Collatz conjecture
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The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integ
The x axis represents starting number, the y axis represents the highest number reached during the chain to 1. This plot shows a restricted y axis: some x values produce intermediates as high as 2.7×107 (for x = 9663)
The number of iterations it takes to get to one for the first 100 million numbers.
A Collatz fractal centered at the origin, with real parts from –5 to 5.
Julia set of the exponential interpolation.
Terence Tao
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Terence Chi-Shen Tao is an Australian and American mathematician who was awarded the Fields Medal in 2006 for his contributions to partial differential equations, combinatorics, harmonic analysis, and
Collatz conjecture
…point that is strictly below its initial value. The proof is based on the distribution of parity vectors and uses the central limit theorem. In 2019, Terence Tao improved this result by showing, using logarithmic density, that almost all (in the sense of logarithmic density) Collatz orbits descend below any given…
Tao in 2026
Tao at ICM 2006
Tao at the age of 10 with mathematician Paul Erdős in 1985
Tao (second from left) with UCLA undergraduate students in 2021