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[7] Jeffrey Lagarias stated in 2010 that the Collatz conjecture "is an extraordinarily difficult problem, completely out of reach of present day mathematics". [8] However, though the Collatz conjecture itself remains open, efforts to solve the problem have led to new techniques and many partial results. [8] [9]
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.
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 ...
[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]
Paul Erdős said about the Collatz conjecture: "Mathematics may not be ready for such problems."[7] Jeffrey Lagarias stated in 2010 that the Collatz conjecture "is an extraordinarily difficult problem, completely out of reach of present day mathematics".[8] FORTUNATELY, THEY WERE NOT CORRECT.
In 2007, researchers Kurtz and Simon, building on earlier work by J.H. Conway in the 1970s, proved that a natural generalization of the Collatz problem is undecidable. [ 7 ] In 2019, Ben-David and colleagues constructed an example of a learning model (named EMX), and showed a family of functions whose learnability in EMX is undecidable in ...
The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. More specifically, the Millennium Prize version of the conjecture is that, if the elliptic curve E has rank r , then the L -function L ( E , s ) associated with it vanishes to order r at s = 1 .
The 3x + 1 semigroup has been used to prove a weaker form of the Collatz conjecture. In fact, it was in such context the concept of the 3 x + 1 semigroup was introduced by H. Farkas in 2005. [ 2 ] Various generalizations of the 3 x + 1 semigroup have been constructed and their properties have been investigated.