DL said:

"If I had met the foundations earlier, I would have no-doubt ended up in love with the field of mathematics. This 'do the dumb stuff first' and 'pay your dues' notion of math instruction is probably a major deterrant to education."

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My experience was similar except I went the full distance and learned to love math. The trick my mentor did was to show that advanced mathematics was useful for practical problems through sucessive approximation. Start with a full description of the physical problem that is mathematically intractable and useless. Then begin simplfying it by sucessive approximation until you have something that is solvable. After you have an answer for a very simple model, go back and make the mathematical model more descriptive so you can learn more about the physical process. Sort of like using a zoom lens. The real challenge is convincing a kid up front that he can do this neat stuff after he goes through the long and tedious process of learning the basic skills. Using a computer to drive the math might be the answer. Thermodynamics in its raw theoretical form is deadly dull. However if you have a computer driving the math then the results can be extremely interesting, e.g. making water go through phase changes or making a gas polymerize into complex organic molecules, etc.

Gary