Sal Anastasio - SUNY at New Paltz
Not Enough Ado about Nothing: The Background to a Wonderful Proof by the Young Vito Volterra
In 1881, Vito Volterra, then a 21 year old student at the Scuola Normale Superiore di Pisa, proved that there could be no function on R which was continuous at every rational number and discontinuous at every irrational number. Volterra's elegant proof will be presented (it pre-dates Baire's proof by a generation and uses only elementary analytic tools), but we will also look at the historical background which led to interest in such pathological functions.
This talk will be primarily historical in nature, but will refer to mathematical concepts and ideas. Students who have completed Calculus II will be able to follow much of the talk, and will enjoy a lot of the history.
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