I have found a beautiful technique to solve math problems such as:
- Goldbach’s conjecture
- Riemann hypothesis
The technique uses the notions of regular languages. The complexity class that contains all the regular languages is REG. Moreover, these mathematical proofs are based on if some unary language belongs to NSPACE(S(log n)), then the binary version of that language belongs to NSPACE(S(n)) and vice versa. The complexity class NSPACE(f(n)) is the set of decision problems that can be solved by a nondeterministic Turing machine M, using space f(n), where n is the length of the input.
We prove there are non-regular languages that define mathematical problems. Indeed, if those math problems are not true, then they have a finite or infinite number of counterexamples (the complement languages contain the counterexample elements). However, we know every finite language is regular. Therefore, those languages are true or they have an infinite number of counterexamples, because if they have a finite number of counterexamples, then the complement language should be in REG, that is, this complement must be a regular language. Indeed, we show some mathematical problems cannot have a finite number of counterexamples using the complexity result, that is, we demonstrate their complement languages cannot be regular. In this way, we prove these problems should be true or they have an infinite number of counterexamples as the remaining only option.
See more in my notions:
https://www.notion.so/ce1d7a1822844af7bc6df4e92cb3aca6?v=615f234f5cdd4da1b62ccb0c73ab34ad
Preprint Proof of the Twin primes Conjecture and Goldbach's conjecture
Preprint Proof of the Twin primes Conjecture and Goldbach's conjecture
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