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Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
Creativity and rigor are not the only psychological aspects of the activity of mathematicians. Some mathematicians can see their activity as a game, more specifically as solving puzzles. [195] This aspect of mathematical activity is emphasized in recreational mathematics. Mathematicians can find an aesthetic value to mathematics.
Algebra includes the study of algebraic structures, which are sets and operations defined on these sets satisfying certain axioms. The field of algebra is further divided according to which structure is studied; for instance, group theory concerns an algebraic structure called group.
With mathematicians pursuing greater rigor and more abstract foundations, some proposed defining mathematics purely in terms of deduction and logic: Mathematics is the science that draws necessary conclusions. [10] Benjamin Peirce 1870. All Mathematics is Symbolic Logic. [8] Bertrand Russell 1903
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
Hard science and soft science are colloquial terms used to compare scientific fields on the basis of perceived methodological rigor, exactitude, and objectivity. [ 1 ] [ 2 ] [ 3 ] In general, the formal sciences and natural sciences are considered hard science , whereas the social sciences and other sciences are described as soft science .
Also called infinitesimal calculus A foundation of calculus, first developed in the 17th century, that makes use of infinitesimal numbers. Calculus of moving surfaces an extension of the theory of tensor calculus to include deforming manifolds. Calculus of variations the field dedicated to maximizing or minimizing functionals. It used to be called functional calculus. Catastrophe theory a ...
Scientific terminology is the part of the language that is used by scientists in the context of their professional activities. While studying nature , scientists often encounter or create new material or immaterial objects and concepts and are compelled to name them.