Gödel's incompleteness theorems demonstrate that any computable system that is sufficiently powerful, cannot be both consistent and syntactically complete.
Godel's second proved, a formula Con_κ associated with the consistency of κ is unprovable if κ is consistent.
If it is not consistent, Ex falso quodlibet (principle of explosion) applies and finding that contradiction allows any proposition or the negation of that proposition to be proven.
> They both can be useful or harmful
It is not lean that is harmful, mistaking finding a proof as being the same as truth. A proof that verifies a theorem does not have to explain why it
holds, and the mathematical assumptions that may have been statistical is exactly why that failed.
Probability theory is just as much of a mathematical branch as λ-calculus. But we probably do differ in opinion on how "demonstrably true" much of mathematics is.
But here is a fairly accessible document related to the crash.
Gödel's incompleteness theorems demonstrate that any computable system that is sufficiently powerful, cannot be both consistent and syntactically complete.
Godel's second proved, a formula Con_κ associated with the consistency of κ is unprovable if κ is consistent.
If it is not consistent, Ex falso quodlibet (principle of explosion) applies and finding that contradiction allows any proposition or the negation of that proposition to be proven.
> They both can be useful or harmful
It is not lean that is harmful, mistaking finding a proof as being the same as truth. A proof that verifies a theorem does not have to explain why it holds, and the mathematical assumptions that may have been statistical is exactly why that failed.
Probability theory is just as much of a mathematical branch as λ-calculus. But we probably do differ in opinion on how "demonstrably true" much of mathematics is.
But here is a fairly accessible document related to the crash.
https://samueldwatts.com/wp-content/uploads/2016/08/Watts-Ga...