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
背诵正弦 余弦 正切的函数公式
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 can not 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 accessibleto 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?”
好的 实际上我知道这个 因为这是一个数学事实——是在1812年
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 will influence
perhaps your understanding later of the women’s movement,
but it won’t to be as absolutelyprerequisite.
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.