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Your teacher might have been talking about the double bonds in the aromatic ring. They don't correspond to the physical reality. In reality the double bond (or electrons involved in it) is delocalized or spread over the entire ring, making it something between the single and double bond (as far as energy goes).
Oh yeah, we learnt all about that. It's just that there's not really any physical 'bond' there, it's just a fuzzy cloud of electrons, you get it into your head that it's more a conceptual idealisation than anything else.
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About your biology comment: I'm a bio(chem) person trying to cross into the mathematical realm. While I'm not an expert in mathematics, I don't consider myself mathematically illiterate. Bad teachers are just bad teachers, no generalization should be made about the entire field just because of them.
Some of my statistics and math. modelling teachers would occasionally say things that make no sense biologically or evolutionary.
However, I do agree that people should get better basic education in mathematics if they are to be involved in any field of science... or if they are to educate generations of future scientists.
Yeah well, I mean, they're not all bad... my DoS at Cambridge is a mathematical biologist, and I want to do mathematical neuroscience after my BA in maths, so...