I suppose I felt doomed to be an artist early on because of the way I drew all over the books that I needed for school, from ancient history to math. I was more interested in drawing in the margins than actually doing the work.
One minute I was playing chess and doing maths all the time, the next I had been rerouted into more 'normal' girls' activities: reading, writing stories and worrying about my clothes.
And for mathematical science, he that doubts their certainty hath need of a dose of hellebore.
I do not think we are ever going to be able to, for a long time, get the kind of quality of school personnel that we need in our schools, especially in the areas of science and math. One of the answers to that problem is to use more educational technology.
You live your life between your ears.
All the math you need in the stock market you get in the fourth grade.
Desire animates the world. It is present in the baby crying for milk, the girl struggling to solve a math problem, the woman running to meet her lover and later deciding to have children, and the old woman, hunched over her walker, moving down the hall of the nursing home at a glacial pace to pick up her mail. Banish desire from the world, and you get a world of frozen beings who have no reason to live and no reason to die.
Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.
It is the story that matters, not just the ending.
Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.
The mathematician, carried along on his flood of symbols, dealing apparently with purely formal truths, may still reach results of endless importance for our description of the physical universe.
The world of ideas is not revealed to us in one stroke; we must both permanently and unceasingly recreate it in our consciousness.
If one must choose between rigour and meaning, I shall unhesitatingly choose the latter.
What you have been obliged to discover by yourself leaves a path in your mind which you can use again when the need arises.
Mathematics is about problems, and problems must be made the focus of a student's mathematical life. Painful and creatively frustrating as it may be, students and their teachers should at all times be engaged in the process - having ideas, not having ideas, discovering patterns, making conjectures, constructing examples and counterexamples, devising arguments, and critiquing each other's work.
... it can often be profitable to try a technique on a problem even if you know in advance that it cannot possibly solve the problem completely.
... commutative algebra is a lot like topology, only backwards.
It's better to work with a nice category containing some nasty objects, than a nasty category containing only nice objects.
All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.
The real irony is that the view of infinity as some forbidden zone or road to insanity - which view was very old and powerful and haunted math for 2000+ years - is precisely what Cantor's own work overturned. Saying that infinity drove Cantor mad is sort of like mourning St. George's loss to the dragon: it's not only wrong but insulting.
A great deal more is known than has been proved.
The electron is a theory we use; it is so useful in understanding the way nature works that we can almost call it real.
The polynomial xn−1 is a force of nature.
It never happens that, when we go home and open the refrigerator, we see all infinitely many prime numbers there.
If we drop money, we are usually very sad if the money is big. But for example, if we drop 310 dollars, we can relax, because this is very small in the 3-adics.
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