I think that everyone in the world could be
a math person if they wanted to. The keyword though, I want to say, is if they
wanted to. That said, I do think that everyone in America
could benefit from having that mathematical background in reasoning just to help everyone
make very good decisions. And here I’m distinguishing already between
math as people usually conceive of it, and decision making and analysis, which is actually
what I think math is. So, for example, I don’t think that being
a math person means that you can recite the formulas between the sines, cosines, tangents
and to use logarithms and exponentials interchangeably. That’s not necessarily what I think everyone
should try to concentrate to understand. The main things to concentrate to understand
are the mathematical principles of reasoning. But let me go back to these sines, cosines
and logarithms. Well actually they do have value. What they are is that they are ways to show
you how these basic building blocks of reasoning can be used to deduce surprising things or
difficult things. In some sense they’re like the historical
coverages of the triumphs of mathematics, so one cannot just talk abstractly about “yes
let’s talk about mathematical logic”, it’s actually quite useful to have case studies
or stories, which are these famous theorems. Now, I actually think that these are accessible
to everyone. I think that actually one reason mathematics
is difficult to understand is actually because of that network of prerequisites. You see, math is one of these strange subjects
for which the concepts are chained in sequences of dependencies. When you have long chains there are very few
starting points—very few things I need to memorize. I don’t need to memorize, for example, all
these things in history such as “when was the war of 1812?” Well actually I know that one, because that’s
a math fact—it was 1812—but I can’t tell you a lot of other facts, which are just purely
memorized. In mathematics you have very few that you
memorize and the rest you deduce as you go through, and this chain of deductions is actually
what’s critical. Now, let me contrast that with other subjects
like say history. History doesn’t have this long chain, in fact
if you fully understand the war of 1812 that’s great, and it is true that that will influence
perhaps your understanding later of the women’s movement, but it won’t to be as absolutely
prerequisite. In the sense that if you think about the concepts
I actually think that history has more concepts than mathematics; it’s just that they’re spread
out broader and they don’t depend on each other as strongly. So, for example, if you miss a week you will
miss the understanding of one unit, but that won’t stop you from understanding all of the
rest of the components. So that’s actually the difference between
math and other subjects in my head. Math has fewer concepts but they’re chained
deeper. And because of the way that we usually learn
when you had deep chains it’s very fragile because you lose any one link—meaning if
you miss a few concepts along the chain you can actually be completely lost. If, for example, you’re sick for a week, or
if your mind is somewhere else for a week, you might make a hole in your prerequisites. And the way that education often works where
it’s almost like riding a train from a beginning to an end, well it’s such that if you have
a hole somewhere in your track the train is not going to pass that hole. Now, I think that the way to help to address
this is to provide a way for everyone to learn at their own pace and in fact to fill in the
holes whenever they are sensed. And I actually feel like if everyone was able
to pick up every one of those prerequisites as necessary, filling in any gap they have,
mathematics would change from being the hardest subject to the easiest subject. I think everyone is a math person, and all
that one has to do is to go through the chain and fill in all the gaps, and you will understand
it better than all the other subjects actually.