The outer core of the Earth was discovered in 1906 by the seismologist Richard Dixon Oldham. At long angular distance from an epicentre, he observed an abnormally large travel time of teleseismic waves. His conclusion was that these waves, propagating deeply in the Earth, cross a central core, where the propagation speed is lower. In 1913, Gutenberg determined the depth of a core-mantle boundary (CMB) by using seismic waves. In 1926, using Earth tides and seismic observations, Harold Jeffreys showed that the core has a much smaller rigidity than the mantle and could be liquid. When studying the waves associated to a particular earthquake, it is seen that there exists a zone where no P and no PKP wave arrives; it is called the shadow zone. In 1936, Inge Lehmann interpreted waves in the shadow zone as P waves that were reflected on a 5000 km deep discontinuity (PKiKP waves in modern terminology): there was thus inside the fluid core a region with different properties. This is the inner core, whose solidity was suggested in the 40ies by Edward Bullen and proven in 1971 by A. M. Dziewonski and F. Gilbert using observations of the Earth's free oscillations.