The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.— John Von Neumann
Satisfaction Mathematical Analysis quotations
Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.
In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical analysis belong to operations, as distinguished from the objects operated upon and from the results of the operations performed upon those objects, is very strikingly defined and separated.
Mathematical Analysis is... the true rational basis of the whole system of our positive knowledge.
Now, the velocity of wave propagation can be seen, without the aid of any mathematical analysis, to depend on the elasticity of the medium and its density; for we can see that if a medium is highly elastic the disturbance would be propagated at a great speed.
The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic.
Hydrodynamics procreated complex analysis, partial differential equations, Lie groups and algebra theory, cohomology theory and scientific computing.
I agree with Warren to keep it simple and not use higher mathematics in your analysis.
Mathematical Analysis is as extensive as nature herself.
The abstract analysis of the world by mathematics and physics rests on the concepts of space and time.
Mathematicians tend to prefer a worst-case analysis, a kind of paranoia that is especially understandable if you live in Israel!
Mathematics is one of the deepest and most powerful expressions of pure human reason, and, at the same time, the most fundamental resource for description and analysis of the experiential world.
The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.
Euclid manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does.
The mathematical difficulties of the theory of rotation arise chiefly from the want of geometrical illustrations and sensible images, by which we might fix the results of analysis in our minds.
In mathematical analysis we call x the undetermined part of line a: the rest we don't call y, as we do in common life, but a-x. Hence mathematical language has great advantages over the common language.
It is the invaluable merit of the great Basle mathematician Leonard Euler, to have freed the analytical calculus from all geometric bounds, and thus to have established analysis as an independent science, which from his time on has maintained an unchallenged leadership in the field of mathematics.
It is interesting thus to follow the intellectual truths of analysis in the phenomena of nature. This correspondence, of which the system of the world will offer us numerous examples, makes one of the greatest charms attached to mathematical speculations.
Combinatorial analysis, in the trivial sense of manipulating binomial and multinomial coefficients, and formally expanding powers of infinite series by applications ad libitum and ad nauseamque of the multinomial theorem, represented the best that academic mathematics could do in the Germany of the late 18th century.
When the stuff of history is available in digital form, it makes it possible for mathematical analysis to very quickly and very conveniently read trends in our history and our culture.
Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.
The further we analyse the manner in which such an engine performs its processes and attains its results, the more we perceive how distinctly it places in a true and just light the mutual relations and connexion of the various steps of mathematical analysis; how clearly it separates those things which are in reality distinct and independent, and unites those which are mutually dependent.
It were much to be desired, that when mathematical processes pass through the human brain instead of through the medium of inanimate mechanism, it were equally a necessity of things that the reasonings connected with operations should hold the same just place as a clear and well-defined branch of the subject of analysis, a fundamental but yet independent ingredient in the science, which they must do in studying the engine.
I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary -- being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived.
I don't like to end my talk with a 700 million dollar loss, even if it shows the importance of Numerical Analysis.
I have to admit that he was not bad at combinatorial analysis - a branch, however, that even then I considered to be dried up.
Toward the end of his life, Gödel feared that he was being poisoned, and he starved himself to death. His theorem is one of the most extraordinary results in mathematics, or in any intellectual field in this century. If ever potential mental instability is detectable by genetic analysis, an embryo of someone with Kurt Gödel's gifts might be aborted.
Whether game theory leads to clear-cut solutions, to vague solutions, or to impasses, it does achieve one thing. In bringing techniques of logical and mathematical analysis gives men an opportunity to bring conflicts up from the level of fights, where the intellect is beclouded by passions, to the level of games, where the intellect has a chance to operate.
There is a certain way of searching for the truth in mathematics that Plato is said first to have discovered. Theon called this analysis.
Analysis does not owe its really significant successes of the last century to any mysterious use of sqrt(-1), but to the quite natural circumstances that one has infinitely more freedom of mathematical movement if he lets quantities vary in a plane instead of only on a line.
When a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached. It is this way that in mathematics speculative theorems and practical canons are reduced by analysis to definitions, axioms and postulates.
Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry.... if mathematical analysis should ever hold a prominent place in chemistry -- an aberration which is happily almost impossible -- it would occasion a rapid and widespread degeneration of that science.
Like Molière's M. Jourdain, who spoke prose all his life without knowing it, mathematicians have been reasoning for at least two millennia without being aware of all the principles underlying what they were doing. The real nature of the tools of their craft has become evident only within recent times A renaissance of logical studies in modern times begins with the publication in 1847 of George Boole's The Mathematical Analysis of Logic.