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The Collatz conjecture [a] ... Then the formula for the map is exactly the same as when the domain is the integers: an 'even' such rational is divided by 2; an 'odd ...
Lothar Collatz (German:; July 6, 1910 – September 26, 1990) was a German mathematician, born in Arnsberg, Westphalia. The "3x + 1" problem is also known as the Collatz conjecture, named after him and still unsolved. The Collatz–Wielandt formula for the Perron–Frobenius eigenvalue of a positive square matrix was also named after him.
This problem is known as the primitive circle problem, as it involves searching for primitive solutions to the original circle problem. [9] It can be intuitively understood as the question of how many trees within a distance of r are visible in the Euclid's orchard , standing in the origin.
Collatz conjecture: number theory: Lothar Collatz: 1440 Cramér's conjecture: number theory: Harald Cramér: 32 Conway's thrackle conjecture: graph theory: John Horton Conway: 150 Deligne conjecture: monodromy: Pierre Deligne: 788 Dittert conjecture: combinatorics: Eric Dittert: 11 Eilenberg−Ganea conjecture: algebraic topology: Samuel ...
Collatz conjecture (also known as the + conjecture) Eden's conjecture that the supremum of the local Lyapunov dimensions on the global attractor is achieved on a stationary point or an unstable periodic orbit embedded into the attractor.
Schanuel's conjecture; Schinzel's hypothesis H; Scholz conjecture; Second Hardy–Littlewood conjecture; Serre's conjecture II; Sexy prime; Sierpiński number; Singmaster's conjecture; Safe and Sophie Germain primes; Stark conjectures; Sums of three cubes; Superperfect number; Supersingular prime (algebraic number theory) Szpiro's conjecture
He is known for the Terras theorem about the Collatz conjecture, published in 1976, [6] which proved that the conjecture holds for "almost all" numbers and established bounds for the conjecture. [7] [8] He married fellow mathematician Audrey Terras. [9]
[4] [6] He proved Keller's conjecture in dimension seven in 2020. [7] In 2018, Heule and Scott Aaronson received funding from the National Science Foundation to apply SAT solving to the Collatz conjecture. [7] In 2023 together with Subercaseaux, he proved that the packing chromatic number of the infinite square grid is 15 [8] [9]