What are advanced concepts? They are those which ''logically'' depend on simpler concepts. However, human beings don't learn using predicate logic so advanced concepts can be taught even to children if you understand them yourself, and aren't incompetent. Moreover, advanced concepts tend to be difficult to teach after the fact, so TeachAdvancedConcepts '''first'''!

Since it's turned out to be necessary to explain what a concept refers to in this context, here it is. A concept is NOT a unit of knowledge, skill or expertise but of ''understanding''. In fact, knowledge is remarkably irrelevant to understanding and so is irrelevant to this page.

This page is based on the assumption that understanding is a good in and of itself, quite independently of how it can be exploited. So arguments in favour of teaching something that permits one to "calculate meaningful results" are simply irrelevant. Additionally, understanding is valuable in any measure and for every person, so comparisons to "professionals" are ludicrous on top of being irrelevant (irrelevant because they're about exploiting understanding).

Understanding doesn't have a "function" or "purpose". To understand the world is a joy in itself. It doesn't matter how little or how much of it you have. It certainly doesn't matter how much of it others have. The idea of declaring one person's understanding less valuable than another's because of its more limited extent is exactly as ludicrous as declaring someone's child less valuable than another's because it's younger or less athletic. 

So, onto the examples.

Examples in physics:
* non-linear waves
* decoherence of wavefunctions
* bosons vs fermions
* three generations
* the block universe (spacetime as opposed to space-time)
* superstrings
* T and R dualities
* p-branes

Examples in biology:
* evolution
* the immune system; antibodies, macrophages, T-cells
* immunorejection and immunosuppression
* electrochemical transmission of nerve impulses

Examples in computer science:
* object-orientation

Examples in math:
* formalism / mathematical logic

Miscellaneous:
* city design

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[discussion of the democratization of learning moved to TeachAdvancedConcepts]

[discussion of Knowledge vs Understanding moved to UnderstandingVsKnowledge]

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See also FractalComprehension