Came here to say "Thank You!". My interest in math got rekindled due no small measure to your site. Now as I try to learn more math, I try very hard to look for an "intuitive" meaning.

That's awesome to hear, thanks. I realize learning is more than knowledge transfer, you have to keep up the momentum to learn (for me, the joy of an intuition keeps me cranking away at tough topics).

> "Did I experience the concept beyond the technical definition?"

Thanks Kalid! Wish there were more resources in that notion available when I was starting my Telecommunications studies.

Thanks Ken, same here when starting school :).

For when I was starting school, I wish the Web had existed :P

Great job Kalid. I try to do this with kids. Simple ideas like why anything to power zero is 1 ? why do we need complex numbers ? Why is limit of something tending to zero/infinity even an interesting and useful concept ?

Thanks. It's great exploring these "What if?" questions with kids (or adults). Math becomes more like a world to explore than something we're supposed to "learn".

One of the analogies i gave to the kids was that why did man have to learn to travel by water. Because walking on land wouldn't get them to the other island. Complex numbers sometimes sometimes are used to get to islands that aren't accessible from working with regular numbers. I was obviously referring to finding roots to cubic equations using complex numbers. Using complex numbers is in some cases like walking on water :-). These are not exact but they make kids excited. The fact that Math is replete with hacks just like real world is something that needs to be made more vivid and interesting

Convergent oscillation between formal definition and aesthetic intuitions is my teacher's goal. Smoothly going up to pure theory so you can forget it and go back to playing music.

ps: I'm not a teacher. But I was I would ..