What is that dream? I don’t know much about it

thrance 20 hours ago | parent | next [-]

The Entscheidungsproblem. Basically, is there an algorithm such that, taking an arbitrary statement as input, can output wether it is true or false? Turing and Church both independently proved that no such algorithm exists.

https://en.wikipedia.org/wiki/Entscheidungsproblem

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ylliu a day ago | parent | prev [-]

[dead]

	▲	jrflo a day ago \| parent \| next [-]
		Mathematics not being axiomatically complete doesn't mean you can't have crazy progress from a formalized and mechanized systems. It just means that there are corners you can't reach mechanically, but we don't know if those corners are at all interesting or not. It could be the case that 99.99% of useful math can be found mechanically.
	▲	sigmoid10 a day ago \| parent \| prev [-]
		Mathematics in the sense of a complete set of axioms can't, but human research into mathematics apparently just needed enough compute to achieve the same output as a high-tier faculty.