discuss a basic question: what the heck am I talking about?

By the way, for those of you who are confused, I started with podcast

number 0, so this one really is the 50th. So, what exactly is

mathematics, and why did I create a new podcast about it?

As for definitions, there are a lot of them floating around on the

net. Dictionary.com, for example, defines math as " the systematic

treatment of magnitude, relationships between figures and forms, and

relations between quantities expressed symbolically." The most

popular definition at Urban Dictionary is similar: "The unified

theorems and theories used in the analysis of order, sequence,

pattern, form, space, figures, and numbers." But I think these common

definitions are really focusing on the trees and missing the forest.

For example, one exciting subdiscipline I have mentioned in numerous

podcasts is the theory of computation-- this clearly seems to be part

of math, yet one could argue that both these definitions exclude it!

I don't think the right way to define mathematics is to enumerate a

list of subtopics.

My favorite concise definition comes from the 19th-century

philosopher Benjamin Pierce. He defined mathematics as "the science

that draws necessary conclusions." And I think that captures what I

find most interesting: the idea that from simple premises, we can

discover surprising consequences. From the basic ideas of length,

area, and angle measurements, we can discover the Pythagorean

Theorem. From the definition that continuous functions don't skip a

value, we find that there must be opposite points on the globe sharing

the same temperature. By extending the concepts of solid geometry, we

can derive properties of multidimensional objects we will never see.

Or from precise definitions of what it means to reason in a formal

system, we are led to Godel's theorem that there are fundamental

limitations to our reasoning abilities.

This is what I find most interesting about mathematics-- the odd

discoveries and surprising consequences, along with the strange quirks

of the people involved in discovering them. Of course, applicability

to the real world, and its resulting presence as a requirement in many

areas of our education, are important, but these areas are

well-covered by other podcasts. If something in the podcast does

happen to apply to the real world or help you out in a college class,

that's great, but that's not the main point. The main point is to

talk about odd corners or applications that I find interesting,

whether they have some real-world purpose or not! I'm betting that

there are plenty of people out there as geeky as me, who also enjoy

these kinds of topics. Perhaps we can help each other to discover new

and fun areas we might have otherwise missed.

By the way, I'd like to thank those of you who have reviewed this

podcast on iTunes; I think the user named 'weepleman' did a good job

of capturing the essence, when he wrote that the podcast gives

"useless but interesting ideas and math". Also, thanks to those of

you who emailed me, at my address erik@mathmutation.com. I like to

hear from listeners out there, mainly to reassure me that I have some,

and ideas for future podcast topics are always welcome.

And this has been your Math Mutation for today.

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