I soon saw an application called "Graphing Calculator", and upon launching it very quickly came up with this:
It wasn't a static image either, it's like a sheet floating in space that you can grab with the mouse and spin in 3-d. Zooming and panning and animating were all perfectly fluid -- no ugly stepping, no entering in plot bounds, no "plot" button to re-click every time the view changes. Any mathematical relationship I could think of was instantly visualized. Any piece of the equation could have an "n" inserted which lets you animate that piece and see the sensitivity to that parameter. It was amazing! 2-d plots are great too, but my mind quickly was unsatisfied with only 2 dimensions. 4-d and beyond suddenly made perfect sense.
Within minutes I had knocked out half my unresolved math questions. What a thrill! Not only that, I'd never seen a computer do anything like that before, I didn't think computers would ever be fast enough to do anything close to what I was seeing right in front of my eyes.
And this was 1996. 66 MHz.
I immediately knew I needed a Mac, and worked like crazy to get one. Graphing Calculator sold me.
The story of how Graphing Calculator got on the Macs is crazy. Crazier still is that Apple didn't buy the guy out (I'm guessing his price was too high).
The advent of OS X in the early 2000s brought with it a crappy "Grapher" app replacing Graphing Calculator. GC was still available on the website, but it was $100 (?!), which I couldn't ever justify spending. For me that took all the fun of math back out of the Mac and has been a sore spot for me for the last 9 years.
Well, for anyone else out there like me, the wait is finally over. $10 on the App Store, the "lite" version has everything I missed. I didn't even blink between seeing the screenshots/price and clicking the "Buy now" button.
Math is already more exciting again. =)