Iwasawa (1959) introduced the μ-invariant of a Zp-extension and observed that it was zero in all cases he calculated.
Iwasawa & Sims (1966) used a computer to check that it vanishes for the cyclotomic Zp-extension of the rationals for all primes less than 4000.
Iwasawa (1971) later conjectured that the μ-invariant vanishes for any Zp-extension, but shortly after Iwasawa (1973) discovered examples of non-cyclotomic extensions of number fields with non-vanishing μ-invariant showing that his original conjecture was wrong.
Iwasawa (1958) showed that the vanishing of the μ-invariant for cyclotomic Zp-extensions of the rationals is equivalent to certain congruences between Bernoulli numbers, and Ferrero & Washington (1979) showed that the μ-invariant vanishes in these cases by proving that these congruences hold.
[1] Iwasawa exhibited Tp(K) as a module over the completion Zp[[T]] and this implies a formula for the exponent of p in the order of the class groups Cm of the form The Ferrero–Washington theorem states that μ is zero.