Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several...

More unsolved problems in mathematics In mathematics, particularly in dynamical systems, the Hilbert–Arnold problem is an unsolved problem concerning the...

Hilbert's thirteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It entails proving whether...

Hilbert's 16th problem was posed by David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900, as part of his list...

two-variable functions, thereby solving Hilbert's thirteenth problem. This is the Kolmogorov–Arnold representation theorem. Arnold obtained his PhD in 1961, with...

1900, he presented a collection of problems that set a course for mathematical research of the 20th century. Hilbert and his students contributed to establishing...

propose a list of problems for the 21st century. Arnold's inspiration came from the list of Hilbert's problems that had been published at the beginning of...

classification for diagonalizable actions in higher-rank groups. Hilbert–Arnold problem – is there a uniform bound on limit cycles in generic finite-parameter...

functions and summing.: 180  The Kolmogorov–Arnold representation theorem is closely related to Hilbert's 13th problem. In his Paris lecture at the International...

deals with, among other things, what he calls the "infinitesimal Hilbert's sixteenth problem", which asks what one can say about the number and location of...

Arnold Johannes Wilhelm Sommerfeld (German: [ˈaʁnɔlt joˈhanəs ˈvɪlhɛlm ˈzɔmɐˌfɛlt]; 5 December 1868 – 26 April 1951) was a German theoretical physicist...

ISBN 978-3-642-86649-4. Van Winter, Clasine (1970). "The n-body problem on a Hilbert space of analytic functions". In Gilbert, Robert P.; Newton, Roger...

a separable complex Hilbert space H {\displaystyle {\mathcal {H}}} . This vector is postulated to be normalized under the Hilbert space's inner product...

(separable) complex Hilbert space H {\displaystyle {\mathcal {H}}} . This vector is postulated to be normalized under the Hilbert space inner product...

demonstrating that this was always possible. However, Arnold himself considered the genuine Hilbert problem to be whether for septics their solutions may be...

Hilbert decided to lend an organizing hand to formalizing the sciences, starting with physics. In 1912, Hilbert asked his friend and colleague Arnold...

any value of αβ is a transcendental number. This is the famous 7th Hilbert's problem. Gelfond proved a special case of the theorem in 1929 when he was...

Landé was sent by Arnold Sommerfeld, his thesis advisor at the University of Munich, to be a special assistant for physics to David Hilbert at the University...

diffeomorphism Vladimir Arnold, an author of the Kolmogorov–Arnold–Moser theorem in dynamical systems, solved Hilbert's 13th problem, raised the ADE classification...

This position led to the Brouwer–Hilbert controversy, in which Brouwer sparred with his formalist colleague David Hilbert. Brouwer's ideas were subsequently...

spelling Dmitry) was a Soviet mathematician famous for his work on Hilbert's sixteenth problem and the related Gudkov's conjecture in algebraic geometry. He...

UCLA in 1962 under Angus Taylor with a dissertation entitled Banach and Hilbert Spaces of Analytic Functions, where he later lectured. At IBM, he taught...

Hilbert spaces, such as the distinction between bounded and unbounded operators; questions of convergence (whether the limit of a sequence of Hilbert-space...

Heaviside (1850–1925) Jules Henri Poincaré (1854–1912) David Hilbert (1862–1943) Arnold Sommerfeld (1868–1951) Constantin Carathéodory (1873–1950) Albert...

vector fields of given degree. The infinitesimal 16th Hilbert problem, formulated by V. I. Arnold, is to decide if there exists an upper bound for the...

differential equations.: 72  The inverse scattering problem is equivalent to a Riemann–Hilbert factorization problem, at least in the case of equations of one space...

David Hilbert in his 23 problems for the advancement of mathematical science, considered the axiomatization of physics as his sixth problem. The problem remains...

include Felix Klein's Erlangen program, Hilbert's problems, Langlands program, and the Millennium Prize Problems. In the Mathematics Subject Classification...

Poisson's equation a few years later. At the start of the 20th century, David Hilbert studied the eigenvalues of integral operators by viewing the operators...

more general inverse spectral methods (often reducible to Riemann–Hilbert problems), which generalize local linear methods like Fourier analysis to nonlocal...