This is "Things Undone" by John Barnes. It can be read online here.
- equation (or series of questions? something like that) written in the 1700s or 1800s
Six hundred years ago, in the One Great Lecture of 1403, Francis
Tyrwhitt articulated the theory of indexical derivability, and after
his death, his eleven students carried the work on. In 1421, a
six-page calculation overthrew all of Aristotelian mechanics and
Ptomelaic astronomy, and told them how to build the telescopes and
chronometers with which to confirm it. In 1429, Marlow discovered the
periodic table of the elements, valence, and carbon chains in his
calculations in a single thick codex; Tyrwhitt's last living student,
Christopher Berkeley Maxwell, laid out the basic equations of
electromagnetism in the notes found in his rooms after his death.
Indexical derivability made all things inevitable. Once you had its
fourteen definitions, seven axioms, and forty-one basic theorems, from
then on if you could describe what you wanted to do, it was just a
matter of doing the steps, deriving the equations (or proving that no
equations could be derived, which was equivalent to absolute
impossibility), and then solving them.
- ANY question posed to it, which led to the development of fantastic technologies.
...but once you could ask a question intelligently, it was only a
matter of a few hours to learn whatever you wanted. As for building
whatever you dreamed up, with such a variety of tech stuff out there,
if you had a Liejt i.d., you could probably get the parts from any
junkyard or hobby store.
The universe still is what it is. Turns out
questions like "How can I love my neighbor?" are impossible to write
in a soluble form, but "How can I make a really big bomb?" and "How
can I go back and change the past?" are easy—just slap it together
following the directions that come out of the tube and off you go.
- The story centered on two (?) time-travel agents
Horejsi (Ruth) and Rastigevat (Simon) doing contract work for a government agency finding rogue time travelers.
- sent back in time to stop the equations/questions from being written/distributed
That part differs:
the person they have to find is the one who is trying to stop the equation from being written/distributed
- and the agents were chosen for their ability to perceive the universe shifting as things were changed in the past and remember past iterations of the universe
If us Feds didn't like what people were doing now, we'd eliminate them
at some time back in the past, and history would close around the
little space they had taken up—not "as if they had never been"—but
just plain, they had never been.
Only freak-memory social isolates like me and Horejsi would recall it.
That was part of how the FBI found us. Say a Com'n boy developed a
crush on his personal slave. You couldn't punish him for that; he was
higher. To punish and forbid meant admitting it was possible to cross
the boundary. So you made it that it never had been crossed; a Federal
agent took a short hop back and the slave girl had some quick,
painless accident as a small girl, and the boy's family was warned to
find more appropriate slaves.
But if three weeks after she ceased to exist, the boy was asking about
her, you knew you had someone who had that kind of memory; you could
fix him by having him talk to a lot of people, but if he wouldn't do
that, he would be either an FBI agent, or someone who needed