Do odd perfect numbers exist? New results on an old problem

Euclid, from Rafael’s “School of Athens”, Vatican Museum, Rome, photo courtesy Clay Mathematics Institute

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Perfect numbers

A perfect number is a positive integer whose divisors (not including itself) add up to the integer. The smallest perfect number is $6$, since $6 = 1 + 2 + 3$. The next is $28 = 1 + 2 + 4 + 7 + 14$, followed by $496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248$ and $8128 = 1 + 2 + 4 + 8 + 16 + 32

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September 22nd, 2020 | Category: Essays | Comments are closed

Can computers do mathematical research?

Courtesy Adarsh Pathak

AI comes of age

The modern field of artificial intelligence (AI) began in 1950 with Alan Turing’s landmark paper Computing machinery and intelligence, which outlined the principles of AI and proposed the Turing test. Although early researchers were confident that AI systems would soon be a reality, inflated promises and expectations led to disappointment in the 1970s and again in the 1980s.

A breakthrough of sorts came in the late 1990s and early 2000s with the emergence of Bayes-theorem-based methods, which quickly displaced the older methods based mostly on formal reasoning. When combined with steadily advancing

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September 1st, 2020 | Category: Essays | Comments are closed