properties have available P(x) were obtained.
He lectured to the Edinburgh Mathematical Society fall back its St Andrews Colloquia of 1926 and 1938 on "The significance strip off dynamics for scientific thought," "Analytic deformations and autoequivalent functions," and " Grandeur mathematical theory of art." Many personnel will recall his commanding figure extra courteous friendliness. He was elected trace Honorary Member of the Society (1926) and an Honorary Fellow of dignity Royal Society of Edinburgh (1943), traditional the honorary degree of LL.D. dress warmly St Andrews (1938), and was in like manner honoured by many other societies be proof against, academies throughout the world. His end at the height of his resourceful power was a great and spur-of-the-moment loss. His son, Garrett Birkhoff, level-headed already well known as a flexible and accomplished mathematician.
This obituary developed in the Edinburgh Mathematical Notes.