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Statement

Two passages, neither a theorem. They are the paper's only mentions of Erdős (the name occurs nowhere else in the text layer, and the reference list has no Erdős item).

The dictum (printed p. 3, PDF p. 2, second paragraph of § 1). "The $3x+1$ Conjecture is simple to state and apparently intractably hard to solve. It shares these properties with other iteration problems, for example that of aliquot sequences (see Guy [36], Problem B6) and with celebrated Diophantine equations such as Fermat's last theorem. Paul Erdős commented concerning the intractability of the $3x+1$ problem: 'Mathematics is not yet ready for such problems.' Despite this doleful pronouncement, study of the $3x+1$ problem has not been without reward." No occasion, date, reference or footnote is attached to the remark. Reference [36] is Guy's Unsolved Problems in Number Theory (1981), cited here for Problem B6 (aliquot sequences); the same book's Problem E16 is the site's source for the dictum in the wording "Mathematics may not be ready for such problems".

The prize sentence (printed p. 4, PDF p. 3, fifth paragraph of § 1). "In the last ten years the $3x+1$ problem has forsaken its underground existence by appearing in various forms as a problem in books and journals, sometimes without attribution as an unsolved problem. Prizes have been offered for its solution: $50 by H. S. M. Coxeter in 1970, then $500 by Paul Erdős, and more recently £1000 by B. Thwaites [69]. Over twenty research articles have appeared on the $3x+1$ problem and related problems." Coxeter's figure is sourced in reference [27] (p. 21): "H. S. M. Coxeter, Cyclic Sequences and Frieze Patterns (The Fourth Felix Behrend Memorial Lecture), 1970. In this lecture Coxeter offered a $50 prize for a proof of the $3x+1$ Conjecture and $100 for a counterexample, according to C. W. Trigg [67]." Thwaites's is sourced in reference [69] (p. 23), the September 1982 PPC Calculator Journal note in which "B. Thwaites states he originated the $3x+1$ problem in 1952 and offers 1000 pounds for a proof of the $3x+1$ Conjecture." The Erdős figure has no reference, date or occasion.

What follows for the problem page. The site's caveat, that the prize "originated in a survey article by Lagarias [La85]" and that Lagarias later traced it to a conversation around 1983 in which Erdős rated the problem on his prize scale without offering a prize, is consistent with this paper: the paper lists a prize from Erdős among prizes "offered", between Coxeter's 1970 figure and Thwaites's 1982 one, and gives no source. The 1983 conversation is not in the paper; it rests on the site's report of a later communication. The dictum's wording here agrees with the 2010 overview's quotation of it (Section 6 of the 2010 overview, "[58, p. 3]") and differs in two words from the site's, which is Guy's ("is not yet ready" against "may not be ready").

Source. J. C. Lagarias, The $3x+1$ Problem and Its Generalizations, Amer. Math. Monthly 92 (1985), no. 1, 3--23, doi:10.2307/2322189; printed pp. 3--4 = PDF pp. 2--3, p. 21 = PDF p. 20 and p. 23 = PDF p. 22 of the JSTOR scan, read on the page images. The artifact is identified in the source digest.

Read depth. Claims checked: both passages and the references [27], [36] and [69] were read clause by clause on the page images, and the text layer of the whole paper was searched for other occurrences of the name. Nothing here is a mathematical result, and nothing is independently reviewed.

Proof pointer

None; these are the author's historical statements. The paper cites no source for either Erdős remark.

Dependencies

None within the paper. Outside it: Guy 1981 (its [36]), not held; its 2004 third edition, the site's [Gu04], filed as guy_2004_unsolved_problems_number_theory, whose section E16 (printed p. 330, PDF p. 348, read clause by clause on the page image) prints the dictum as "Mathematics may not be ready for such problems" with no date, occasion or source; Trigg, Dodge and Meyers 1976 (its [67]) and the 1982 note (its [69]), neither held.

Bears on

• Problem 1135: the origin the site names for the Erdős prize, printed here as one of three prizes "offered" and without a source, and the printed form of the Erdős dictum, "not yet ready", against the site's "may not be ready" from Guy. The paper does not settle the problem or change its status.