Where do electric circuit topologies come from?
Ans:  inventors create them.  From nothing.  Then everyone else hooks them together as &quot;building blocks&quot; to create more complicated systems.   Then sometimes years later, mathematicians work out the rigorous theoretical descriptions.
Simple example: look up the history of the Hartley Oscillator, the Colpitts, Dynatron, Clapp, Armstrong, or perhaps the vacuum-tube differential amplifier &quot;long-tailed pair.&quot;  Or even the Klystron uWave amp.  Oscillators were invented before 1890, with math description only happening in 1921.
(It's like asking, where do new symphonies come from, where do famous poems come from, how was John Lennon (or ANY sane human) able to write the music that he did? )
PS
How is &quot;technical creativity&quot; performed?  Mathematician Henri Poincaré was one of the early investigators.  He discovered that he could come up with amazing breakthroughs ...out of nothing.   They just appeared in his head, in great detail, fully formed.  Poincaré became curious about this, and asked top-level colleagues in other math departments.  It turned out that everyone was doing this!  (They all kept it secret, thinking that they were the only ones who were &quot;cheating&quot; in this way.)
They weren't solving puzzles.  Instead, they were taking long showers, or perhaps listening to music. Micro-dosing LSD, like Watson and Crick.  Getting into slightly-altered mental states, trying to trigger Genius insights.  (Poincaré made his greatest discovery when leaving for vacation, stepping onto a streetcar.)
In &quot;Science and Method,&quot; Poincaré gives the secret formula:

work on a problem for weeks, months, and be utterly defeated.  You've failed.
give up.
work on something else.  Or better yet, go on vacation.   Or take a long night-time highway drive, like Cary Mullis or Atanasoff did.
suddenly in an instant, your brain is filled with an immense amount of detailed information, all from nowhere.
Pull over to the side of the road, get out your little notebook or stack of napkins, and spend hours scribbling it all down, before it all goes away again.

Many discoveries (including many totally new circuit ideas) come from imagination: &quot;flashes of inspiration.&quot;  But they don't come without lots of work, since the &quot;creative leaps&quot; seem often to be the resolution of a major personal failure, after some huge amounts of background research which, lacking the breakthrough idea, was all going to be wasted.
PPS
Me, I think some of these &quot;flashes&quot; come from temporal paradoxes.  If you're to be the creator of a famous invention. then if only you could see into your own future, you could steal the idea ...from yourself.  Then build it and claim to have invented it.  But who then was the actual inventor?  Why you, of course!  See the RAH sf story &quot;All You Zombies&quot; ...or go and listen to &quot;I'm my own grandpa.&quot;
PPPS
The late Ralph Hartley was my roommate at the U. Rochester.
(No, not the original Oscillator Ralph.  This was his grandson.)
PPPPS
Speaking of topology, how could any normal human ever come up with the song I'M MY OWN GRANDPA?  Where did the original idea come from?  Outa freakin' nowhere?
https://www.youtube.com/watch?v=4SnI963ZzgY