Equipose, I bet if you poked around some math books aimed at non-mathematicians, you’d get a lot of what you missed by having really obnoxious and horribly bigoted teachers. And, as a possible future math teacher, I pledge, in your name, that no student of mine will suffer what you suffered.
As for cool-- it doesn’t get cooler than Goedel’s Incompleteness Theorem. Among other things, it gives us an infinite amount of not yet invented cool math.
It does get cooler than that. Check out the work of Kolmogorov and Chaitin.
Here’s a fun and impressive parlor trick with math. I’m sure some of you are familiar with it already (Samuel Beckett mentioned it in his novel Watt, for one thing), but I’m sure some of you aren’t:
Hand someone a calculator. Tell them to choose a number between 1 and 99. Now have them use the calculator to find the cube of that number. Have them tell you the cube, and in a few seconds you can tell them the original number. It’s really impressive, but not very difficult.
Here’s how it works: First, the number you’re working from has to be a perfect cube; that’s important.
Let’s say the cube they give you is 373,248. Look at the last digit and use the following:
(Last digit of cube/last digit of root)
1 / 1
2 / 8
3 / 7
4 / 4
5 / 5
6 / 6
7 / 3
8 / 2
9 / 9
Note that there are no repeats; each digit will result in a uniue corresponging final digit on the cube. Since the last digit of our example is 8, the last digit of the cube root will be 2.
Now strip off the last three digits of the cube, in this case leaving us with 373. You’ll need to memorize the cubes of numbers 1 through 10; not too difficult:
1[sup]3[/sup] = 1
2[sup]3[/sup] = 8
3[sup]3[/sup] = 27
4[sup]3[/sup] = 64
5[sup]3[/sup] = 125
6[sup]3[/sup] = 316
7[sup]3[/sup] = 343
8[sup]3[/sup] = 512
9[sup]3[/sup] = 729
Find the cube that is closest to but LESS than your number. In this case, the cube number is 373, so 343, or 7[sup]3[/sup], is the closest.
So the first digit is 7, second digit 2:
72[sup]3[/sup] = 373,248
Pretty neat trick, I think.
All of this can be simplified and extended as follows: take any integer. Add and subtract alternating digits. If the result is divisible by 11, the whole number is divisible by 11.
So let’s take 165893603421634
1-6+5-8+9-3+6-0+3-4+2-1+6-3+4 = 11, so the whole thing is divisible by 11. (And in fact equals 11 times 15081236674694)
I got tears in my eyes when I read that. Thank you.
j_sum1, thank you for your comments too. I agree that math is like a foreign language, but I love music sung in foreign languages. Everything (music, vocals, inflections) is more heightened when you don’t understand the language. The actual lyrics might be about something mundane. For instance, the Bulgarian Chorus might be singing about crops growing or the weather, but if you don’t hear the words as words, it sounds like angels singing from on high, about very profound things, and it’s gorgeous.
I don’t mean that math is mundane, but even though I don’t understand a “word” of math, it’s still all very pretty to look at, which is why I read this thread in the first place. I love the singing. 
Disclaimer: I don’t believe in angels, but if they existed, they’d probably sound like Le Mystere des voix Bulgares, and be mathematicians
Curry’s paradox is pretty cool.
Equipoise ditto what j_sum1 said. I taught myself for the most part. How many thousands, hell hundreds of thousands of math problems have I worked over the years, before I ever taught math. Dozens of textbooks later…and I solve every problem in a text from cover to cover some of them several times.
In order to truly teach something you need to have a full understanding of the subject. If a student isn’t grasping the concept, go at it from another direction. Not everyone learns in the same manner. I realize that mainstream teachers don’t have the time for individual tutoring in the classroom.
But that is no excuse for the experiences that YOU and many of us have endured.
I have never tutored any student that didn’t pass with at least a C average, most got A’s. I’m talking about kids that were “unteachable” or “lost causes” That’s bullshit IMO it just takes a different mindset and approach.
anyway…hijacked again
Anamorphic hang in there, take a deck of cards (stacked in order) and cut them perfectly (26each) and shuffle them perfectly. Then lay them out and watch the pattern develop. After four shuffles the cards start grouping into suits and pairs. By the eighth shuffle they are back where they started.
Practice shuffling the cards until you can do it right every time and poker becomes math. When I used to play poker, they finally decided I could play but not shuffle.
What can I say? When I lived in Dallas, that and pool (geometry) payed the bills. I practically lived at “Speeds”, hey I was young. 