Top 1200 Mathematical Analysis Quotes & Sayings - Page 3

Their [BBC] idea of bipartisanship is to try not to offend the Conservative party, try not to offend the Labour party.There is no analysis of anything beyond that, and these two parties are exactly identical, following the same Neoliberal policies for thirty years. And it's no criticism outside of that, it's just that there's basically sectarian pandering to these two individual parties, these two individual organisations. They still make a lot of great programmes and do a lot of great things, but there's not much political analysis happening broader to that.

Statistics: the mathematical theory of ignorance.

Fourier is a mathematical poem.

Music is a science, in many ways it's mathematical.

Nature is written in mathematical language.

We shall see that the mathematical treatment of the subject [of electricity] has been greatly developed by writers who express themselves in terms of the 'Two Fluids' theory. Their results, however, have been deduced entirely from data which can be proved by experiment, and which must therefore be true, whether we adopt the theory of two fluids or not. The experimental verification of the mathematical results therefore is no evidence for or against the peculiar doctrines of this theory.

I actually wanted to be an astronaut, but I don't have a mathematical brain.

Mathematics is not only real, but it is the only reality. That is that entire universe is made of matter, obviously. And matter is made of particles. It's made of electrons and neutrons and protons. So the entire universe is made out of particles. Now what are the particles made out of They're not made out of anything. The only thing you can say about the reality of an electron is to cite its mathematical properties. So there's a sense in which matter has completely dissolved and what is left is just a mathematical structure.

Neither concepts nor mathematical formulae can explain the infinite.

Can the existence of a mathematical entity be proved without defining it ?

The peculiarity of the evidence of mathematical truths is that all the argument is on one side.

We humans have a wide range of abilities that help us perceive and analyze mathematical content. We perceive abstract notions not just through seeing but also by hearing, by feeling, by our sense of body motion and position. Our geometric and spatial skills are highly trainable, just as in other high-performance activities. In mathematics we can use the modules of our minds in flexible ways - even metaphorically. A whole-mind approach to mathematical thinking is vastly more effective than the common approach that manipulates only symbols.

A physical law must possess mathematical beauty.

As for everything else, so for a mathematical theory: beauty can be perceived but not explained.

Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.

Mathematical reasoning may be regarded.

Dull minds are never either intuitive or mathematical.

There is coming an era for people with a mathematical state of mind

Indeed, it is a proven mathematical theorem that a doughnut is topologically distinct from a sphere.

There's a mathematical way to get success.

There has to be a mathematical explanation for how bad that tie is.

The profound study of nature is the most fertile source of mathematical discovery.

We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of science are mathematics and logic; the mathematical set puts out the logical eye, the logical set puts out the mathematical eye; each believing that it sees better with one eye than with two. Note that De Morgan, himself, only had sight with only one eye.

Like music or art, mathematical equations can have a natural progression and logic that can evoke rare passions in a scientist. Although the lay public considers mathematical equations to be rather opaque, to a scientist an equation is very much like a movement in a larger symphony. Simplicity. Elegance. These are the qualities that have inspired some of the greatest artists to create their masterpieces, and they are precisely the same qualities that motivate scientists to search for the laws of nature. LIke a work of art or a haunting poem, equations have a beauty and rhythm all their own.

I guess I'm a really analytical person, but when I'm writing, all that stuff goes behind a screen. Analysis and taking things apart is really important and really interesting, but it's the direct opposite of creating something, which has to do with taking things and putting them together and hoping to make something unique that's more than the sum of its parts. And you can't do that with analysis, you can only take things into smaller and smaller pieces.

Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.

One cannot really argue with a mathematical theorem.

The mathematical expectation of the speculator is zero.

A mathematical equation stands forever.

Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics.

A mathematical proof must be perspicuous.

There's nothing mathematical to my writing. It's a feeling.

Our external physical reality is a mathematical structure.

There is no perfect mathematical formula for pricing a business.

In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.

Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box - a valuable ability in today's world.

The moving power of mathematical invention is not reasoning but imagination.

A theory is just a mathematical model to describe the observations.

Poverty is a mathematical proof of the fact that mankind is a big failure!

Music is a secret and unconscious mathematical problem of the soul.

God forbid that Truth should be confined to Mathematical Demonstration!

Here at Wisconsin we didn't get an undergraduate course in mathematical logic until the '60s.

Another characteristic of mathematical thought is that it can have no success where it cannot generalize.

What I realized is that if we're going to be able to have a theory about what happens in, for example, nature there has to ultimately be some rule by which nature operates. But the issue is does that rule have to correspond to something like a mathematical equation, something that we have sort of created in our human mathematics? And what I realized is that now with our understanding of computation and computer programs and so on, there is actually a much bigger universe of possible rules to describe the natural world than just the mathematical equation kinds of things.

Take nothing for granted as beautiful or ugly, but take every building to pieces, and challenge every feature. Learn to distinguish the curious from the beautiful. Get the habit of analysis - analysis will in time enable synthesis to become your habit of mind. 'Think simples' as my old master used to say - meaning to reduce the whole of its parts into the simplest terms, getting back to first principles.

Millions of people never analyze themselves. Mentally they are mechanical products of the factory of their environment, preoccupied with breakfast, lunch, and dinner, working and sleeping, and going here and there to be entertained. They don't know what or why they are seeking, nor why they never realize complete happiness and lasting satisfaction. By evading self-analysis, people go on being robots, conditioned by their environment. True self-analysis is the greatest art of progress.

As long as there is a mathematical chance, we have to keep on going.

Words are a pretty fuzzy substitute for mathematical equations.

Ex-Professor Moriarty of mathematical celebrity... is the Napoleon of crime, Watson.

It's like a mathematical law, Grace.

Music assists him in the use of harmonic and mathematical proportion.

Do mathematics have a relation to reality or are they only a mathematical symbol?

The laws of nature are but the mathematical thoughts of God.

Homeopathy seemed . . . both mathematical and poetic.

I'm always trying to calculate the mathematical probability of certain outcomes.

But as the work proceeded I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was not more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.

Has the mathematical abilities of a Clydesdale.

Topology is precisely the mathematical discipline that allows the passage from local to global.

I knew that he was as reliable as a mathematical formula.

Mathematical Reasoning is not only exact; it has its own criteria of reality.