Analysis, if it is really carried out with a complete concentration of his powers, forms and completes a chess player. — Lev Polugaevsky
In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy. — G. H. Hardy
Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform. — Bertrand Russell
The highest form of pure thought is in mathematics. — Plato
Mathematics allows for no hypocrisy and no vagueness. — Stendhal
Pure mathematics is, in its way, the poetry of logical ideas. — Albert Einstein
Analysis Is the Critical Starting Point of Strategic Thinking — Kenichi Ohmae
All the mathematical sciences are founded on relations between physical laws and laws of numbers. — James Clerk Maxwell
Mathematical Equations Quotes
Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality. — Nikola Tesla
In order to solve this differential equation you look at it until a solution occurs to you. — George Polya
The mathematical sciences particularly exhibit order symmetry and limitations; and these are the greatest forms of the beautiful. — Aristotle
Lottery: A tax on people who are bad at math.
It is more important to have beauty in one's equations than to have them fit experiment. — Paul Dirac
Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding. — William Thurston
If equations are trains threading the landscape of numbers, then no train stops at pi. — Richard Preston
If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries. — Carl Friedrich Gauss
The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved. — Paul Dirac
Geometry is the science of correct reasoning on incorrect figures. — George Polya
Love and you shall be loved. All love is mathematically just, as much as the two sides of an algebraic equation. — Ralph Waldo Emerson
Applied Mathematics Quotes
The only way to learn mathematics is to do mathematics. — Paul Halmos
Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians. — Edsger Dijkstra
I started John W. Henry & Company because I enjoyed applying mathematics to markets, and it was a profound challenge that resonated within me. — John W. Henry
It was as though applied mathematics was my spouse, and pure mathematics was my secret lover. — Edward Frenkel
I count Maxwell and Einstein, Eddington and Dirac, among "real" mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are at present at any rate, almost as "useless" as the theory of numbers. — G. H. Hardy
Technology is applied science. Science is the study of nature. Mathematics is the language of nature. Philosophy is the root of mathematics. All tightly interrelated. — Naval Ravikant
I was fortunate to find an extraordinary mathematics and applied mathematics program in Toronto. — Walter Kohn
Applied mathematics will always need pure mathematics just as anteaters will always need ants. — Paul Halmos
Mathematics should be mixed not only with physics but with ethics. — Henry David Thoreau
The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics. — Henry David Thoreau
Mathematical Models Quotes
The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing? — Stephen Hawking
I'm very good at integral and differential calculus, I know the scientific names of beings animalculous; In short, in matters vegetable, animal, and mineral, I am the very model of a modern Major-General. — W. S. Gilbert
What distinguishes a mathematical model from, say, a poem, a song, a portrait or any other kind of "model," is that the mathematical model is an image or picture of reality painted with logical symbols instead of with words, sounds or watercolors. — John L. Casti
We have three criteria: If it’s publicly traded, liquid and amenable to modeling, we trade it. — Jim Simons
We are not a teaching organization. We are a research organization. We hire people to make mathematical models of the markets in which we invest. — Jim Simons
Do not trust financial market risk models. Despite the predilection of some analysts to model the financial markets using sophisticated mathematics, the markets are governed by behavioral science, not physical science. — Seth Klarman
The core of science is not a mathematical modeling--it is intellectual honesty. It is a willingness to have our certainties about the world constrained by good evidence and good argument. — Sam Harris
I recognize that I have a unique position to be a role model to young girls because I am doing something that they consider glamorous, which is acting, and yet I took a time to really get my education and study mathematics, and I think math is the cat's meow. — Danica McKellar
A theory is just a mathematical model to describe the observations. — Karl Popper
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
Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician. — Gottlob Frege
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. — Ada Lovelace
Mathematical Analysis is... the true rational basis of the whole system of our positive knowledge. — Auguste Comte
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. — Albert A. Michelson
The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic. — Ronald Fisher
Hydrodynamics procreated complex analysis, partial differential equations, Lie groups and algebra theory, cohomology theory and scientific computing. — Vladimir Arnold
I agree with Warren to keep it simple and not use higher mathematics in your analysis. — Walter Schloss
Mathematical Analysis is as extensive as nature herself. — Joseph Fourier
The abstract analysis of the world by mathematics and physics rests on the concepts of space and time. — James J. Gibson
Mathematicians tend to prefer a worst-case analysis, a kind of paranoia that is especially understandable if you live in Israel! — Noga Alon
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. — Hyman Bass
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. — Bertrand Russell
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. — Lucio Russo
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. — James Clerk Maxwell
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. — Georg C. Lichtenberg
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. — Thomas Reid
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. — Pierre-Simon Laplace
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. — Richard Askey
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. — Jean-Baptiste Michel
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. — Richard Courant
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. — Ada Lovelace
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. — Ada Lovelace
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. — George Boole
I don't like to end my talk with a 700 million dollar loss, even if it shows the importance of Numerical Analysis. — Richard A. Falk
I have to admit that he was not bad at combinatorial analysis - a branch, however, that even then I considered to be dried up. — Stanislaw Lem
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. — Brian L. Silver
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. — Anatol Rapoport
There is a certain way of searching for the truth in mathematics that Plato is said first to have discovered. Theon called this analysis. — Francois Viete
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. — Leopold Kronecker
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. — Gottfried Leibniz
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. — Auguste Comte
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. — Ernest Nagel
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