New Scientist: Around 1932 Hungarian mathematician Paul Erdös showed that if one adds the values of a random infinite sequence of +1s and −1s, rather than equaling 0, the total will be at least 1. Erdös went on to wonder whether the discrepancy could ever be greater than 1. Although mathematicians believed the answer to be yes, no one had been able to prove it until recently. Last year Alexei Lisitsa and Boris Konev of the University of Liverpool in the UK used a computer program to prove that the discrepancy can equal 2. However, the 13-GB file that resulted was too large to be checked by a human. Now, by using traditional mathematics and crowdsourced work, Terence Tao of UCLA has given mathematical proof that the discrepancy is infinite. The achievement is significant because it shows that while computers are a useful tool, human brain power is still required to solve some problems.
The finding that the Saturnian moon may host layers of icy slush instead of a global ocean could change how planetary scientists think about other icy moons as well.
Modeling the shapes of tree branches, neurons, and blood vessels is a thorny problem, but researchers have just discovered that much of the math has already been done.
January 29, 2026 12:52 PM
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