Contrary to popular opinion, mathematics is about simplifying life, not complicating it. A child learns a bag of candies can be shared fairly by counting them out: That is numeracy. She abstracts that notion to dividing a candy bar into equal pieces: arithmetic. Then, she learns how to calculate how much cocoa and sugar she will need to make enough chocolate for fifteen friends: algebra.

It was the ancient Egyptians who first figured out that numbers could, if you added and subtracted them, be used to form mathematics; this made it possible, for the first time, to build the pyramids as well as keep score in bowling.

It’s easy to convince people that children need to learn the alphabet and numbers. . . . How do we help people to realize that what matters even more than the superimposition of adult symbols is how a person’s inner life finally puts together the alphabet and numbers of his outer life? What really matters is whether he uses the alphabet for the declaration of war or the description of a sunrise — his numbers for the final count at Buchenwald or the specifics of a brand-new bridge.

I think it’s our culture,” explains Tiffany Liao, a poised Swarthmore-bound high school senior whose parents are from Taiwan. “Study, do well, don’t create waves. It’s inbred in us to be more quiet. When I was a kid and would go to my parents’ friends’ house and didn’t want to talk, I would bring a book. It was like this shield, and they would be like, ‘She’s so studious!’ And that was praise.” It’s hard to imagine other American moms and dads outside Cupertino smiling on a child who reads in public while everyone else is gathered around the barbecue. But parents schooled a generation ago in Asian countries were likely taught this quieter style as children. In many East Asian classrooms, the traditional curriculum emphasizes listening, writing, reading, and memorization. Talking is simply not a focus, and is even discouraged.

It turns out languages are like children. Once you have six, adding a seventh hardly makes any difference.

I have asked many teachers and parents what they thought mathematics to be and why it was important to learn it. Few held a view of mathematics that was sufficiently coherent to justify devoting several thousand hours of a child's life to learning it, and children sense this. When a teacher tells a student that the reason for those many hours of arithmetic is to be able to check the change at the supermarket, the teacher is simply not believed. Children see such "reasons" as one more example of adult double talk. The same effect is produced when children are told school math is "fun" when they are pretty sure that teachers who say so spend their leisure hours on anything except this allegedly fun-filled activity. Nor does it help to tell them that they need math to become scientists---most children don't have such a plan. The children can see perfectly well that the teacher does not enjoy math any more than they do and that the reason for doing it is simply that it has been inscribed into the curriculum. All of this erodes children's confidence in the adult world and the process of education. And I think it introduces a deep element of dishonestly into the education relationship.

But I think that so many of the rest of us do what we can to avoid this math because if we do the subtraction, do the addition, our own personal sum will be unbearable sorrow, terror, and a feeling of being entirely out of control. I think many of us do what we can to avoid this math because we know that if we do the subtraction, do the addition, our psyches and our consciences and our lives will forever be changed; and we know that no matter how fierce the momentum that leads to this subtraction and addition, no matter our fears that we may be crushed (or perhaps more fearsome, ridiculed), that we will be led in some way to oppose the subtraction of life and the addition of toxics to this planet that is our only home.

[T]he Mayan[s]... had a scheme for predicting... when Venus was a morning... or . ...[T]hey had a rule for... making corrections and... had a very good way of predicting when Venus was coming up. ...Suppose that the professors (the priests in those days) ...were giving a lecture ...to explain ... these wonderful predictions ...He would say, "What we're doing is counting the days, just like you're putting nuts in a pod." ...[The students] did not know a quick and tricky way to add 365 x 8. ...These students were learning ...the laws of arithmetic. Something... to us now, because we have public, free, general education, almost everybody has to... learn... by a tricky scheme... The waitress, just an ordinary person, in two minutes does that. How..? ...She's ...counting ...415 pennies ...then ...287 more ...and telling you how many pennies you would have got if you counted ...beginning to the end. But it's highly educated and very trained to... do that... quickly. ...In the 14th century [it was] mathematicians... who could do that.

We are so accustomed to hear arithmetic spoken of as one of the three fundamental ingredients in all schemes of instruction, that it seems like inquiring too curiously to ask why this should be. Reading, Writing, and Arithmetic—these three are assumed to be of co-ordinate rank. Are they indeed co-ordinate, and if so on what grounds?
In this modern “trivium” the art of reading is put first. Well, there is no doubt as to its right to the foremost place. For reading is the instrument of all our acquisition. It is indispensable. There is not an hour in our lives in which it does not make a great difference to us whether we can read or not. And the art of Writing, too; that is the instrument of all communication, and it becomes, in one form or other, useful to us every day. But Counting—doing sums,—how often in life does this accomplishment come into exercise? Beyond the simplest additions, and the power to check the items of a bill, the arithmetical knowledge required of any well-informed person in private life is very limited. For all practical purposes, whatever I may have learned at school of fractions, or proportion, or decimals, is, unless I happen to be in business, far less available to me in life than a knowledge, say, of history of my own country, or the elementary truths of physics. The truth is, that regarded as practical arts, reading, writing, and arithmetic have no right to be classed together as co-ordinate elements of education; for the last of these is considerably less useful to the average man or woman not only than the other two, but than 267 many others that might be named. But reading, writing, and such mathematical or logical exercise as may be gained in connection with the manifestation of numbers, have a right to constitute the primary elements of instruction. And I believe that arithmetic, if it deserves the high place that it conventionally holds in our educational system, deserves it mainly on the ground that it is to be treated as a logical exercise. It is the only branch of mathematics which has found its way into primary and early education; other departments of pure science being reserved for what is called higher or university instruction. But all the arguments in favor of teaching algebra and trigonometry to advanced students, apply equally to the teaching of the principles or theory of arithmetic to schoolboys. It is calculated to do for them exactly the same kind of service, to educate one side of their minds, to bring into play one set of faculties which cannot be so severely or properly exercised in any other department of learning. In short, relatively to the needs of a beginner, Arithmetic, as a science, is just as valuable—it is certainly quite as intelligible—as the higher mathematics to a university student.

They learn to speak, write, and do arithmetic. They have a phenomenal memory. If one read them the Encyclopedia Britannica they could repeat everything back in order, but they never think up anything original. They'd make fine university professors.

When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system.

In a way, you'd say my life is a convex combination of English and mathematics. ... And not only that, I want my kids to be that way: use left brain, right brain at the same time – you got a lot more done. That was part of the bargain.

One does not have to have experience raising children through school, dealing with family tragedies, and so forth, to be able to find three numbers whose fourth powers add up to another one.

[S]poken or colloquial Chinese is [...] in fact the language of a child. Now as a proof of this, we all know how easily European children learn colloquial or spoken Chinese, while learned philogues and sinologues insist in saying that Chinese is so difficult. Chinese, colloquial Chinese, I say again is the language of a child. My first advice therefore to my foreign friends who want to learn Chinese is "Be ye like little children, you will then not only enter into the Kingdom of Heaven, but you will also be able to learn Chinese."