Hi, from the past two days, we have seen that
mathematics gives us the power to create new
ideas and the power to recognize patterns and
structure. Today, I would like to suggest that
maybe math's greatest gift is something even
more personal. Mathematics changes the way we
think. Now, many believe that success in math
comes from memorizing formulas. Now, while formulas
certainly have their place, they are only tools.
The real work of mathematics is deciding which
tools to use and why it works and how to adapt
when the problem changes. That is why two students
can know the exact same formulas but approach
a problem in different ways. One student might
immediately start plugging numbers into an equation.
The other might pause and ask what information
is important, draw a diagram, consider different
strategies, and develops a plan before beginning.
This second student is thinking mathematically.
One of the beautiful things about math is that
there is more than one path to a solution. You
may solve a problem using algebra, by graphing,
or numerically, or even through a clever insight.
And as you gain experience, you begin building
what I like to think of as a mathematical toolbox.
Every theorem and every formula and every technique
becomes another tool that you can reach for.
The challenge is not memorizing every tool. but
it is learning when each tool is most useful.
And these habits do not stay in the classroom.
Mathematics teaches us to ask good questions,
to examine assumptions, and to recognize when
an argument does not follow logically from its
premises. These same skills helps us evaluate
claims that we hear in the news. to make thoughtful
decisions at work, and to communicate our own
ideas more clearly. Now, our goal is not to become
someone who always has the right answer. Our
goal is to become someone who knows how to think
carefully when the answer is not obvious. Okay,
tomorrow we will see these ways of thinking can
lead us to make more informed decisions during
uncertainty, by using probability and mathematical
modeling.