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So, a permutation is a special arrangement of symbols. A “superpermutation,” in a sense, is a special arrangement of permutations: It is a sequence of symbols that contains every possible permutation of those symbols. For example, stringing together all six permutations of {A, B, C} gives us ABCACBBACBCACABCBA, a superpermutation ...Read More
"A little high school geometry can help you understand the basic math behind movie recommendation engines."
I remember reading these papers when they were first widely available. I am no great mathematician (and certainly not adequate to adjudicate the controversy in Corollary 3.12), but I remember having a sense of how the proof might work. In essence, Mochizuki is trying to arrive at a more abstract understanding of numbers, whereby manipulating the fundamental attributes of numbers changes the relationships inherent in basic operators. The way I conceptualize it is roughly analogous to the following: 1 + 1 = 2 is true, but only within certain ...Read More
"Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work."
"A founder of modern geometric analysis who produced “some of the most dramatic advances in mathematics in the last 40 years,” Uhlenbeck is the first woman to be"
"In requiring theories to be beautiful and natural, we may be pre-rejecting reality."