  We retrace the first steps towards understanding neutrinos, particles
predicted by Pauli in 1930 to avoid a supposed violation of time-translation
symmetry. Despite the tendency to reduce the whole story to his intuition and
the skill of Reines & Cowan, according to history great strides were made in
thirties thanks to precious intellectual tools that combined ideas and
mathematics. I refer primarily to the contribution of Fermi, who proposed in
1933 a theory in which matter particles can appear and disappear, prototypical
of those at the basis of today's particle physics. This theory, despite its
limitations, led physicists towards the observation of neutrinos, paved the way
for further developments - e.g., it anticipated the characteristic of crossing
symmetry - and had an impressive scientific legacy. We reconstruct the chain of
arguments in the most accessible terms for a modern reader, emphasising the
role of theoretical physics and reflecting on some alternative assessments of
Fermi's contribution. A few technical remarks are collected in the appendix.
