First, it is worth remembering what a neutrino is.  During early
studies of radioactivity it was discovered that a neutron could decay.
The decay products appeared to be just a proton and electron.
However, if these are the only decay products, an ugly problem rears
its head.  If one considers a neutron at rest, it has a certain amount
of energy.  (Its mass is equivalent to a rest energy because of E =
mc^2.)  If one then sums the energies of the decay products---the
masses of the electron and proton and their kinetic energy---it never
equals that of the rest energy of a neutron.  Thus, one has two
choices, either energy is not conserved or there is a third decay
product.

Wolfgang Pauli was uncomfortable with abandoning the principle of
energy conservation so he proposed, in 1930, that there was a third
particle (which Enrico Fermi called the "little neutral one" or
neutrino) produced in the decay of a neutron.  It has to be neutral,
i.e., carry no charge or have charge 0, because a neutron is neutral
whereas an electron has charge -1 and a proton has a charge +1.  In
1956 Pauli and Fermi were vindicated when a neutrino was detected
directly by Reines & Cowan.  (For his experimental work, Reines
received the 1995 Nobel Prize in Physics.)

The long gap between the Pauli's proposal and the neutrino's discovery
is due to the way that a neutrino interacts.  Unlike the electron and
protron that can interact via the electromagnetic force, the neutrino
interacts only via the weak force.  (The electron can also interact
via the weak force.)  As its name suggests, weak force interactions
are weak.  A neutrino can pass through our planet without a problem.
Indeed, as you read this, billions of neutrinos are passing through
your body.  As one might imagine, building an experimental appartus to
detect neutrinos is challenging.

Since 1956, additional kinds of neutrinos have been discovered.  The
electron has more massive counterparts, the muon and tau lepton.  Each
of these has an associated neutrino.  Thus there is an electron
neutrino, mu neutrino, and tau neutrino.  (In addition, each has an
anti-particle as well, so there is an electron anti-neutrino, mu
anti-neutrino, and tau anti-neutrino.  Furthermore, it was realized
that in order to get the equations to balance, the decay of a neutron
actually produces an electron, a protron, and electron anti-neutrino.)
Early work assumed that the neutrino had no mass and experiments
revealed quickly that, if the electron neutrino and anti-neutrino have
any mass, it must be quite small.

In the 1960s Raymond Davis, Jr., realized that the Sun should be a
copious source of neutrinos, *if* it shines by nuclear fusion.
Various fusion reactions that are thought to be important in producing
energy in the core of the Sun produce neutrinos as a by-product.  In a
now-famous experiment at the Homestake Mine, he set out to detect some
of these solar neutrinos.  John Bahcall has collaborated with Davis to
write a history of this experiment at
<URL:http://www.sns.ias.edu/~jnb/>.  Although quite difficult, in a
few years, it became evident that there was a discrepancy.  The number
of neutrinos detected at Homestake was far lower than what models of
the Sun predicted.  Moreover, as new experiments came online in the
late 1980s and early 1990s, the problem became even more severe.  Not
only was the number of neutrinos lower than expected, their energies
were not what was predicted.

There are three ways to resolve this problem.  (1) Our models of the
Sun are wrong.  In particular, if the temperature of the Sun's core is
just slightly lower than predicted that reduces the fusion reaction
rates and therefore the number of neutrinos that should be detected at
the Earth.  (2) Our understanding of neutrinos is incomplete and,
namely, the neutrino has mass.  (3) Both.

Astronomers were uncomfortable with explanation (1).  The fusion
reaction rate in the Sun's core is *quite* sensitive to its
temperature.  Adopting explanation (1) seemed to require some
elaborate "fine-tuning" of the model.  (Observations of the Sun in the
1990s have supported this initial reluctance of astronomers.  Using
helioseismology, <URL:http://antwrp.gsfc.nasa.gov/apod/ap990615.html>,
astronomers have a second way of probing beneath the Sun's surface, and
it does appear that the temperature of the Sun's core is just about
what our best models predict.)

In contrast explanation (2) seemed reasonable.  After all, just
detecting neutrinos was challenging.  The possibility that they might
have mass was not unreasonable.  In the 1970s Vera Rubin and her
collaborators were also demonstrating that spiral galaxies appeared to
have a lot of unseen matter in them.  If neutrinos has mass, one might
be able to solve two problems at once, both matching the solar
neutrino observations and accounting for some of the "missing matter"
or dark matter.

Explanation (2) is the following.  Suppose the neutrino has mass.
Then the neutrinos we observe, the electron neutrino, mu neutrino, and
tau neutrino, might not be the "true" neutrinos.  The true neutrinos,
call them nu1, nu2, and nu3, would combine in various ways to produce
the observed neutrinos.  Moreover, various properties of quantum
mechanics would allow the observed neutrinos to "oscillate" between
the various flavors.  Thus, an electron neutrino could be produced in
the core of the Sun but oscillate to become a mu neutrino by the time
it reached the Earth.  Because the early experiments detected only
electron neutrinos, if the electron neutrinos were changing to a
different kind of neutrino, the apparent discrepancy would be
resolved.  This explanation is known as the MSW effect after
the three physicists Mikheyev, Smirnov, and Wolfenstein who proposed
it first.

The second explanation now appears correct.  Various terrestrial
experiments, such as the Sudbury Neutrino Observatory (SNO), the
Super-Kamiokande Observatory, the Liquid Scintillator Neutrino
Detector (LSND) experiment, and Main Injector Neutrino Oscillation
Search (MINOS), appear to be detecting neutrino oscillations directly.

The mass required to explain neutrino oscillations is quite small.
The mass is sufficiently small that all of the neutrinos in the
Universe are unlikely to make a substantial contribution to the
density of the Universe.  However, it does appear to be sufficient to
resolve the solar neutrino problem.

Additional information on neutrinos is at
<URL:http://wwwlapp.in2p3.fr/neutrinos/aneut.html>.