Math’s “Oldest Problem Ever” Gets a New Answer
Number theorists are always looking for hidden structure. And when confronted by a numerical pattern that seems unavoidable, they test its mettle, trying hard—and often failing—to devise situations in which a given pattern cannot appear.
One of the latest results to demonstrate the resilience of such patterns, by Thomas Bloom of the University of Oxford, answers a question with roots that extend all the way back to ancient Egypt.
“It might be the oldest problem ever,” said Carl Pomerance of Dartmouth College.
The question involves fractions that feature a 1 in their numerator, like /, /, or /. These “unit fractions” were especially important to the ancient Egyptians because they were the only types of fractions their number system contained: With the exception of a single symbol for /, they could only express more complicated fractions (like /) as sums of unit fractions (/ + /).
