Marveling At The Historical

Math Oldies But Goodies

  • About This Blog

    This blog is mostly about math procedures in textbooks dated from about 1825-1900. I’m writing about them because some of the procedures are exquisite and much more powerful, and simpler, than some of the procedures in current text books. Really!

    I update this blog as frequently as possible ... every 2-3 days. And, if you are a lover of old texts and unique procedures, you might want to talk to me about them, at I’m not an antiquarian; the books I have are dusty, musty, brown-paged scribbled-in texts written by authors with insights into how math works. Unfortunately, most of their procedures have vanished. They’ve been overcome by more traditional perspectives, but you have to realize that at that time, they were teaching the traditional methods.

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The Definition of Math is …

Posted by mark schwartz on February 25, 2017


Do you have a definition of math that you’ve come to by virtue of your experience or have you adopted a particularly viable definition offered by an outstanding mathematician? In either case, does the definition help you understand math in a way which enables you to help others make sense of math?

The Story

I have a definition which has evolved over time and is likely to continue to evolve. I came to my current definition by virtue of discussing math as a concept with students. When a student offers me “when am I ever going to use this stuff in real life?”, I offer my definition. I do this because I can link my definition to actual daily behaviors. I’ll give you an example later.

My current definition is: math is a set of tools we use to identify, connect and summarize quantifiable relationships. The ‘set of tools’ part usually drives everyone nuts because it’s vague but if you think about it, this set of tools is built into our brain. One of the things we do automatically and in nano-seconds is to make judgements. Some of these judgements are quantifiable. A simple example is to toss an object to someone and ask them to catch it. Then ask: is there any math here? This discussion leads students to become aware of the quantifiable judgements made in order to catch the object – judging velocity, trajectory, position of object, etc.

If you are willing to accept that we have this set of tools, even without a clear delineation of what they are, what part of the brain is operational at that moment and how they function, then this allows for the rest of my definition to come into play.

If we can identify a quantifiable ‘event’, and thus have a bunch of these quantifiable events, we can then identify quantifiable relationships. Ever engage in a conversation where the topic was define love? Not exactly quantifiable. This is likely quite different from talking about an equation defining the relationship between x and y.

So basically, I’ve addressed not only identifying a quantifiable event but also connecting these events. I hope I need not make a somewhat exhaustive list to help you understand what I’ve stated. Rather, I’m hoping that your experiences can generate a list of examples.

Summarizing quantifiable relationships is nothing more than a formula such as y = mx + b!

If this definition seems too simplistic and doesn’t accommodate the kind of math you consider, then – since this is my current evolving definition – how about having a little discussion about it? Write to me at and let me know why this doesn’t work for you and let me know of your current definition, if you have one. I realize it’s not necessary to define math in order to learn or teach it well but by having one, I can talk to students about math in a context which seems to make sense to them and … it has helped many of my remedial students believe they can master math.


2 Responses to “The Definition of Math is …”

  1. tom said

    I don’t know what math is but I know it when I see it.

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