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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]
English: This is a graph, generated in bottom-up fashion, of the orbits of all numbers under the Collatz map with an orbit length of 20 or less. Created with Graphviz, with the help of this Python program: # This python script generates a graph that shows 20 levels of the Collatz Conjecture.
Directed graph showing the orbits of the first 1000 numbers in the Collatz conjecture. The integers from 1 to 1000 are colored from red to violet according to their value. French
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.
[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]
Josh Stein’s victory in this year’s North Carolina governor’s race was huge. And his opponent was widely seen as the weakest Republican in a major race this cycle.
Gold partition conjecture [9] order theory: n/a: 25 Goldberg–Seymour conjecture: graph theory: Mark K. Goldberg and Paul Seymour: 57 Goormaghtigh conjecture: number theory: René Goormaghtigh: 14 Green's conjecture: algebraic curves: Mark Lee Green: 150 Grimm's conjecture: number theory: Carl Albert Grimm: 46 Grothendieck–Katz p-curvature ...
From January 2011 to December 2012, if you bought shares in companies when Eric C. Wiseman joined the board, and sold them when he left, you would have a 41.2 percent return on your investment, compared to a 12.1 percent return from the S&P 500.