Many mathematicians reserve the term equation exclusively for the second type, to signify an equality which is not an identity.

Many mathematicians feel that to call their area a science is to downplay the importance of its aesthetic side, and its history in the traditional seven liberal arts ; others feel that to ignore its connection to the sciences is to turn a blind eye to the fact that the interface between mathematics and its applications in science and engineering has driven much development in mathematics.

Many great mathematicians of the past were preoccupied by numerical analysis, as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.

Many working mathematicians have been mathematical realists ; they see themselves as discoverers of naturally occurring objects.

Many practising mathematicians have been drawn to their subject because of a sense of beauty they perceive in it.

Many attempted to find a proof by contradiction, including Persian mathematicians Ibn al-Haytham ( Alhazen, 11th century ), Omar Khayyám ( 12th century ) and Nasīr al-Dīn al-Tūsī ( 13th century ), and the Italian mathematician Giovanni Girolamo Saccheri ( 18th century ).

Many famous mathematicians have studied such problems, including Euler, Legendre, and Gauss.

Many famous Chinese mathematicians such like Shiing-Shen Chern and Luogeng Hua became well-known to the world from it.

Many mathematicians believe these generalizations of the Riemann hypothesis to be true.

( Many mathematicians use the label generalized Riemann hypothesis to cover the extension of the Riemann hypothesis to all global L-functions,

Many biomedical physics departments today are of necessity multi-disciplinary and may include not only physicists but also engineers, mathematicians and sometimes chemists and physicians.

Many of Pell's manuscripts fell into the hands of Richard Busby, master of Westminster School, and afterwards came into the possession of the Royal Society ; they are still preserved in nearly forty folio volumes in the British Library, which contain, not only Pell's own memoirs, but much of his correspondence with the mathematicians of his time.

Many other winners of the Mathematical Olympiad became outstanding mathematicians and physicists.

Many amateur mathematicians have produced genuinely solid new mathematical results.

Many of the mathematicians, especially those of Jewish background, fled this southeastern part of Poland in 1941 when it became clear that it would be invaded by Germany.

Many of the great mathematicians since then have given attention to the various problems involved ; throughout the 18th and 19th centuries there was demand for accurate tables of the position of the Moon and planets for purposes of navigation at sea.

Many mathematicians have simplified parts of the original Feit – Thompson proof.

Many mathematicians and hobbyists search for large prime numbers.

Many prominent applied mathematicians and physicists were among the faculty at Bashkir State University at different times, including Academicians Nikolay N. Bogolyubov, Alexei F. Leontiev, Valentin V. Napalkov and Professor of Philology Gabdulkhay Kh.

Many compare mathematicians to other professions, typically physicists, engineers, or the " soft " sciences in a form similar to an Englishman, an Irishman and a Scotsman.

Many computational languages exist which are not Turing complete.

Many research projects are staffed and supported by multiple divisions, with computational and engineering integrated across the biosciences, general sciences, and energy sciences.

Many of Mann's inventions pertain to the field of computational photography.

Many linear algebra algorithms require significantly less computational effort when applied to triangular matrices, and this improvement often carries over to Hessenberg matrices as well.

Many linear algebra algorithms require significantly less computational effort when applied to diagonal matrices, and this improvement often carries over to tridiagonal matrices as well.

Many of these models bear similarity to the algorithms used in search engines ( for example, see Griffiths, et al., 2007 and Anderson, 1990 ), though it is not yet clear whether they really use the same computational mechanisms.

Many interdisciplinary approaches to intelligence ( e. g. cognitive science, computational intelligence and decision making ) tend to emphasise the need to consider additional traits such as imagination ( taken as the ability to form mental images and concepts that were not programmed in ) and autonomy.

Many natural computational problems occupy the lower levels, W and W.

Many of the included examples are characterised by highly complex, nonlinear, and supercomplex mechanisms, as it is being increasingly recognised that the result of such interactions may only be understood through a combination of mathematical, logical, physical / chemical, molecular and computational models.

Many other methodologies — including computational modeling, experimental and quasi-experimental research, and non-interventionist ethnographic-style qualitative research methodologies -- have long been and continue to be employed in learning sciences.

Many computational architectures have been devised to solve Bongard problems, the most extensive of which being Phaeaco, by Dr. Harry Foundalis.

Many facets are however shared with large scale problems in other computational sciences like computational fluid dynamics, electromagnetics, and solid mechanics.

* Many benchmarks focus entirely on the speed of computational performance, neglecting other important features of a computer system, such as:

Many of the philosophical controversies surrounding computational neuroscience involve the role of simulation and modeling as explanation.

Many modern baseball theorists believe that a new pitch will swing the balance of power back to the pitcher.

Many of today's academics that employ the term, cultural imperialism, are heavily informed by the work of Foucault, Derrida, Said, and other poststructrualist and postcolonialist theorists.

Many theorists suggest that there are two opposing conceptions of citizenship: an economic one, and a political one.

Many other group theorists define the commutator as

Many other group theorists define the conjugate of a by x as xax < sup >− 1 </ sup >.

Many practitioners take Edward Saïd's book Orientalism ( 1978 ) as the theory's founding work ( although French theorists such as Aimé Césaire and Frantz Fanon made similar claims decades before Said ).

Many later Marxist theorists ( e. g. Eric Wolfe ) have generalized this characterization to include non-European societies, grouping feudalism together with Imperial Chinese and pre-Columbian Incan societies as ' tributary.

Many media theorists concerned with language and media bias point towards the media of the United States, a large country where English is spoken by the vast majority of the population.

Many theorists who have been called " post-structuralist " have rejected the label.

Many of the ideas developed by historical and modern personality theorists stem from the basic philosophical assumptions they hold.

Many modern theorists have stated that this ideal cannot be achieved independently of some analysis of additional factors.

Many symphonies are tonal works in four movements with the first in sonata form, which is often described by music theorists as the structure of a " classical " symphony, although many symphonies by the acknowledged classical masters of the form, Joseph Haydn, Wolfgang Amadeus Mozart, and Ludwig van Beethoven do not conform to this model.

Many genre theorists contributed to these universally accepted forms of poetry.

Many writers, critics and theorists made assertions about vanguard culture during the formative years of modernism, although the initial definitive statement on the avant-garde was the essay Avant-Garde and Kitsch by New York art critic Clement Greenberg, published in Partisan Review in 1939.

Many instructional design theorists began to adopt an information-processing-based approach to the design of instruction.

Many theorists have presented models of the brain and have established a range of estimates of the amount of computing power needed for partial and complete simulations.

Many business theorists view service provision as a performance or act ( sometimes humorously referred to as dramalurgy, perhaps in reference to dramaturgy ).

Many theorists attempt to analyze the process of romantic love.

Many theories in urban sociology have been criticized, most prominently directed toward the ethnocentric approaches taken by many early theorists that lay groundwork for urban studies throughout the 20th century.

Many of the theorists were affiliated with Yale University in the late 1970s, although a number of the theorists — including Derrida himself — subsequently moved to or became affiliated with the University of California at Irvine.

Many theorists supported Thompson's argument that an analysis " based on structuration's ontology of structures as norms, interpretative schemes and power resources radically limits itself if it does not frame and locate itself within a more broadly conceived notion of social structures.

Many students completing a doctoral program enter the field as researchers, theorists, analysts, policy makers and professors in higher education.

Many of the notions were first elaborated by Howard Hanson ( 1960 ) in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as Allen Forte ( 1973 ), drawing on the work in twelve-tone theory of Milton Babbitt.