The crucial problem of physics was first formulated by Democritus in t
he 5th century BC: to find the ''alphatauomualpha'' or smallest uncutt
able bits of matter. That has not changed ever since. Among the curren
t candidates are electron and positron, the least expensive of today's
bona fide alphatuaomualpha. Experimental tests of their non-composite
ness by precisely measuring the gyromagnetic ratios of the individual
trapped particles are reviewed.