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Packing up the household for a recent move, I was delving into shoeboxes, photo albums, and file folders that had not been opened in decades. One of my discoveries, found in an envelope at the back of a file drawer, was the paper sleeve from a drinking straw, imprinted with a saccharine message: This flimsy slip of paper seems like an odd scrap to preserve for the ages, but when I pulled it out of
Are the prime numbers sprinkled randomly along the number line, like windblown seeds? Of course not: Primality is not a matter of chance but a product of simple arithmetic. A number is prime if and only if no smaller positive integer other than 1 divides it evenly. Yet that’s not the end of the story. The distribution of the primes looks random, with irregular gaps and clusters that seem quite hap
Five years ago I wrote about a rumored proof of the abc conjecture, an idea from the 1980s that stands at the juncture between the additive and the multiplicative parts of number theory. Now there’s more abc news, and this time it’s not just a rumor. Shinichi Mochizuki of Kyoto University has released a series of four long papers in which he claims to provide a proof. I have nothing useful to say
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