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I want to take this next bit of time to just tell you a little bit about what makes

mathematicians excited about solving problems.

So I will warn you for all of you practically minded scientists, there is very little practicality in this talk.

But hopefully there will be some things that are delightful in their own way.

So just kind of a broad outline of what I'm going to be talking about today.

I want to give you kind of an idea of what is being studied currently among mathematicians.

So the pure side, the applied side, and kind of things in between.

And then give you an idea of what motivates mathematicians to solve a problem and give you three particular examples of theorems and conjectures that have

gained some fame in the mathematical world in one way or another.

And then finally, since we are talking about the natural sciences, I want to ask whether

mathematicians care about the physical world and what

we think about when scientists use mathematics. So just kind of a broad overview of math, we

generally split math into pure math and applied math. And pure mathematics, you can think about

this as being the study of structure in general.

So as mathematicians, we've kind of expanded from looking at numbers and looking at geometry

to looking at kind of what is this underlying structure.

And some of these subtopics include algebra, where we're really looking at the way that we

combine different numbers.

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