Many inventors tried to fix these problems, but without commercial success.

Many practical problems are actually " easy ", so the SAT solver can easily find a solution, or prove that none exists, relatively quickly, even though the instance has thousands of variables and tens of thousands of constraints.

Many other decision problems, such as graph coloring problems, planning problems, and scheduling problems, can be easily encoded into SAT.

Many people with dyslexia have auditory processing problems and may develop their own logographic cues to compensate for this type of deficit.

Many were seen as reflections of broad underlying conflicts or maladaptive reactions to life problems, rooted in a distinction between neurosis and psychosis ( roughly, anxiety / depression broadly in touch with reality, or hallucinations / delusions appearing disconnected from reality ).

Many problems of the design of experiments involve combinatorial designs, as in this example.

The author of the Easton's article concludes, " Many Christians today still find this letter to speak to modern-day problems within church communities.

Many problems of practical interest can be represented by graphs.

Many problems have to do with various ways of coloring graphs, for example:

Many problems involve characterizing the members of various classes of graphs.

Many minor problems that existed in the first edition were fixed making it, according to many, the most stable release of the Windows 9x family.

Many community members worried that the library would become a tourist attraction, causing particular problems with traffic congestion.

Many patients say they have balance problems and fall easily, as the muscles cannot compensate for an off-balanced posture.

Many mine workers perished and were injured during the life of the mine — the mine was plagued by water flooding problems.

Many different problems are addressed, like foreign policy, declarations of war, the legitimacy of leaders, and the introduction of new ideas and laws.

Many mutations arise as a result of problems caused by the DNA lesions during replication, resulting in errors in replication.

Many common health problems can be prevented or alleviated with a healthy diet.

Many natural computer science problems are covered by the class NP.

Many things can happen to packets as they travel from origin to destination, resulting in the following problems as seen from the point of view of the sender and receiver:

Many of the issues that he takes on in these books have to do with the kinds of problems that adolescents experience.

According to anthropologists John Monaghan and Peter Just, Many of the great world religions appear to have begun as revitalization movements of some sort, as the vision of a charismatic prophet fires the imaginations of people seeking a more comprehensive answer to their problems than they feel is provided by everyday beliefs.

Many Australian and UK soap operas explore social realist storylines such as family discord, marriage breakdown, or financial problems.

Many of the refugee children being hidden in Chambon attended Cévenol and it was at this school that Grothendieck apparently first became fascinated with mathematics.

Many significant areas of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be stated, and proved, in a much simpler way than without the use of categories.

Many important constructions in mathematics can be studied in this context.

Many objects in mathematics have natural group actions defined on them.

Many Greek and Arabic texts on mathematics were then translated into Latin, which led to further development of mathematics in medieval Europe.

Many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing.

Many philosophers believe that mathematics is not experimentally falsifiable, and thus not a science according to the definition of Karl Popper.

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 of these structures are drawn from functional analysis, a research area within pure mathematics that was influenced in part by the needs of quantum mechanics.

Many different kinds of products are studied in mathematics:

Many formalists would say that in practice, the axiom systems to be studied will be suggested by the demands of science or other areas of mathematics.

Many sophists specialized in using the tools of philosophy and rhetoric, though other sophists taught subjects such as music, athletics, and mathematics.

Many important categories in mathematics ( such as the category of sets ), although not small, are at least locally small.

Many logicians believe that Gödel's incompleteness theorems struck a fatal blow to David Hilbert's second problem, which asked for a finitary consistency proof for mathematics.

Many of Plato's dialogues concern the search for a definition of some important concept ( justice, truth, the Good ), and it is likely that Plato was impressed by the importance of definition in mathematics.

Many recognized specialists in the knowledge areas where Korzybski claimed to have anchored general semantics — biology, epistemology, mathematics, neurology, physics, psychiatry, etc .— supported his work in his lifetime, including Cassius J. Keyser, C. B. Bridges, W. E. Ritter, P. W. Bridgman, G. E. Coghill, William Alanson White, Clarence B. Farrar, David Fairchild, and Erich Kähler.

Many fundamental tasks in mathematics, geometry, trigonometry, graph theory and graphing are performed in a two-dimensional space, or in other words, in the plane.

Many fields of mathematics bear the imprint of their creators for notation: the differential operator is due to Leibniz, the cardinal infinities to Georg Cantor ( in addition to the lemniscate (∞) of John Wallis ), the congruence symbol (≡) to Gauss, and so forth.

Many different branches of mathematics are being covered by the fields of interest of different researchers at the institute.

Many text formatting programs can also typeset mathematics: TeX was developed specifically for high-quality mathematical typesetting.

Many significant areas of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be stated, and proved, in a much simpler way than without the use of categories.

Many examples of such functions were familiar in nineteenth-century mathematics: abelian functions, theta functions, and some hypergeometric series.