Norman Shapiro

Norman Z. Shapiro (born 1932) is an American mathematician, who is the co-author of the Rice–Shapiro theorem.

Shapiro spent the summer of 1954 at Bell Laboratories in Murray Hill, New Jersey where, in collaboration with Karel de Leeuw, Ed Moore, and Claude Shannon, he investigated the question of whether providing a Turing machine augmented with an oracle machine producing an infinite sequence of random events (like the tosses of a fair coin) would enable the machine to output a non-computable sequence. The well-known efficacy of Monte Carlo methods might have led one to think otherwise, but the result was negative. Stated precisely:

Moreover, the result continues to hold if the output probability is any positive number, and the probability of an oracle machine inquiry yielding 1 is any computable real number.

Shapiro obtained a BS in Mathematics at University of Illinois in 1952. Shapiro obtained his Ph.D from Princeton University in 1955 under the advisorship of Alonzo Church. In 1955, as a Princeton PhD student, Shapiro coined the phrase "strong reducibility" for a computability theory currently called the many-one reduction. His thesis was titled Degrees of Computability and was published in 1958.

Shapiro was a leading mathematician and computer scientist at the RAND Corporation think tank from 1959 until 1999. In the late 1960s and early 1970s Shapiro was the lead designer of one of the first computer-based mapping and cartography systems.

In the 1970s Shapiro co-designed the MH Message Handling System. MH was the first mail system to utilize Unix design principles by using shell commands to manipulate messages as individual files.

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