My seven-year-old son is into big numbers. "Dad," he'll ask over the breakfast table, his mouth stuffed with cereal, "What's a million, billion, zillion thousand plus 10 gajillion million trillion?"

"Lots," I will reply, before embarking on a dismissive lecture on how both "gajillion" and "zillion" are not formally defined quantities.

My answer, not surprisingly, does not satisfy him, for what he is groping for is a way to come to grips with the concept of infinity

He is anxious to pin down nothing less than the biggest number and he, like many before him, finds the going difficult.

On the other hand, my son is not much into ordinary numbers. Getting him to grapple with his times tables or ordinary subtraction is usually a difficult task, for he finds the whole business incredibly boring.

But here's the dirty little secret that's been rumbling around educational circles for the last four to five thousand years: he's right, it is boring.

It never ceases to amaze me how many otherwise educated adults confuse mathematics with arithmetic, viewing professional mathematicians as glorified high school algebra teachers.

Most people do not have the desire or opportunity to improve their mathematical knowledge beyond high school and are left with a perception that the beautiful, creative and mysterious arena of mathematics is somehow equivalent to the dreary tools of calculation that enable one to speak its language.

It is exactly as if people discarded Shakespeare by equating it to the rules for conjugating English verbs: one needs to know how to conjugate English verbs to appreciate Shakespeare, but there is a lot more going on than that.

So my son doesn't like to multiply. He finds times tables uninspiring (which they are) and highly arbitrary (which they aren't).

But just as a musician recognizes the importance of the dexterity hewn from practising scales to accomplishing beautiful music, we must do more to inspire our kids to recognize that basic mathematical concepts are a passport to grappling with bigger and more exciting concepts in the mathematical experience. Like infinity.

The concept of infinity is nothing less than one of the most captivating notions in the history of human thought: from Zeno's earliest conundrums of motion to the development of calculus, from the millennia-old struggle to reduce Euclid's Fifth Postulate (which in turn led to the development of non-Euclidean geometry, a concept later profoundly implemented by Einstein in his General Theory of Relativity) to Georg Cantor's mesmerizing hierarchy of infinities describing how some infinite sets can clearly be "bigger" than others, our understanding of the infinite continues to develop and surprise.

That is a story anyone would find exciting. We must do a better job of telling it.

Howard Burton writes each Monday for the Learning section. For more on the topic, he recommends Everything and More: A Compact History of Infinity (W.W. Norton), written by novelist David Foster Wallace for the Great Discoveries series.

PLEASURES OF MATH

Robert and Ellen Kaplan, co-authors of The Art of the Infinite: The Pleasures of Mathematics, will give a free public talk Wednesday as part of the Perimeter Institute's speaker series.

In 1994, the Kaplans, discouraged by the quality of math teaching in public schools, founded The Math Circle, based in Cambridge, Mass., to offer enriched discussion and instruction after school and on weekends. Within a few years, more than 200 children, starting at age five, were enrolled.