In the 1960s, mathematician Hillel Furstenberg proposed a conjecture: that a number cannot appear “simple and highly regular” under two “independent” rulers simultaneously.
Put simply, if a number is written in a binary system – using only two digits or elements to represent a quantity – its sequence is relatively regular and simple.
In contrast, when rewriting that number in ternary – using three elements as its base – its sequence will almost certainly become relatively more complex and different in structure.
The conjecture seems intuitively obvious, yet for half a century the part relating to intersecting sets went unproven.
That changed in 2019 when Chinese mathematician Wu Meng, then an associate professor at the University of Oulu, one of Finland’s largest universities, solved the problem.
Afterwards, Wu published “A Proof of Furstenberg’s Conjecture on the Intersections of ×p and ×q Invariant Sets” in Annals of Mathematics, a top journal. The work earned him the 2023 International Congress of Chinese Mathematicians (ICCM) Best Paper Award.
