Electrons are 3 dimensional quantized waves (wave functions)?

This physics professor says that electrons are waves in 3 dimensional space time. But I thought that the wave functions were only a probability of finding an electron?

Actually, that's not what the Professor wrote. In fact he wrote:

Electrons (as well as all particles) are partially particle-like and partially wave-like, depending on the situation. When bound in atoms in an undisturbed state, electrons act like waves. These waves are three-dimensional probability density waves that spread out to fill the entire atom.

But in Quantum Physics particles are mathematically described by wave functions $psi$ that contains all the measurable information about the particle.

So electrons sometimes show particle-like properties, sometimes show wave-like properties and are fully described by their wave function $psi$.

I thought that electron wave functions were only mathematical of [where] to find the electron

They are mathematical, but they tell you more than just where you can find it and with which frequencies. You could get that from the square of the modulus of the wave function.

A wavefunction tells you everything. It tells you how it evolves in time (two different modulus squared could evolve differently, for instance a wave traveling to the left and one traveling tot the right could have the same square). It feels you the frequency of creating spin results, or creating momentum results or energy results. Etcetera.

This physics professor says that electrons are waves in 3 dimensional space time.

Wavefunctions are not defined in 3d space. If you have $n$ particles then there is one wave function for all of them, and it is defined on a $3n$ dimensional space, $mathbb R^{3n}.$ And they are mapped into a joint spin state, which is a single spin state describing spin of all of them, again in a best information way, not just a probability of a few specific interactions.

But I thought that the wave functions were only a probability of finding an electron?

No. A wave function is a complete description of the entire system.

The problem with electrons as with any other subatomic particles is the Uncertainty Principle. Which basically means that it is not physically possible to know the exact position and momentum of them at any particular time accurately, though we can measure either one of them. That means we cannot really predict what trajectory an electron will follow and where it will be at a particular time later on simply because we may never know both its instantaneous velocity and position at any given time.

That for physicists mean that, we can no longer play ball with the electron and all we are left with is probabilities...and guesses. But still we do know that for most part of the time a bound electron has to stay closer to the nucleas more than it stays away from it, so we say that the probability of it being at $infty$ tends to zero...Similarly some other logical conclusions based upon our understanding of waves, and the wave nature of electrons (which was first shown through electron-diffraction experiments) give us our understanding of electrons, and we know the following:

1. The wave nature needs to be invoked, without which we cannot explain electron diffraction among other things.
2. that we need to accept the fact that we can only talk in terms of probabilities...and the wave equations are our formulations to understand this wavy play of probabilities! That's probably the best we know about electrons!