mm this is very interesting, in school we only learn what is 'relevant', hah.
what is this magical number that confers aromaticy, 4n + 2?
by playing with numbers i figure that there has to be an odd number of electrons above and below, since (4n + 2)/2 gives u an odd number everytime, hehe.
As victor said, the answer lies in molecular orbital theory. I'll try to offer a simple explanation based on example, showing why benzene's molecular orbitals (which has 6 = 4n + 2 pi electrons) are stable when conjugated but cyclobutadiene (which has 4 = 4n pi electrons) is not stable.
Benzene's conjugated pi system is a combination of six p-orbitals, one from each carbon. This means that the combination of these six atomic orbitals must form six molecular orbitals. From symmetry arguments, three of these molecular orbitals are bonding orbitals and three are antibonding. Since the system contains six pi electrons (one from each carbon), all six electrons populate the three bonding orbitals. Since all of the bonding orbitals are completely filled and there are no electrons in the antibonding orbitals, benzene is stable.
Cyclobutadiene's conjugated pi system is a combination of four p-orbitals, and therefore consists of four molecular orbitals. By symmetry arguments, there is one bonding orbital, two degenerate non-bonding orbitals (i.e. the two non-bonding orbitals are of the same energy), and one antibonding orbital. Since cyclobutadiene has four pi electrons, the first to fill the bonding orbital. However, because the orbitals with the next highest energy (the non-bonding orbitals) are degenerate, one electron goes into each orbital (by
Hund's rule). Therefore if cyclobutadiene forms an aromatic system, it becomes a highly unstable diradical species. Since having these two unpaired electrons is very energetically unfavorable, cyclobutadiene will not form an aromatic system and will instead deform so that the Pi orbitals are no longer conjugated.
For a visual of the molecular orbital energy diagrams of benzene and cyclobutadiene see:
http://www.usm.maine.edu/~newton/Chy251_253/Lectures/Aromaticity/OrbitalArrays.GIF