So how does one go about proving something like this? It’s not like being a lawyer, where the goal is to persuade other people; nor is it like a scientist testing a theory. This is...

No mathematician in the world would bother making these senseless distinctions: 2 1/2 is a “mixed number ” while 5/2 is an “improper fraction.” They’re EQUAL for crying out loud. They are the exact same...

Mathematics is the art of explanation.

Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.

Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion—not because it makes no sense to...

A good problem is something you don’t know how to solve. That’s what makes it a good puzzle and a good opportunity.

If teaching is reduced to mere data transmission, if there is no sharing or excitement and wonder, if teachers themselves are passive recipients of information and not creators of new ideas, what hope is there...

Why don’t we want our children to learn to do mathematics? Is it that we don’t trust them, that we think it’s too hard? We seem to feel that they are capable of making arguments...

Mathematicians enjoy thinking about the simplest possible things, and the simplestpossible things are imaginary.

[Math] curriculum is obsessed with jargon and nomenclature seemingly for no other purpose than to provide teachers with something to test the students on.

I don’t see how it’s doing society any good to have it’s members walking around with vague memories of algebraic formulas and geometric diagrams, and clear memories of hating them.

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...

And I’ll go even further and say that mathematics, this art of abstract pattern-making — even more than storytelling, painting, or music – is our most quintessentially human art form. This is what our brains...

Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.

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...

It is the story that matters not just the ending.

Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to? The effect of such a production being made over something so simple is to make people doubt their...