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To Settle Infinity Dispute, a New Law of Logic
...as the fundamental laws of mathematics. Most mathematicians simply ignore the holes, which lie in abstract realms with few practical or scientific ramifications. But for the stewards of math’s logical...
The New Science of Evolutionary Forecasting
...said. “I evidently was wrong-headed.” Getting Complex Without Getting Random Lenski’s results have inspired other scientists to set up more complex experiments. Michael Doebeli, a mathematical biologist at the University...
A Design Dilemma Solved, Minus Designs
...the exception, mathematicians wondered, or the rule? “It was one of the most famous problems in combinatorics,” said Gil Kalai, a mathematician at the Hebrew University of Jerusalem. He recalls...
Can Information Rise From Randomness?
...in a recent Math Horizons article, I believe that our human love of solving puzzles is a reflection of the unique cognitive-emotional link that makes us the intelligent creatures we...
The Slippery Eel of Probability
In school, we are trained to think that math problems always have one correct answer. But this is not necessarily true for problems dealing with probability, if the method used...
The Connoisseur of Number Sequences
...with the Zentralblatt — the German equivalent of Math Reviews’ MathSciNet — about making it possible to search for formulas in the OEIS. Suppose you want the summation of xn...
Visions of Future Physics
...matter, and the exploration of new mathematical structures in gauge theory scattering amplitudes” — Arkani-Hamed, 43, a professor at the Institute for Advanced Study (IAS) in Princeton, N.J., is widely...
A New Map Traces the Limits of Computation
...mathematical proof that the current best algorithm was “optimal” — in other words, that finding a more efficient way to compute edit distance was mathematically impossible. The Boston Globe celebrated...
A Twisted Path to Equation-Free Prediction
...late 1970s, the Dutch mathematician Floris Takens was studying chaos theory, which had begun to emerge in the 1960s as scientists recognized that many of nature’s complex phenomena seem to...