mazdâhik (#), riyâzi (#)
Of, relating to, or of the nature of mathematics.
Fr.: beauté mathématique
Same as → mathematical elegance.
Fr.: élégance mathématique
A mathematical solution or demonstration when it yields a result in a surprising way (e.g., from apparently unrelated theorems), is short, and is based on fundamental concepts. According to Henri Poincaré, what gives the feeling of elegance "is the harmony of the different parts, their symmetry, and their happy adjustment; it is, in a word, all that introduces order, all that gives them unity, that enables us to obtain a clear comprehension of the whole as well as of the parts. ... Elegance may result from the feeling of surprise caused by the un-looked-for occurrence together of objects not habitually associated. ... Briefly stated, the sentiment of mathematical elegance is nothing but the satisfaction due to some conformity between the solution we wish to discover and the necessities of our mind" (Henri Poincaré, Science and Method, 1908). According to Bertrand Russell, "Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show" (Bertrand Russell, A History of Western Philosophy, 1945).
omid-e mazdâhik, bayuseš-e ~, ~ riyâzi
Fr.: espérance mathématique
In probability and statistics, of a random variable, the summation or integration, over all values of the random variable, of the product of the value and its probability of occurrence. Also called → expectation, → expected value.
barâxt-e mazdâhik, ~ riyâzi
Fr.: objet mathématique
An → abstract object dealt with in mathematics that has a definition, obeys certain properties, and can be the target of certain operations. It is often built out of other, already defined objects. Some examples are → numbers, → functions, → triangles, martices (→ matrix), → groups, and entities such as → vector spaces, and → infinite series.