I’ve always found it terribly difficult to understand why anyone at all believes in homeopathy (other than the fact that there are many deluded people out there) but research out today shows that one of the ideas used to bolster it, that water has memory, seems to have been thoroughly debunked:

Homoeopaths have been encouraged by the thought that
if the interactions were sufficiently strong and long-lasting, water
might "remember" a structural arrangement.

Although
it has long been proved incorrect, this argument is still put forward
to explain why homeopathic remedies can be effective: even if solutions
are so diluted that no active molecules are present, the water in the
solution is supposed to "remember" the perturbation of its structure
from when the molecules were initially present, before dilution.

By
using an extremely thin cell filled with water and monitoring
vibrations in the bonds within water molecules, the researchers studied
how perturbations induced by a laser light change the structure of
liquid water, and for how long these changes persist. The results show
that the "memory" of any distinct structures will not last for more
than 50 femtoseconds, a thousandth of a millionth of a millionth of a
second, one tenth of what was thought previously by scientists, said
Prof Dwayne Miller, who leads the University of Toronto effort.

"We
found that water loses any kind of memory or structural dependence on
its frequency or hydrogen bond network in an incredibly short time," he
said. "In so much as homoeopathic medicine [is said] to depend on the
structure of water being perturbed by minute amounts of additives, I
can say that water is incapable of retaining any correlations that such
a material might have imposed. Water simply loses its correlations or
memory too quickly."

However, he added: "I cannot
really say that we have found that homeopathic medicines can’t work on
a fundamental basis, only that the original ideas of how they might
work are clearly wrong."

As the professor states, this does not prove that homeopathic medicines do not work, or do even. For that we need double blind trials. None have been done that shows that it does work….so we have to conclude that it does not.
Won’t stop the quacks of course.