For an example of using the Wolfram automata-view to look at a problem, think of Fermat's Last Theorem. Can a specific cube (or any higher power, really) be ex

For an example of using the Wolfram automata-view to look at a problem, think of Fermat's Last Theorem. Can a specific cube (or any higher power, really) be expressed as the sum of two other cubes? The automata view shows us the answer because when you look at the list of cubes (or any higher power) as binary the resulting image meets the Wolfram test for randomness. Looking at these numbers in any other base has no obvious meaning, but in binary you can instantly see whether some set at least looks like a random automata. When I look at number theory or indeed any insoluble math problem it always seems to be some variation on people trying to write an equation that satisfies something from a random automata. Essentially all unsolved problems boil down to an argument about whether you believe automata show randomness or not.