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
正弦 余弦 正切
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…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 gaps they have.
Mathematics would change from being the hardest subject
to the easiest subject.
I think everyone’s a math person,
and all that one has to do
is to go through the chain,
and fill in all the gaps.
And you’ll understand it easier,
more better than all the other subjects actually.