Top 1200 Mathematical Models Quotes & Sayings

Theoretical physicists accept the need for mathematical beauty as an act of faith... For example, the main reason why the theory of relativity is so universally accepted is its mathematical beauty.

There's a lot of amazing women out there. There's a lot of hot models. But models are the worst, because they're models, you have to always step up and always look good.

I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts... When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through the process of 'seeing'.

The "seriousness" of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects.

For far too long economists have sought to define themselves in terms of their supposedly scientific methods. In fact, those methods rely on an immoderate use of mathematical models, which are frequently no more than an excuse for occupying the terrain and masking the vacuity of the content.

One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?

Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates. Indeed, the beauty and elegance of the physical laws themselves are only apparent when expressed in the appropriate mathematical framework.

The magic of the mechanisms inside each genetic structure saying exactly where that nerve cell should go - the complexity of these mathematical models is beyond human comprehension.

Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.

Models, even male models - how small they've gotten! It looks great for the clothes, but it's not what you want in real life.

I think we, as a fasion industry, need to hold people accountable for their actions. I want people to realize that models have a voice, and a powerful one at that. I want all models to be treated with more respect because that's what we all want - basic respect and to not be treated like objects with no will. I hope that models can be more empowered to say 'no' or give their opinion without being labeled as difficult. Modeling should be a collaboration. If the makeup artist, photographer and stylist all contribute, why can't models?

Nothing has done more to render modern economic theory a sterile and irrelevant exercise in autoeroticism than its practitioners’ obsession with mathematical, general-equilibrium models.

The constructs of the mathematical mind are at the same time free and necessary. The individual mathematician feels free to define his notions and set up his axioms as he pleases. But the question is will he get his fellow mathematician interested in the constructs of his imagination. We cannot help the feeling that certain mathematical structures which have evolved through the combined efforts of the mathematical community bear the stamp of a necessity not affected by the accidents of their historical birth.

What a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the principle of mathematical induction. The validity of these premises is an entirely independent matter which can safely be left to philosophers.

Formal logic is mathematics, and there are philosophers like Wittgenstein that are very mathematical, but what they're really doing is mathematics - it's not talking about things that have affected computer science; it's mathematical logic.

There is a history of mathematical models of oligopolistic competition dating from Cournot to the theory of games. There is also a literature generated by institutional economists, lawyers, and administrators interested in formulating and implementing public policy. It has been the tendency of these groups to work almost as though the other did not exist.

We’re seeing that business models and philanthropic models are not mutually exclusive.

Mathematical Mark all mathematical heads, which be only and wholly bent to those sciences, how solitary they be themselves, how unfit to live with others, and how unapt to serve in the world.

The problem with cinema nowadays is that it's a math problem. People can read a film mathematically; they know when this comes or that comes; in about 30 minutes, it's going to be over and have an ending. So film has become a mathematical solution. And that is boring, because art is not mathematical.

The difference is that we have the hardest and most painful evidence that there was a Holocaust. But, for the global warming scenario that is causing such hysteria, we have only a movie made by a politician and mathematical models whose results change drastically when you change a few of the arbitrarily selected variables.

[Referring to Fourier's mathematical theory of the conduction of heat] ... Fourier's great mathematical poem.

My brother is a genius. When we went to Italy, he was on the local television channel as a prodigy, who could solve very sophisticated mathematical equations. He was only seven or eight years old but he could solve mathematical problems for fourteen year olds.

As a graduate student, I wrote a long paper connecting the dots between mathematical models of learning and language development in children. It was published in a major journal.

There are great slender models, great tall models, Amazonian models, great busty models - my point is models of all shapes and sizes, age, ethnic background should be embraced and celebrated.

The once-surprising existence of non-Euclidean models of Euclid's first four axioms can be seen as a sort of mathematical joke.

Modern economics is a set of formal models and equations purporting to fully determine human behaviour, at least in the economic realm. And there is no way that uncertainty can be compressed into determinate mathematical models.

Investors should be skeptical of history-based models. Constructed by a nerdy-sounding priesthood using esoteric terms such as beta, gamma, sigma and the like, these models tend to look impressive. Too often, though, investors forget to examine the assumptions behind the models. Beware of geeks bearing formulas.

An old French mathematician said: "A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street." This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us.

My reasons are the same as for any mathematical conjecture: (1) It is a legitimate mathematical possibility, and (2) I do not know.

Many persons entertain a prejudice against mathematical language, arising out of a confusion between the ideas of a mathematical science and an exact science. ...in reality, there is no such thing as an exact science.

I don't want to be anyone's role model. My mole models were assholes. My role models are dead. My role models never made it to 30, so I'm a bad person to ask for advice.

The emphasis on mathematical methods seems to be shifted more towards combinatorics and set theory - and away from the algorithm of differential equations which dominates mathematical physics.

I never really think of anyone as models, even the models.

It is clear that the building of models is not a purely mechanical process but requires skill of a high order - not merely mathematical skill but a sensitivity to the relative importance of different factors and a critical, almost an artistic, faculty in the selection of behaviour equations which are reasonable, tentative hypotheses in explaining the behaviour of actual economies.

Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.

All models are wrong; some models are useful.

The mathematical is that evident aspect of things within which we are always already moving and according to which we experience them as things at all, and as such things. The mathematical is this fundamental position we take toward things by which we take up things as already given to us, and as they must and should be given. Therefore, the mathematical is the fundamental presupposition of the knowledge of things.

I believe that no one who is familiar, either with mathematical advances in other fields, or with the range of special biological conditions to be considered, would ever conceive that everything could be summed up in a single mathematical formula, however complex.

The oldest problem in economic education is how to exclude the incompetent. A certain glib mastery of verbiage-the ability to speak portentously and sententiously about the relation of money supply to the price level-is easy for the unlearned and may even be aided by a mildly enfeebled intellect. The requirement that there be ability to master difficult models, including ones for which mathematical competence is required, is a highly useful screening device.

The challenge for me, and for Asian models in general has been convincing editors, stylists and photographers that we can have mass appeal, but Asian, especially Chinese models have become a stronger presence. Just a season or two ago, there weren't many models for me to talk with backstage in my native Mandarin. Now I usually have no trouble finding someone at any show.

The validity of mathematical propositions is independent of the actual world-the world of existing subject-matters-is logically prior to it, and would remain unaffected were it to vanish from being. Mathematical propositions, if true, are eternal verities.

There is a rumour that I can't draw and never could. This is probably because I work so much with models. Models are one of the most beautiful design tools, but I still do the finest drawings you can imagine.

If I were asked to name, in one word, the pole star round which the mathematical firmament revolves, the central idea which pervades the whole corpus of mathematical doctrine, I should point to Continuity as contained in our notions of space, and say, it is this, it is this!

The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work-that is, correctly to describe phenomena from a reasonably wide area.

In the 1940s, economics started getting highly mathematical. It was basically because economists weren't smart enough to write down models of real behavior that they started writing down models of highly rational behavior - and they kind of forgot about humans.

The climate-studies people who work with models always tend to overestimate their models. They come to believe models are real and forget they are only models.

I did gymnastics, I wanted to be like Dominique Dawes. But the good think about role models is that you don't just have them when you are kid. My role models from WWE came when I was older. When I was 27, my role models from WWE became Jacqueline and Beth Phoenix.

It really bugs me the way people criticise how actors look. We're not models. Models exist.

Much of my work in this period was concerned with exploring the logic of economic models, but also with attempting to reconcile the models with everyday observation.

Of course there are some models who are not good, but it has been proven that some models can act. Look at Kim Basinger, Sharon Stone or Andie MacDowell, who were all models - they are really fantastic actresses.

In studying mathematics or simply using a mathematical principle, if we get the wrong answer in sort of algebraic equation, we do not suddenly feel that there is an anti-mathematical principle that is luring us into the wrong answers.

Scientists often seek predictively accurate models, rather than models that are true.

Is war an inevitable outcome of competing interests in a complex society? In other words, would war be the same even if human nature were very different? There are mathematical models of large groups working together that lead to conflict on a reliable basis. So there's a whole other view of war that is not psychological at all.

My attempt has been really to, beyond making a record of contemporary life, which is what you inevitably do, is trying to make beautiful books - books that are in some way beautiful, that are models of how to use the language, models of honest feeling, models of care.

All models are approximations. Essentially, all models are wrong, but some are useful. However, the approximate nature of the model must always be borne in mind.

If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.

The good news is that, at least in economics, I've seen movement away from its overemphasis on mathematical models of purely rational behavior to a more eclectic and commonsense approach: research that is, among other things, more respectful of insights from psychology.

Much of my work in this period was concerned with exploring the logic of economic models, but also with attempting to reconcile the models with every day observation.

It would be lovely to live in a world where trans-female models were treated as female models, and trans-male models were treated the same as male models rather than being a niche commodity.

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.