Number Theory General • It is at this point that we encounter a change: people working on mathematics of no obvious value to common people doing their daily work. • Number theory is used in cryptography and cosmology. Strong students with knowledge of number theory are in demand at the National Security Agency. But these uses came late and as an afterthought. • What is/was the justiFcation? ◦ Stobaeus, Extracts : “A youth who had begun to read geometry with Euclid, when he had learnt the Frst proposition, inquired, ‘What do I get by learning these things?’ So Euclid called a slave and said ‘Give him threepence, since he must make a gain out of what he learns.”’ ◦ Henri Poincare, The Value of Science : “The search for truth should be the goal of our activities; it is the sole end worthy of them. Doubtless we should Frst bend our e±orts to assuage human su±ering, but why? Not to su±er is a negative ideal more surely attained by the annihilation of the world. If we wish more and more to free man from
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This note was uploaded on 12/29/2011 for the course MATH 378 taught by Professor Wen during the Fall '10 term at SUNY Stony Brook.