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The Collatz conjecture [a] ... this inverse relation forms a tree except for the 1–2–4 loop ... (positive or negative) rational numbers which have odd ...
For example, the following loop will, in theory, never stop. However, it may halt when executed on a physical machine due to arithmetic overflow: either leading to an exception or causing the counter to wrap to a negative value and enabling the loop condition to be fulfilled. i := 1 loop until i = 0 i := i + 1
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.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
Conjecture Field Comments Eponym(s) Cites 1/3–2/3 conjecture: order theory: n/a: 70 abc conjecture: number theory: ⇔Granville–Langevin conjecture, Vojta's conjecture in dimension 1 ⇒Erdős–Woods conjecture, Fermat–Catalan conjecture Formulated by David Masser and Joseph Oesterlé. [1] Proof claimed in 2012 by Shinichi Mochizuki: n/a ...
- if no divergent trajectory exists AND - if no loop exist then the Collatz-conjecture is settled. A general loop is still not disproven, but Ray Steiner (1978) and Benne de Weger/John Simons(2000 and 2002) succeeded in disproving certain types of loops (called 1-cycle (Steiner) resp. m-cycle with m=1 to 68 (deWeger/Simons)).
Examples of non-normalizing systems (not weakly or strongly) include counting to infinity (1 ⇒ 2 ⇒ 3 ⇒ ...) and loops such as the transformation function of the Collatz conjecture (1 ⇒ 2 ⇒ 4 ⇒ 1 ⇒ ..., it is an open problem if there are any other loops of the Collatz transformation). [7]
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]