Cambridge University Press
Cambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by King Henry VIII in 1534, it is the world's oldest publishing house and the second-largest university press in the world, it holds letters patent as the Queen's Printer. The press mission is "to further the University's mission by disseminating knowledge in the pursuit of education and research at the highest international levels of excellence". Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. With a global sales presence, publishing hubs, offices in more than 40 countries, it publishes over 50,000 titles by authors from over 100 countries, its publishing includes academic journals, reference works and English language teaching and learning publications. Cambridge University Press is a charitable enterprise that transfers part of its annual surplus back to the university. Cambridge University Press is both the oldest publishing house in the world and the oldest university press.
It originated from letters patent granted to the University of Cambridge by Henry VIII in 1534, has been producing books continuously since the first University Press book was printed. Cambridge is one of the two privileged presses. Authors published by Cambridge have included John Milton, William Harvey, Isaac Newton, Bertrand Russell, Stephen Hawking. University printing began in Cambridge when the first practising University Printer, Thomas Thomas, set up a printing house on the site of what became the Senate House lawn – a few yards from where the press's bookshop now stands. In those days, the Stationers' Company in London jealously guarded its monopoly of printing, which explains the delay between the date of the university's letters patent and the printing of the first book. In 1591, Thomas's successor, John Legate, printed the first Cambridge Bible, an octavo edition of the popular Geneva Bible; the London Stationers objected strenuously. The university's response was to point out the provision in its charter to print "all manner of books".
Thus began the press's tradition of publishing the Bible, a tradition that has endured for over four centuries, beginning with the Geneva Bible, continuing with the Authorized Version, the Revised Version, the New English Bible and the Revised English Bible. The restrictions and compromises forced upon Cambridge by the dispute with the London Stationers did not come to an end until the scholar Richard Bentley was given the power to set up a'new-style press' in 1696. In July 1697 the Duke of Somerset made a loan of £200 to the university "towards the printing house and presse" and James Halman, Registrary of the University, lent £100 for the same purpose, it was in Bentley's time, in 1698, that a body of senior scholars was appointed to be responsible to the university for the press's affairs. The Press Syndicate's publishing committee still meets and its role still includes the review and approval of the press's planned output. John Baskerville became University Printer in the mid-eighteenth century.
Baskerville's concern was the production of the finest possible books using his own type-design and printing techniques. Baskerville wrote, "The importance of the work demands all my attention. Caxton would have found nothing to surprise him if he had walked into the press's printing house in the eighteenth century: all the type was still being set by hand. A technological breakthrough was badly needed, it came when Lord Stanhope perfected the making of stereotype plates; this involved making a mould of the whole surface of a page of type and casting plates from that mould. The press was the first to use this technique, in 1805 produced the technically successful and much-reprinted Cambridge Stereotype Bible. By the 1850s the press was using steam-powered machine presses, employing two to three hundred people, occupying several buildings in the Silver Street and Mill Lane area, including the one that the press still occupies, the Pitt Building, built for the press and in honour of William Pitt the Younger.
Under the stewardship of C. J. Clay, University Printer from 1854 to 1882, the press increased the size and scale of its academic and educational publishing operation. An important factor in this increase was the inauguration of its list of schoolbooks. During Clay's administration, the press undertook a sizeable co-publishing venture with Oxford: the Revised Version of the Bible, begun in 1870 and completed in 1885, it was in this period as well that the Syndics of the press turned down what became the Oxford English Dictionary—a proposal for, brought to Cambridge by James Murray before he turned to Oxford. The appointment of R. T. Wright as Secretary of the Press Syndicate in 1892 marked the beginning of the press's development as a modern publishing business with a defined editorial policy and administrative structure, it was Wright who devised the plan for one of the most distinctive Cambridge contributions to publishing—the Cambridge Histories. The Cambridge Modern History was published
Hairy ball theorem
The hairy ball theorem of algebraic topology states that there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres. For the ordinary sphere, or 2‑sphere, if f is a continuous function that assigns a vector in R3 to every point p on a sphere such that f is always tangent to the sphere at p there is at least one p such that f = 0. In other words, whenever one attempts to comb a hairy ball flat, there will always be at least one tuft of hair at one point on the ball; the theorem was first stated by Henri Poincaré in the late 19th century. This is famously stated as "you can't comb a hairy ball flat without creating a cowlick", "you can't comb the hair on a coconut", or sometimes "every cow must have at least one cowlick." It can be written as, "Every smooth vector field on a sphere has a singular point." It was first proven in 1912 by Brouwer. From a more advanced point of view: every zero of a vector field has a "index", it can be shown that the sum of all of the indices at all of the zeros must be two.
Therefore, there must be at least one zero. This is a consequence of the Poincaré–Hopf theorem. In the case of the torus, the Euler characteristic is 0. In this regard, it follows that for any compact regular 2-dimensional manifold with non-zero Euler characteristic, any continuous tangent vector field has at least one zero. A curious meteorological application of this theorem involves considering the wind as a vector defined at every point continuously over the surface of a planet with an atmosphere; as an idealisation, take wind to be a two-dimensional vector: suppose that relative to the planetary diameter of the Earth, its vertical motion is negligible. One scenario, in which there is no wind, corresponds to a field of zero-vectors; this scenario is uninteresting from the point of view of this theorem, physically unrealistic. In the case where there is at least some wind, the Hairy Ball Theorem dictates that at all times there must be at least one point on a planet with no wind at all and therefore a tuft.
This corresponds to the above statement that there will always be p such that f = 0. In a physical sense, this zero-wind point will be the center of a anticyclone. In brief the theorem dictates that, given at least some wind on Earth, there must at all times be a cyclone or anticyclone somewhere. Note that the center with zero wind can be arbitrarily large or small. Mathematical consistency dictates the wind forms a cyclonic wind pattern for at least one point on the planet, but this does not require the cyclone be a violent storm; this is not true as the air above the earth has multiple layers, but for each layer there must be a point with zero horizontal windspeed. A common problem in computer graphics is to generate a non-zero vector in R3, orthogonal to a given non-zero one. There is no single continuous function; this is a corollary of the hairy ball theorem. To see this, consider the given vector as the radius of a sphere and note that finding a non-zero vector orthogonal to the given one is equivalent to finding a non-zero vector, tangent to the surface of that sphere where it touches the radius.
However, the hairy ball theorem says there exists no continuous function that can do this for every point on the sphere. There is a related argument from algebraic topology, using the Lefschetz fixed-point theorem. Since the Betti numbers of a 2-sphere are 1, 0, 1, 0, 0... the Lefschetz number of the identity mapping is 2. By integrating a vector field we get a one-parameter group of diffeomorphisms on the sphere. Therefore, they all have Lefschetz number 2, also. Hence they have fixed points; some more work would be needed to show that this implies there must be a zero of the vector field. It does suggest the correct statement of the more general Poincaré-Hopf index theorem. A consequence of the hairy ball theorem is that any continuous function that maps an even-dimensional sphere into itself has either a fixed point or a point that maps onto its own antipodal point; this can be seen by transforming the function into a tangential vector field. Let s be the function mapping the sphere to itself, let v be the tangential vector function to be constructed.
For each point p, construct the stereographic projection of s with p as the point of tangency. V is the displacement vector of this projected point relative to p. According to the hairy ball theorem, there is a p such that v = 0, so that s = p; this argument breaks down only if there exists a point p for which s is the antipodal point of p, since such a point is the only one that cannot be stereographically projected onto the tangent plane of p. The connection with the Euler characteristic χ suggests the correct generalisation: the 2n-sphere has no non-vanishing vector field for n ≥ 1; the difference between and odd dimensions is that, because the only nonzero Betti numbers of the m-sphere are b0 and bm, their alternating sum χ is 2 for m and 0 for m odd. Eisenberg, Murray.
Adolf Hurwitz was a German mathematician who worked on algebra, analysis and number theory. He was born in Hildesheim, former Kingdom of Hanover, to a Jewish family and died in Zürich, in Switzerland, his father Salomon Hurwitz, a merchant, was not well off. Hurwitz's mother, Elise Wertheimer, died. Family records indicate that he had siblings and cousins. Hurwitz entered the Realgymnasium Andreanum in Hildesheim in 1868, he was taught mathematics there by Hermann Schubert. Schubert persuaded Hurwitz's father to allow him to go to university, arranged for Hurwitz to study with Felix Klein at Munich. Salomon Hurwitz could not afford to send his son to university, but his friend, Mr Edwards, agreed to help out financially. Hurwitz entered the University of Munich in 1877, aged 18, he spent one year there attending lectures by Klein, before spending the academic year 1877–1878 at the University of Berlin where he attended classes by Kummer and Kronecker, after which he returned to Munich. In October 1880, Felix Klein moved to the University of Leipzig.
Hurwitz followed him there, became a doctoral student under Klein's direction, finishing a dissertation on elliptic modular functions in 1881. Following two years at the University of Göttingen, in 1884 he was invited to become an Extraordinary Professor at the Albertus Universität in Königsberg. Following the departure of Frobenius, Hurwitz took a chair at the Eidgenössische Polytechnikum Zürich in 1892, remained there for the rest of his life. Throughout his time in Zürich, Hurwitz suffered from continual ill health, caused when he contracted typhoid whilst a student in Munich, he suffered from severe migraines, in 1905, his kidneys became diseased and he had one removed. He was one of the early students of the Riemann surface theory, used it to prove many of the foundational results on algebraic curves; this work anticipates a number of theories, such as the general theory of algebraic correspondences, Hecke operators, Lefschetz fixed-point theorem. He had deep interests in number theory, he studied the maximal order theory for the quaternions, defining the Hurwitz quaternions that are now named for him.
In the field of control systems and dynamical systems theory he derived the Routh–Hurwitz stability criterion for determining whether a linear system is stable in 1895, independently of Edward John Routh who had derived it earlier by a different method. In 1884, whilst at Königsberg, Hurwitz met and married Ida Samuel, the daughter of a professor in the faculty of medicine, they had three children. Hurwitz, A. 1898. Ueber die Composition der quadratischen Formen von beliebig vielen Variablen. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 1898, pp. 309–316. Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen. Edited and supplemented by a section on geometric Funktionentheorie by Richard Courant. Springer, Berlin 1922 Mathematische Werke. Publlished by the Department of Mathematics and Physics of the Eidgenössischen Technischen Hochschule in Zürich. 2 vols. Birkhäuser, Basel 1932–1933 Übungen zur Zahlentheorie. 1891–1918. Translated by Barbara Aquilino.
As a duplicated manuscript edited by Beat Glaus. ETH-Bibliothek, Zürich 1993, doi:10.3929/ethz-a-001313794. Lectures on Number Theory. Edited for publication by Nikolaos Kritikos. Translated with some additional material by William C. Schulz. Springer, New York 1986, ISBN 0-387-96236-0. Karl Weierstraß: Einleitung in die Theorie der analytischen Funktionen. Vorlesung Berlin 1878. In a transcript by Adolf Hurwitz. Edited by Peter Ullrich. Vieweg, Braunschweig 1988, ISBN 3-528-06334-3. Adolf Hurwitz at the Mathematics Genealogy Project LMS obituary O'Connor, John J.. Recording of the 2008 "Hurwitz Memorial Lecture"
John Frank Adams FRS was a British mathematician, one of the major contributors to homotopy theory. He was born in Woolwich, a suburb in south-east London, attended Bedford School, he soon switched to algebraic topology. He received his Ph. D. from the University of Cambridge in 1956. His thesis, written under the direction of Shaun Wylie, was titled On spectral sequences and self-obstruction invariants, he held the Fielden Chair at the University of Manchester, became Lowndean Professor of Astronomy and Geometry at the University of Cambridge. He was elected a Fellow of the Royal Society in 1964, his interests included mountaineering—he would demonstrate how to climb right round a table at parties —and the game of Go. He died in a car accident in Brampton, Cambridgeshire. There is a memorial plaque for him in the Chapel of Cambridge. In the 1950s, homotopy theory was at an early stage of development, unsolved problems abounded. Adams made a number of important theoretical advances in algebraic topology, but his innovations were always motivated by specific problems.
Influenced by the French school of Henri Cartan and Jean-Pierre Serre, he reformulated and strengthened their method of killing homotopy groups in spectral sequence terms, creating the basic tool of stable homotopy theory now known as the Adams spectral sequence. This begins with Ext groups calculated over the ring of cohomology operations, the Steenrod algebra in the classical case, he used this spectral sequence to attack the celebrated Hopf invariant one problem, which he solved in a 1960 paper by making a deep analysis of secondary cohomology operations. The Adams–Novikov spectral sequence is an analogue of the Adams spectral sequence using an extraordinary cohomology theory in place of classical cohomology: it is a computational tool of great potential scope. Adams was a pioneer in the application of K-theory, he invented the Adams operations in K-theory. Adams introduced them in a 1962 paper to solve the famous vector fields on spheres problem. Subsequently he used them to investigate the Adams conjecture, concerned with the image of the J-homomorphism in the stable homotopy groups of spheres.
A paper of Adams and Michael F. Atiyah uses the Adams operations to give an elegant and much faster version of the above-mentioned Hopf invariant one result. In 1974 Adams became the first recipient of the Senior Whitehead Prize, awarded by the London Mathematical Society, he was a visiting scholar at the Institute for Advanced Study in 1957–58. Adams had many talented students, was influential in the development of algebraic topology in Britain and worldwide, his University of Chicago lectures were published in a 1996 series titled "Chicago Lectures in Mathematics Series", such as Lectures on Exceptional Lie Groups and Stable Homotopy and Generalised Homology ISBN 0-226-00524-0. The main mathematics research seminar room in the Alan Turing Building at the University of Manchester is named in his honour. Adams, J. Frank, May, J. Peter; the selected works of J. Frank Adams. Vol. I, Cambridge University Press, ISBN 0-521-41063-0, MR 1203312 Adams, J. Frank, May, J. Peter; the selected works of J. Frank Adams.
Vol. II, Cambridge University Press, ISBN 978-0-521-11068-6, MR 1203312 Frank Adams at Find a Grave
Beno Eckmann was a Swiss mathematician, a student of Heinz Hopf. Born in Bern, Eckmann received his master's degree from Eidgenössische Technische Hochschule Zürich in 1939, he studied there under Heinz Hopf, obtaining his Ph. D. in 1941. Eckmann was the 2008 recipient of the Albert Einstein Medal. Calabi–Eckmann manifolds, Eckmann–Hilton duality, the Eckmann–Hilton argument, the Eckmann–Shapiro lemma are named after Eckmann. Eckmann's son is mathematical physicist Jean-Pierre Eckmann. Beno Eckmann at the Mathematics Genealogy Project Biography of Beno Eckmann
Johann Karl August Radon was an Austrian mathematician. His doctoral dissertation was on the calculus of variations. Radon was born in Tetschen, Austria-Hungary, now Děčín, Czech Republic, he received his doctoral degree at the University of Vienna in 1910. He spent the winter semester 1910/11 at the University of Göttingen he was an assistant at the German Technical University in Brno, from 1912 to 1919 at the Technical University of Vienna. In 1913/14, he passed his habilitation at the University of Vienna. Due to his near-sightedness, he was exempt from the draft during wartime. In 1919, he was called to become Professor extraordinarius at the newly founded University of Hamburg, he was Ordinarius at the University of Breslau from 1928 to 1945. After a short stay at the University of Innsbruck he became Ordinarius at the Institute of Mathematics of the University of Vienna on 1 October 1946. In 1954/55, he was rector of the University of Vienna. In 1939, Radon became corresponding member of the Austrian Academy of Sciences, in 1947, he became a member.
From 1952 to 1956, he was Secretary of the Class of Science of this Academy. From 1948 to 1950, he was president of the Austrian Mathematical Society. Johann Radon married Maria Rigele, a secondary school teacher, in 1916, they had three sons who died young or young. Their daughter Brigitte, born in 1924, obtained a Ph. D. in mathematics at the University of Innsbruck and married the Austrian mathematician Erich Bukovics in 1950. Brigitte lives in Vienna. Radon, as Curt C. Christian described him in 1987 at the occasion of the unveiling of his brass bust at the University of Vienna, was a friendly, good-natured man esteemed by students and colleagues alike, a noble personality, he did make the impression of a quiet scholar, but he was sociable and willing to celebrate. He loved music, he played music with friends at home, being an excellent violinist himself, a good singer, his love for classical literature lasted through all his life. In 2003, the Austrian Academy of Sciences founded an Institute for Computational and Applied Mathematics and named it after Johann Radon.
Radon is known for a number of lasting contributions, including: his part in the Radon–Nikodym theorem. He is the first to make use of the so-called Radon–Riesz property. O'Connor, John J.. Johann Radon at the Mathematics Genealogy Project Johann Radon Institute for Computational and Applied Mathematics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize and predict natural phenomena. This is in contrast to experimental physics; the advancement of science depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations. For example, while developing special relativity, Albert Einstein was concerned with the Lorentz transformation which left Maxwell's equations invariant, but was uninterested in the Michelson–Morley experiment on Earth's drift through a luminiferous aether. Conversely, Einstein was awarded the Nobel Prize for explaining the photoelectric effect an experimental result lacking a theoretical formulation. A physical theory is a model of physical events, it is judged by the extent. The quality of a physical theory is judged on its ability to make new predictions which can be verified by new observations.
A physical theory differs from a mathematical theorem in that while both are based on some form of axioms, judgment of mathematical applicability is not based on agreement with any experimental results. A physical theory differs from a mathematical theory, in the sense that the word "theory" has a different meaning in mathematical terms. A physical theory involves one or more relationships between various measurable quantities. Archimedes realized that a ship floats by displacing its mass of water, Pythagoras understood the relation between the length of a vibrating string and the musical tone it produces. Other examples include entropy as a measure of the uncertainty regarding the positions and motions of unseen particles and the quantum mechanical idea that energy are not continuously variable. Theoretical physics consists of several different approaches. In this regard, theoretical particle physics forms a good example. For instance: "phenomenologists" might employ empirical formulas to agree with experimental results without deep physical understanding.
"Modelers" appear much like phenomenologists, but try to model speculative theories that have certain desirable features, or apply the techniques of mathematical modeling to physics problems. Some attempt to create approximate theories, called effective theories, because developed theories may be regarded as unsolvable or too complicated. Other theorists may try to unify, reinterpret or generalise extant theories, or create new ones altogether. Sometimes the vision provided by pure mathematical systems can provide clues to how a physical system might be modeled. Theoretical problems that need computational investigation are the concern of computational physics. Theoretical advances may consist in setting aside old, incorrect paradigms or may be an alternative model that provides answers that are more accurate or that can be more applied. In the latter case, a correspondence principle will be required to recover the known result. Sometimes though, advances may proceed along different paths. For example, an correct theory may need some conceptual or factual revisions.
However, an exception to all the above is the wave–particle duality, a theory combining aspects of different, opposing models via the Bohr complementarity principle. Physical theories become accepted if they are able to make correct predictions and no incorrect ones; the theory should have, at least as a secondary objective, a certain economy and elegance, a notion sometimes called "Occam's razor" after the 13th-century English philosopher William of Occam, in which the simpler of two theories that describe the same matter just as adequately is preferred. They are more to be accepted if they connect a wide range of phenomena. Testing the consequences of a theory is part of the scientific method. Physical theories can be grouped into three categories: mainstream theories, proposed theories and fringe theories. Theoretical physics began at least 2,300 years ago, under the Pre-socratic philosophy, continued by Plato and Aristotle, whose views held sway for a millennium. During the rise of medieval universities, the only acknowledged intellectual disciplines were the seven liberal arts of the Trivium like grammar and rhetoric and of the Quadrivium like arithmetic, geometry and astronomy.
During the Middle Ages and Renaissance, the concept of experimental science, the counterpoint to theory, began with scholars such as Ibn al-Haytham and Francis Bacon. As the Scientific Revolution gathered pace, the concepts of matter, space and causality began to acquire the form we know today, other sciences spun off from the rubric of natural philosophy, thus began the modern era of theory with the Copernican paradigm shift in astronomy, soon followed by Johannes Kepler's expressions for planetary orbits, which summarized the meticulous observations of Tycho Brahe.