Quantum entanglement was first studied in 1935, in a famous paper by Albert Einstein, Boris Podolsky, and Nathan Rosen. These scientists collectively have come to be known as EPR, an acronym that derives from the first letter of each of their last names.In their paper, the authors considered a certain instance of entanglement that has since come to be known as the EPR paradox or the EPR experiment. The purpose of their paper was to use the paradox to demonstrate that quantum mechanics could not provide a complete description of reality.
The term “entanglement” was not coined by EPR.Instead, it was first used by Erwin Schrodinger, one of the fathers of quantum mechanics, in a letter to Albert Einstein discussing the EPR experiment. In a paper following the original paper by EPR, Schrodinger stressed that entanglement is a key property of quantum physics that distinguishes it from the “classical” physics that came before it.

The EPR experiment generated much discussion in the physics world about the structure and interpretation of quantum mechanics .In 1964, the physicist John Stewart Bell showed that there was a flaw in the argument of EPR, which claimed that quantum mechanics is incomplete. He used a mathematical fact now known as Bell’s theorem to demonstrate that one of EPR’s key assumptions, the principle of locality, is at odds with the experimentally verifiable predictions of quantum mechanics.

For elaboration on why quantum entanglement is such a strange, interesting phenomenon, check out Quantum entanglement - What’s the big deal?

Quantum entanglement is a phenomenon that occurs because our universe fundamentally behaves according to the laws of quantum mechanics. Entanglement is by no means the only interesting phenomenon in quantum mechanics.As mentioned in the video, a central aspect of quantum mechanics is that systems can occupy so-called superposition states. When a system is in a superposition state, taking measurements of the system can yield one of multiple possibilities each with a certain probability. This probabilistic aspect of measurement outcomes in quantum mechanics is another central aspect of the quantum world. To learn more about how probability enters into quantum mechanics, watch “The uncertain location of electrons.”

When physicists study all of these aspects of quantum mechanics, they do so in a precise way using some pretty powerful mathematics.Quantum mechanics is primarily a mathematical model based on a field of mathematics called linear algebra. In particular, quantum mechanics models the states of systems, such as superposition states, as certain mathematical objects described in linear algebra called vectors. Linear algebra is the study of vectors and certain operations on vectors called linear transformations. Observable quantities in quantum mechanics, such as the position of an electron, are modeled as such linear transformations. If you’re really interested in mathematics and want to learn some hardcore linear algebra then check out this course.