The mathematician is entirely free, within the limits of his imagination, to construct what worlds he pleases. What he is to imagine is a matter for his own caprice; he is not thereby discovering the fundamental principles of the universe nor becoming acquainted with the ideas of God.
Most people who open restaurants will fail, because they lack the fundamental understanding of restaurant math. Either they think they're superstar cooks or they think they're superstar hosts.
One of the nice things about math and science is it’s obvious, you get the answer or you don’t get the answer.
My algebra was relatively poor. I found it very difficult to use equations that substituted numbers - to which I had a synesthetic and emotional response - for letters, to which I had none. It was because of this that I decided not to continue math at Advanced level, but chose to study history, French and German instead.
As far as I know, Clifford Pickover is the first mathematician to write a book about areas where math and theology overlap. Are there mathematical proofs of God? Who are the great mathematicians who believed in a deity? Does numerology lead anywhere when applied to sacred literature? Pickover covers these and many other off-trail topics with his usual verve, humor, and clarity. And along the way the reader will learn a great deal of serious mathematics.
Although I was first drawn to math and science by the certainty they promised, today I find the unanswered questions and the unexpected connections at least as attractive.
C.S. Lewis says that fiction is able to sneak past the watchful dragons of religion. It becomes more powerful to speak in poetry. The song goes straight to the heart while the numbers and the math of it will never be able to reach that.
I'm a good example of wanting to apologize only for my precise share of a problem--as I calculate it, of course--and I expect my husband Steve to apologize for his share, also as I calculate it. Since we're not always of one mind on the math, it can lead to the theater of the absurd.
Students coming from father-present families score higher in math and science even when they come from weaker schools.
I mean can you walk to school on your own? Can you study science? Can you study math? Can you go to a normal school? Do you need to go to a special school? What is going to become of you when you grow up? Are you going to have to live on social security and SSI?
I guess the approach to song writing for me so far has been to use more chords and less math.
[Math] curriculum is obsessed with jargon and nomenclature seemingly for no other purpose than to provide teachers with something to test the students on.
Sometimes in studying Ramanujan's work, [George Andrews] said at another time, "I have wondered how much Ramanujan could have done if he had had MACSYMA or SCRATCHPAD or some other symbolic algebra package."
In fact, NSF was the leading successful efforts to improve U.S. math and science education long before the Department of Education was even created.
The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was "out there" all along I just couldn't see it. And now I can! This is really what keeps me in the math game- the chance that I might glimpse some kind of secret underlying truth, some sort of message from the gods.
The physical five oranges goes up the ladder to the picture of the five oranges which goes up to the representation of the five oranges as a numeral. This points in the direction of a definition of abstraction: when we abstract we voluntarily ignore details of a context, so that we can accomplish a goal.
Those who are accustomed to judge by feeling do not understand the process of reasoning, because they want to comprehend at a glance and are not used to seeking for first principles. Those, on the other hand, who are accustomed to reason from first principles do not understand matters of feeling at all, because they look for first principles and are unable to comprehend at a glance.
In the study of ideas, it is necessary to remember that insistence on hard-headed clarity issues from sentimental feeling, as it were a mist, cloaking the perplexities of fact. Insistence on clarity at all costs is based on sheer superstition as to the mode in which human intelligence functions. Our reasonings grasp at straws for premises and float on gossamers for deductions.
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.
The greatest reward lies in making the discovery; recognition can add little or nothing to that.
Such is the advantage of a well constructed language that its simplified notation often becomes the source of profound theories.
Prayers for the condemned man will be offered on an adding machine. Numbers constitute the only universal language.
I love the psychology versus math and logic. In algebra, "X" means any possible variable. I sort of think about "X" in terms of the equation of my own life. Adding "X" to my own life has given me a freedom that I didn't have before in the equation of my own existence.
Make your mistakes work for you by learning from them.
Figures don't lie, but liars figure.
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