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profile Edward Nelson

Edward Nelson (May 4, 1932 – September 10, 2014) was a professor in the Mathematics Department at Princeton University. He was known for his work on mathematical physics and mathematical logic. In mathematical logic, he was noted especially for his internal set theory, and his controversial views on ultrafinitism and the consistency of arithmetic. He also wrote on the relationship between religion and mathematics. Nelson was born in Decatur, Georgia. He received his Ph.D. in 1955 from the University of Chicago, where he worked with Irving Segal. He was a member of the Institute for Advanced Study from 1956 to 1959. He held a position at Princeton University starting in 1959, attaining the rank of professor there in 1964 and retiring in 2013. In 2012 he became a fellow of the American Mathematical Society. He died in Princeton, New Jersey on September 10, 2014. Nelson made contributions to the theory of infinite-dimensional group representations, the mathematical treatment of quantum field theory, the use of stochastic processes in quantum mechanics, and the reformulation of probability theory in terms of non-standard analysis. For many years he worked on mathematical physics and probability theory, and retained a residual interest in these fields, particularly in possible extensions of stochastic mechanics to field theory. In 1950, Nelson formulated a popular variant of the four color problem. What is the chromatic number, denoted \chi, of the plane? In more detail, what is the smallest number of colors sufficient for coloring the points of the Euclidean plane in such a way that no two points of the same color are unit distance apart? We know by simple arguments that 4 ≤ χ ≤ 7. The problem was introduced to a wide mathematical audience by Martin Gardner in his October 1960 Mathematical Games column. The chromatic number problem, also now known as the Hadwiger–Nelson problem, was also a favorite of Paul Erdős, who mentioned it frequently in his problems lectures. In the later part of his career, he worked on mathematical logic and the foundations of mathematics. One of his goals was to extend IST (Internal Set Theory—a version of a portion of Abraham Robinson's non-standard analysis) in a natural way to include external functions and sets, in a way that provides an external function with specified properties unless there is a finitary obstacle to its existence. Other work centered on fragments of arithmetic, studying the divide between those theories interpretable in Raphael Robinson's Arithmetic and those that are not; computational complexity, including the problem of whether P is equal to NP or not; and automated proof checking. In September 2011, Nelson announced that he had proved that Peano arithmetic was logically inconsistent. An error was found in the proof, and he retracted the claim.

profile Bei-Lok Hu

Prof Bei-Lok Hu got his PhD in theoretical physics from Princeton University in 1972 under the late Professor John A. Wheeler. After postdoctoral work at Stanford University, University of California, Berkeley and Santa Barbara in mathematics, physics and astrophysics, he was appointed an honorary research fellow at Harvard University in 1979 before he assumed his current position at the University of Maryland in 1980. Prof Hu's research in the 70's was on quantum field theory in curved spacetime with applications to quantum processes in the early universe, for that work he was elected Fellow of the American Physical Society. Professor Hu began pioneering work on nonequilibrium quantum field theory in the 80's which resulted in a book with Dr. Calzetta by this title published in 2008 in the Cambridge Monograph in Mathematical Physics series. In 1990 Prof Hu began his seminal work on quantum decoherence and non-Markovian processes of open quantum systems. Since 2000 he has been studying quantum entanglement dynamics in atomic-optical systems with applications to quantum information processing. He is a founding fellow of the Joint Quantum Institute dedicated to the advancement of quantum science and its applications. He is also the chief architect in the inauguration of the International Society for Relativistic Quantum Information in 2010. His current research interest is on foundational issues of quantum and statistical mechanics behind macroscopic quantum phenomena and quantum thermodynamics. Prof Hu is a world-renowned leader in quantum gravity research. His long-held critically independent viewpoint that general relativity is a hydrodynamic theory first presented at the Second Sakharov Conference in 1996 has, alongside with his Maryland colleague Jacobson's 1995 paper on viewing Einstein's equation as an equation of state, as well as work from the condensed matter community by Volovik and Wen, helped ushered in a vibrant field known today as emergent gravity. (source: HKUST Jockey Club Institute for Advanced Study)

profile Gerard ’t Hooft

His work concentrates on gauge theory, black holes, quantum gravity and fundamental aspects of quantum mechanics. His contributions to physics include a proof that gauge theories are renormalizable, dimensional regularization, and the holographic principle. After obtaining his doctorate 't Hooft went to CERN in Geneva, where he had a fellowship. He further refined his methods for Yang–Mills theories with Veltman (who went back to Geneva). In this time he became interested in the possibility that the strong interaction could be described as a massless Yang–Mills theory, i.e. one of a type that he had just proved to be renormalizable and hence be susceptible to detailed calculation and comparison with experiment. According to his calculations, this type of theory possessed just the right kind of scaling properties (asymptotic freedom) that this theory should have according to deep inelastic scattering experiments. This was contrary to popular perception of Yang–Mills theories at the time, that like gravitation and electrodynamics, their intensity should decrease with increasing distance between the interacting particles; such conventional behaviour with distance was unable to explain the results of deep inelastic scattering, whereas 't Hooft's calculations could. When he mentioned his results at a small conference at Marseilles in 1972, Kurt Symanzik urged him to publish this result. He did not, and the result was eventually rediscovered and published by Hugh David Politzer, David Gross, and Frank Wilczek in 1973, which led to them earning the 2004 Nobel Prize in Physics.

profile Basil J. Hiley

Basil J. Hiley is a British quantum physicist and professor emeritus of the University of London. He received the Majorana Prize "Best person in physics" in 2012. Long-time co-worker of David Bohm, Hiley is known for his work with Bohm on implicate orders and for his work on algebraic descriptions of quantum physics in terms of underlying symplectic and orthogonal Clifford algebras. Hiley co-authored the book The Undivided Universe with David Bohm, which is considered the main reference for Bohm's interpretation of quantum theory. The work of Bohm and Hiley has been characterized as primarily addressing the question "whether we can have an adequate conception of the reality of a quantum system, be this causal or be it stochastic or be it of any other nature" and meeting the scientific challenge of providing a mathematical description of quantum systems that matches the idea of an implicate order. Basil Hiley was born 1935 in Burma, where his father worked for the military for the British Raj. He moved to Hampshire, England, at the age of twelve, where he attended secondary school. His interest in science was stimulated by his teachers at secondary school and by books, in particular The Mysterious Universe by James Hopwood Jeans and Mr Tompkins in Wonderland by George Gamow. Hiley performed undergraduate studies at King's College London. He published a paper in 1961 on the random walk of a macromolecule, followed by further papers on the Ising model, and on lattice constant systems defined in graph theoretical terms. In 1962 he obtained his PhD from King's College in condensed matter physics, more specifically on cooperative phenomena in ferromagnets and long chain polymer models, under the supervision of Cyril Domb and Michael Fisher. Hiley first met David Bohm during a week-end meeting organized by the student society of King's College at Cumberland Lodge, where Bohm held a lecture. In 1961 Hiley was appointed assistant lecturer at Birkbeck College, where Bohm had taken the chair of Theoretical Physics shortly before. Hiley wanted to investigate how physics could be based on a notion of process, and he found that David Bohm held similar ideas. He reports that during the seminars he held together with Roger Penrose he was particularly fascinated by John Wheeler's "sum over three geometries" ideas that he was using to quantise gravity. Hiley worked with David Bohm for many years on fundamental problems of theoretical physics. Initially Bohm's model of 1952 did not feature in their discussions; this changed when Hiley asked himself whether the "Einstein-Schrödinger equation", as Wheeler called it, might be found by studying the full implications of that model. They worked together closely for three decades. Together they wrote many publications, including the book The Undivided Universe: An Ontological Interpretation of Quantum Theory, published 1993, which is now considered the major reference for Bohm's interpretation of quantum theory. In 1995, Basil Hiley was appointed to the chair in physics at Birkbeck College at the University of London. He was awarded the 2012 Majorana Prize in the category The Best Person in Physics for the algebraic approach to quantum mechanics and furthermore in recognition of ″his paramount importance as natural philosopher, his critical and open minded attitude towards the role of science in contemporary culture". (source: Wikipedia)