Cédric Pilatte Jun 2023

It's a question of Erdős
Mathematics Discovery 2023

Cédric Pilatte
The Idea
Construct an infinite set of integers:

  • No two pairs of integers have the same sum
  • Any integer may be produced as the sum of only three integers
The question of whether such a set exists has lingered for decades, ever since it was posed by the prolific Hungarian mathematician Paul Erdős and two collaborators in 1993. Erdős’ fascination with Sidon sets can be traced to a conversation he had in 1932 with their inventor Simon Sidon, who at the time was interested in understanding the growth rate of these sets.

Erdős would later describe Sidon as “crazier than the average mathematician,” which he almost certainly meant as a compliment.

Another anecdote: The Hungarian mathematician Simon Sidon was famed for his reclusive nature. One afternoon, Paul Erdős and another mathematician named Turan showed up on Sidon’s doorstep unannounced. Sidon opened the door a crack, peeked out, and implored his visitors to “please visit another time—and especially another person.” https://anecdotage.com/anecdotes/simon-sidon-please-visit-another-time

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