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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

31 votes

Are there examples of conjectures supported by heuristic arguments that have been finally di...

This is extremely common in the field of cryptography. It was popular to design key exchange systems in the 1980s without proof of security, just giving intuitive arguments which were often quite conv …
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