## Panic Zone

I see you pressed the math panic button. Let's have a little talk about why math is so abstract.

Roughly (and incompletely) speaking mathematics is the study of objects, relationships between objects, and ways of transforming objects into other objects. Sounds weird doesn’t it? What the heck is an object anyway? That’s the neat part; an object can be anything! This whole notion of “objects” and “transformations” instead of only “numbers” and specific functions (like addition, multiplication, f(x) = x^2 ...) is just part of the

Believe it or not, we start learning abstract math in kindergarten. If one puts 3 apples into a previously empty box and then puts 5 more apples into the box and we then count the number of apples in the box we find 8. Nobody is all that surprised that things work pretty much the same with oranges, bananas, and even non-fruits. We express this abstractly as 3+5 = 8. What do we have 3 and 5 of and what do they taste like? Who cares, it’s not important, so we abstract away that details that we don’t need and just use the concept of number instead. Much of mathematics just continues this idea of abstraction. In fact there is a whole area of mathematics, abstract algebra, which works almost solely with abstract objects.

With such general, abstract ideas mathematics can be applied concretely to almost every field. So we can add apples, oranges, or just about anything else you can think of. From physics where it serves as a language to express the workings of the universe, to computer science where it is a framework to answer fundamental questions about what problems can be solved by computer (and how fast), through to statistics to analyze data for use in vast array of fields... There are so many other fields that there is just not room to list them all.

So do mathematicians always know exactly what they’re talking about? Not always, but they do know the important common details that let them say some pretty profound things about all kinds of objects all at once. Be they apples, oranges, bananas ... or kumquats.

*abstraction*that we use in math to generalize ideas by stripping away unnecessary details. Maybe this idea of abstraction is a bit scary, even the word sounds scary, but we use it all the time.Believe it or not, we start learning abstract math in kindergarten. If one puts 3 apples into a previously empty box and then puts 5 more apples into the box and we then count the number of apples in the box we find 8. Nobody is all that surprised that things work pretty much the same with oranges, bananas, and even non-fruits. We express this abstractly as 3+5 = 8. What do we have 3 and 5 of and what do they taste like? Who cares, it’s not important, so we abstract away that details that we don’t need and just use the concept of number instead. Much of mathematics just continues this idea of abstraction. In fact there is a whole area of mathematics, abstract algebra, which works almost solely with abstract objects.

With such general, abstract ideas mathematics can be applied concretely to almost every field. So we can add apples, oranges, or just about anything else you can think of. From physics where it serves as a language to express the workings of the universe, to computer science where it is a framework to answer fundamental questions about what problems can be solved by computer (and how fast), through to statistics to analyze data for use in vast array of fields... There are so many other fields that there is just not room to list them all.

So do mathematicians always know exactly what they’re talking about? Not always, but they do know the important common details that let them say some pretty profound things about all kinds of objects all at once. Be they apples, oranges, bananas ... or kumquats.