In Chapter 25 of The Science of Interstellar by physicist Kip Thorne, it's confirmed that the equations on the board were written by physicists (mostly all by Thorne himself, though some of his students were involved in writing equations in notebooks and helping explain to the actors what to write when they were actually shown writing things on blackboards). They're supposed to involve some new future physics involving higher dimensions which are an attempt to explain "gravitational anomalies" that, in the movie's universe, had been observed in very careful measurements of gravitational tidal forces around the Earth. So, a lot of the equations would have been at least partly fictional, though inspired by real physics. Here's a part that talks about it:
For the Professor, the key to understanding and controlling the
anomalies is an equation he has written on his blackboard (Figure
25.7, below). In the movie, he and Murph struggle to solve his equation.
Murph's and the Professor's Notebooks—and the Blackboard
Before filming began, two impressive Caltech physics students filled
notebooks with calculations about the Professor's equation. Elena
Murchikova filled a clean, new notebook with calculations by grown-up
Murph, calculations written with elegant calligraphy. Keith Matthews
filled a beat up, old notebook with calculations by Professor Brand,
in the more sloppy handwriting common for old guys like the Professor
In the movie, grown-up Murph (played by Jessica Chastain) discusses
the math in her notebook with the Professor (played by Michael Caine).
Murchikova, an expert in quantum gravity and cosmology, was on set to advise Chastain about her dialog and notebook, and things she was
to write on the blackboard.
Thorne goes on to explain that the equation they were trying to find dealt with a higher spatial dimension, "the bulk", which in reality is theorized in models of brane cosmology (an extension of superstring theory). Part of the idea in the movie that the gravitational constant might depend on fields in the bulk, which would allow it to vary. Thorne writes that
the Professor tried to build a mathematical description of the bulk
fields and how they might generate anomalies, control our universe's
gravitational constant G, hold the wormhole open, and prevent our
brane from collisions.
The Professor embodied all his insights in a single equation, THE
equation, which he wrote on one of the sixteen blackboards in his
office (Figure 25.7). Cooper sees the equation on his first visit to
NASA, and the equation is still there thirty years later, when Murph
has grown up to become a brilliant physicist in her own right, and is
helping the Professor try to solve it.
This equation is called an "Action." There is a well-known (to
physicists) mathematical procedure to begin with such an Action, and
from it deduce all the nonquantum physical laws. The Professor's
equation, in effect, is the mother of all nonquantum laws. But for it
to give birth to the right laws—the laws that predict correctly
how the anomalies are produced, how the wormhole his held open, how G
is controlled, and how our universe is protected—the equation must
have precisely the correct mathematical form. The Professor doesn't
know the correct form. He is guessing. His is an educated guess, but a
His equation contains lots of guessing: guesses for things called
"U(Q), H_ij (Q^2), W_ij, and M (standard model fields)" on his
blackboard (Figure 25.7). In effect, these are guesses for the nature
of the bulk fields' force lines, and how they influence our brane, and
how fields in our brane influence them.
In the movie, when the Professor is very old, we see him and grown-up
Murph trying to solve his equation by iterations. On a blackboard,
they make a list of guesses for the unknown things (guesses that I
wrote on the board just before the scene was filmed; Figures 25.8 and
25.9). Then, in my extrapolation, Murph inserted each guess into a huge computer program they've written. The program computes the
physical laws for that guess, and those laws' predictions for how the
gravitational anomalies behave.
In my extrapolation, none of the guesses predicts anomalies that look
anything like the observations. But in the movie, the Professor and
Murph keep trying. They keep iterating: making a guess, computing the
consequences, abandoning the guess, and going on to the next guess,
one guess after another after another, until exhaustion sets in. Then
they begin again the next day.
Finally, in a note at the end of the chapter Thorne adds this about "the equation" that the Professor and Murph are trying to guess the correct form of:
The meaning of the various symbols in the other equation are spelled
out on the Professor's other fifteen blackboards, along with the other
information about the equation, all of which I ghost-wrote for the
movie's filming. You can see photographs of all sixteen blackboards
on this book's page at Interstellar.withgoogle.com.
For the photos of all the blackboards, go to the section of the site titled "Transmissions", click "Kip Thorne" and then "Explore Kip Thorne's new book", then scroll to the bottom of the page.