Analytical number theory employs the machinery of analysis and complex analysis to tackle questions about integers. The prime number theorem and the related Riemann hypothesis are examples. Warings problem (representing a given integer as a sum of squares, cubes etc.), the Twin Prime Conjecture (finding infinitely many prime pairs with difference 2) and Goldbach's conjecture (writing even integers as sums of two primes) are being attacked with analytical methods as well. Proofs of the transcendence of mathematical constants, such as π or e, are also classified as analytical number theory. Note that these studies of transcendental numbers have seemingly moved away from simply the study of integers...
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