I wonder: consider the decision problem of determining whether or not a given still life is glider-constructible. Is this problem known to be undecidable?
It's straightforward to show that an "inverse" of this problem -- given an arbitrary glider construction sequence, does it result in a still life? -- is undecidable, because gliders can construct patterns that behave like arbitrary Turing machines.
[0] https://conwaylife.com/forums/viewtopic.php?f=2&t=6830&p=201...
Someone should invent a GoL (that is still interesting) with that property.
Game for two persons. The game runs, you can go back in time and modify by introducing gliders. Only problem is, how to turn it into a real game, what is the object. Maybe split the world in two and try building a stable configuration. The opponenent can launch the glider towards your turf, or something like that.
no, thank you. I already have hobbies to consume my life.
I think Gemini (an LLM) and me are in agreement that the proof will likely be found by a neuro-symbolic AI. As evidence for this, see AlphaEvolve and the agents which received IMO Gold.
