I agree, I remember having problems with the math in both statistical thermo (micro thermo) and advanced fluids classes (unstable differential equation solutions). In both cases I did well because the classes were taught well, but I still don't really understand the math at a fundimental level. I also didn't go to grad school until 10 years after my BS.

I almost think that engineering students need a full year of serious math before they start taking engineering classes. American high schools don't provide an adequate background for technical studies. On the original topic, I know some women who understand math at a very fundimental level.

Math is a strange subject. It seems like lots of people can 'do it' but much fewer 'understand it'. This even applies to math teachers. Even more odd is the fact that we can invent these highly abstract symbol systems which in many ways seem just like mind games but which seem to connect with basic structural components of the universe. If there is anything within our experience which would count as the 'language of God' it would seem to be Math.

My wife had an absolutely brilliant Math teacher at Metropolitan State College in her Math education class. He didn't 'teach' Math. The class consisted of a series of problems, which the students were charged to solve. The solutions were all basic aspects of Math. There weren't that many problems and each one would take a couple of weeks to solve. But in the end, my wife, who prior to the class had absolutely no interest in Math, ended up with the mind of a Mathematician. The key element in that approach is that each student's mind must generate the solution instead of starting with a known solution and then trying to understand it.
It goes back to Socrates/Plato's argument in the Meno that mathematical ideas are innate in our minds and must simply be drawn out.

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1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13

I'm not an expert on math history, but I believe the Greeks tended to use a geometric approach to math. That tended to limit their abstractions, the had problems with the concepts of infinity and limits.

I think I would say that mathematical ideas are innate in nature, not just in our minds, and must be discovered (not invented). Just take a look at Euler's identity if you believe math is a human construct.

Can't tell you how many times the quadratic formula has saved my life . . . honestly, I can't.

As you can see, the amount of pirates has decreased as the rate of temperature has increased. Therefore we need more pirates to combat the rise of global warming!

To further prove my point, Somali has the highest concentration of pirates in the world and the lowest greenhouse gas emissions!

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-Typos courtesy of my mobile phone.

My advanced algebra and trigonometry teacher in 11th grade taught it to us as a song to the tune of Frere Jacques. I still remember it and have used it quite a few times, though I can't say it's ever saved anyone's life.

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Whoever said there's nothing more expensive than a cheap Mercedes never had a cheap Jaguar.

83 300D Turbo with manual conversion, early W126 vented front rotors and H4 headlights 401,xxx miles
08 Suzuki GSX-R600 M4 Slip-on 26,xxx miles
88 Jaguar XJS V12 94,xxx miles. Work in progress.
99 Mazda Miata 183,xxx miles.