{Replying to G. H. Hardy's suggestion that the number of a taxi (1729) was 'dull', showing off his spontaneous mathematical genius}No, it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways, the two ways being 13 + 123 and 93 + 103.
The language of categories is affectionately known as "abstract nonsense," so named by Norman Steenrod. This term is essentially accurate and not necessarily derogatory: categories refer to "nonsense" in the sense that they are all about the "structure," and not about the "meaning," of what they represent.
How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.
When you can measure what you are speaking about, and express it in numbers, you know something about it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarely, in your thoughts advanced to the stage of science.
Do you mean ter tell me," he growled at the Dursleys, "that this boy—this boy!—knows nothin' abou'—about ANYTHING?"Harry thought this was going a bit far. He had been to school, after all, and his marks weren't bad."I know some things," he said. "I can, you know, do math and stuff.
Excel suffers from an image problem. Most people assume that spreadsheet programs such as Excel are intended for accountants, analysts, financiers, scientists, mathematicians, and other geeky types. Creating a spreadsheet, sorting data, using functions, and making charts seems daunting, and best left to the nerds.
One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.
In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and that is just what mathematics can provide -- a relief from daily life, an anodyne to the practical workaday world.
The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.
[Regarding mathematics,] there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true; indeed it is probable, since the sensational triumphs of Einstein, that stellar astronomy and atomic physics are the only sciences which stand higher in popular estimation.
Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
If market pricing is the only legitimate test of quality, why are we still bothering with proven theorems? Why don't we just have a vote on whether a theorem is true? To make it better we'll have everyone vote on it, especially the hundreds of millions of people who don't understand the math. Would that satisfy you?
The only reason I don’t know more about love is because there just isn’t more to know. In fact, I’ve reduced love to a mathematical formula: Hdgk(X)=H2k(X,Q)∩Hk,k(X). Actually, that’s not right. That’s the statement piece of the Hodge conjecture, but I’m sure you already knew that.
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.
I don’t understand people who eat Chinese food with chopsticks when the restaurant also offers silverware. As a tool, chopsticks are inferior to western utensils like the spoon and fork. So why use them? That’s like showing up to a math test with an abacus, knowing that the teacher is going to be handing out calculators.
