Download PDFOpen PDF in browserCurrent versionThe Complexity of MathematicsEasyChair Preprint no. 3062, version 97 pages•Date: June 11, 2020AbstractIn mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Many consider it to be the most important unsolved problem in pure mathematics. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US 1,000,000 prize for the first correct solution. We prove the Riemann hypothesis using the Complexity Theory. Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integervalued functions. The Goldbach's conjecture is one of the most important and unsolved problems in number theory. Nowadays, it is one of the open problems of Hilbert and Landau. We demonstrate the Goldbach's conjecture is true or this has an infinite number of counterexamples using the Complexity Theory as well. An important complexity class is NSPACE(S(n)) for some S(n). 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. Keyphrases: complexity classes, Conjecture, number theory, primes, reduction, regular languages
