Education is what remains after one has forgotten what one has learned in school.
Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.
Mathematics is the queen of the sciences.
The Good Lord made all the integers; the rest is man's doing.
But in the new (math) approach, the important thing is to understand what you're doing, rather than to get the right answer.
Mathematics is like draughts in being suitable for the young, not too difficult, amusing, and without peril to the state.
The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver.
The best teacher is not the one who knows most but the one who is most capable of reducing knowledge to that simple compound of the obvious and wonderful.
It is the mark of an educated mind to be able to entertain a thought without accepting it.
What humans do with the language of mathematics is to describe patterns.
Mathematics, in the common lay view, is a static discipline based on formulas...But outside the public view, mathematics continues to grow at a rapid rate...the guid to this growth is not calculation and formulas, but an open ended search for pattern.
The aim (of education) must be the training of independently acting and thinking individuals who, however, see in the service to the community their highest life problem.
A teacher affects eternity; he can never tell where his influence stops.
If you think you can't, you're right.
I'm sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it.
I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind.
Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean.
Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.
I was x years old in the year x2.
The study of mathematics is apt to commence in disappointment.
More than fifty years ago Sputnik dramatically raised the nation's awareness of what was lacking in science and math education in America. What we need to wake people up to now is the crisis in imagination and concern for the greater good.
America ranks 21st when it comes to math education. We rank 25th when it comes to science. We used to be number one in the proportion of college graduates. We now rank ninth. And at an age where knowledge, skills, are the determinant of how successful we're going to be, unless we reverse that we're going to keep slipping behind economically to a lot of other countries.
I had done quite a bit of research about math education when I spoke before Congress in 2000 about the importance of women in mathematics. The session of Congress was all about raising more scholarships for girls in college. I told them I felt that it's too late by college.
I have been involved with science and math education my whole life. My hope is to continue to promote the love of these beautiful disciplines to the next generation.
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