Moore designed his pinball machine to complete the analogy to the Turing machine. The starting position of the pinball represents the data on the tape being fed into the Turing machine. Crucially (and unrealistically), the player must be able to adjust the ball’s starting location with infinite precision, meaning thatContinue Reading
Fisher did not take Neyman and Pearson’s criticisms well. In response, he called their methods “childish” and “absurdly academic.” In particular, Fisher disagreed with the idea of deciding between two hypotheses, rather than calculating the “significance” of available evidence, as he’d proposed. Whereas a decision is final, his significance testsContinue Reading
But one of Malle’s graduate students was on the case. Britta Späth. “Our Obsession” In 2003, Späth arrived at the University of Kassel to start her doctorate with Malle. She was almost perfectly suited for working on the McKay conjecture: Even in high school, she could spend days or weeksContinue Reading
In a 1985 paper, the computer scientist Andrew Yao, who would go on to win the A.M. Turing Award, asserted that among hash tables with a specific set of properties, the best way to find an individual element or an empty spot is to just go through potential spots randomly—anContinue Reading
The original version of this story appeared in Quanta Magazine. Calculus is a powerful mathematical tool. But for hundreds of years after its invention in the 17th century, it stood on a shaky foundation. Its core concepts were rooted in intuition and informal arguments, rather than precise, formal definitions. TwoContinue Reading
