The following is an itemization of the historical science hoaxes on which DIO and/or DR have published thorough analyses. [See also the sources for the stark itemization, of DR's successes in this regard, at the end [p.70] of DIO 18 .]
DR's have been mostly in professional journals,
including DIO (of which he is Publisher) —
whose refereeing and prize boards
boast the most technically able scholars in the field of history of astronomy,
most of whom have experience in evaluation of hoaxes: e.g.,
DIO 7.1 
‡1 & R.Peary);
R.Bryce (F.Cook: New York Times 1998/11/26 p.1);
DIO 9.1 
DIO 12 
Univ.Cambridge's R.Headland (Byrd: Baltimore Sun 1996/5/15 p.1);
D.Rawlins (Byrd: New York Times 1996/5/9 p.1;
among other cases: see below).]
Accumulating over a stretch of 4 decades, DIO's total number of such investigations happens to have become the largest ever — despite the fact that the majority of DR's (and most of his colleagues') writings have not been on the subject of fakery.
Eratosthenes (c.230BC) appears to have pretended that he measured the size of the Earth by comparing the height of the Summer Solstice local-noon Sun at Alexandria with that at Aswan. The sign & and large size of his value's error shows that its actual source was non-astronomical and probably pre-Eratosthenes: based on measuring how far Sostratos' Alexandria Lighthouse was visible over the sea. (Archive for History of Exact Sciences 1982; Griffith Observer 82.8 2018/8 pp.9-16 [esp. p.16 on eminent Hist.sci-ignored sources]; DIO 14  ‡1 [pp.2-12].)
Hipparchos (c.130BC) published elements of his lunisolar theory that evidently purported to solve simultaneously for three unknowns. But the actual procedure was a one-unknown solution, using presumed, non-original (perhaps Aristarchan) values for the other two. (DIO 1.3 ; H.Thurston Isis 93.1:58 .)
Later investigation of Robert Newton's discernment of a 1° problem found (DIO 20  ‡3 §G4 [p.26]) that a long-recognized 1° disjunct in the above-cited Hipparchos analysis was due to deliberate forgery by someone in Hipparchos' school.
Adding to evidence highlighted by Tycho, J.Delambre, C.Peters, & R.Newton,
DIO produced several new proofs that Claudius Ptolemy (c.160AD)
plagiarized the entire Ancient Star Catalog (1025 stars) from Hipparchos,
as astronomers had long suspected.
(DIO 4.1 
DIO 10 
K.Pickering & D.Duke
DIO 12 
(See also Publ. Astr. Soc. Pacific 94:359 .)
Ptolemy's theft of prior elements of Mercury's orbit and his fabrication of “observations” from said elements, was proven by analyses (American Journal of Physics 55:235 ) which converted the eminent mathematician B.L.van der Waerden among others to the view that Ptolemy had finally been utterly proven to have been “a liar”, who (as recognized among astronomers for centuries) systematically faked alleged celestial observations by computing them indoors. (DIO 1.2 ; DIO 9.1  ‡3.)
Revealed Ptolemy's previously unknown practice of altering star-longitudes so as to bring genuine astronomers' differential star-based observations of Venus, into accord with the requirements of faked Venus longitudes. (DIO 11.3 .)
DR is editor of the first and only critical edition of the justly famous 1004-star catalog (1598AD) of the genuinely great astronomer Tycho Brahe. (DIO 3 .) But DR is also discoverer of two small bunches of hitherto-unsuspected faked stars in it, which Tycho's school used to get the catalog's total number of stars up to his long-promised 1000. (DIO 2.1  ‡4 Tables 1&2.)
The 1846 theoretical prediction (to within 1°) of the position of
the unknown planet Neptune by Paris Observatory's Urbain Leverrier
(from the planet's gravitational perturbations of Uranus' motion) is
the grandest predictive event in astronomy's long history.
But the giant planet's 1846/9/23 discovery was instantly
followed by Britain's claim that its brilliant mathematician J.Adams
had made the same prediction, comparably accurately, in 1845 Sept-Oct.
Up to the 1990s, it was generally accepted that
Adams had priority; thus, the prediction was commonly called
the “Adams-Leverrier” discovery.
But DR found a cascade of problems with this claim, and showed that Adams' final position was post-Leverrier and off by 12°. (See Sky&Telescope 38:180 ; Bulletin Amer Astr Soc 16:734 ; DIO 2.3  ‡4; DIO 9.1  ‡1; Scientific American [2004 Dec].)
When in the 1960s DR 1st looked into the Neptune case, he wrote Astronomer Royal R.Wooley, requesting access to the Royal Greenwich Observatory's Neptune-case file. The file disappeared for over 30 years. DR publicly spotlighted the Astronomer Royal's colleague (and sometime Chief Ass't) as the thief. (DIO 4.2 .) In 1998, he died; and the entire file was found in his home. DIO 9.1  ‡1.
In 1992, DR had pointed to Astronomer Royal G.Airy's l846/12/8 letter to A.Sedgwick as having been deep-sixed for 150 years, suggesting that it would have revealed that Airy was rightly enraged at crestfallen Adams' try at blaming Airy for his own publication-indecision's loss of his priority. (DIO 2.3  ‡9 §A6; DIO 7.1  ‡5 §A5 [p.25].) In 1999 July, Nick Kollerstrom and Adam Perkins recovered the letter at DR's request, and its crucial contents (via Airy's deft sarcasm) starkly verified the DR prediction. (See this letter and the rest of Kollerstrom's Royal Astronomical Society-funded cullings from the long-lost R.G.O. Neptune files, an invaluable historical collection which now resides exclusively on the DIO website.)
The 1853-1855 US polar expedition of E.K.Kane reported to SecNavy its alleged discovery of a non-existent Open Polar Sea. DR found that Kane had altered-expanded its size by 40% between reports to SecNavy. The expedition's 2nd-in-command, J.Petersen, told the truth: “none of us has seen any Polar Ocean.” (DR Peary at the North Pole: Fact or Fiction?  p.22. See ibid for Kane's exaggerated latitudes that falsely claimed to have reached farther north on land than anyone in 1854. Among numerous positive reviews of Fiction, see those of Arctic, Arctic Institute of N.America ; and Annals of the Association of American Geographers 65:79-82 .)
The Kane expedition's surgeon, I.I.Hayes, led the next US expedition north,
with wider prominent institutional backing
than any US polar expedition in history. On his return, Hayes claimed
to have in 1861 reached coastal land at 81°35'N, 70°30'E
(repeating [by exceeding] Kane's false claim of a farthest-north on land).
But that position is inland, far from the coast;
so Hayes' claim has long been disbelieved.
But DR was the 1st scholar to examine Hayes' original field records,
instigating & publicly revealing AGS Librarian Lynn Mullins' discovery
that a page had been scissored-out at the alleged Farthest North.
From this document, DR determined
that Hayes stopped at Cape Collinson, barely past 80°N.
(DR Peary … Fiction  p.25.)
[DR subsequently discovered a fascinating hypothesis consistent with the striking fact that Hayes' longitude is exactly correct: he knew just where he was, and simply inverted a digit in his sextant double-altitude latitude observation, converting a nine into a six, thereby adding the 1°1/2 of latitude that created his “farthest”.]
The US' greatest polar explorer was also its top polar faker. After his earlier questionable claim of discovering a fictional “Peary Channel” (plus the 1st degenerate glaciers in history: Fiction p.46), Peary unsuccessfully tried (1899-1903) claim-jumping Otto Sverdrup's Axel Heiberg Land and re-naming it Jesup Land for his chief backer, M.Jesup. DR checked the original mss of the transit observations of the day of the supposed discovery and found that the only reported geographical point for which no data existed in the transit records was Jesup Land.
Umberto Cagni's 1900 Italian expedition claimed a Farthest North of 86°35'N, after alleged sledge-speeds (over the Arctic Ocean that surrounds the N.Pole) that increased drastically as soon as Cagni stopped sharing his sextant with anyone. That his reported final position was as discrepant from reality as Hayes' is shown by the fact that large errors in compass variation appear only for the independently-suspicious final leg (Fiction p.65).
In 1906, Frederick Cook claimed the 1st ascent of Mt.McKinley, presenting a cropped photo of the scene of his “summit” which was crowned by his US flag, held by companion E.Barrille. DIO's Rob't Bryce discovered the original of the full uncropped photo. Its publication in DIO 7.2  with photo-comparisons arranged by DIO's Keith Pickering, so utterly ended the controversy at a stroke that the New York Times ran Bryce's find on its front page, New York Times1998/11/26, with generous credit to DIO. The full photo proved that it been taken far from McKinley, atop a zit whose altitude (above sea-level) was barely 1/4 McK's.
The same year as Cook's molehill→mountain exaggeration, Robert Peary claimed he attained a Farthest North of 87°06'N (1906/4/21). Fiction p.69 noted that this was the 1st modern Farthest that lacked an explicitly written longitude, and that Peary's two maps of the trip showed discrepant values for it. (Sir Wally Herbert later discovered the crusher: a surviving typescript of Peary's “lost” 1906 April diary contradicted any chance that he got near 87°N. See Herbert Noose of Laurels or DIO 1.1  ‡4.)
Shortly afterward, Peary claimed to have seen (1906/6/24&28) a non-existent “Crocker Land” to the northwest of Ellesmere Land. This was universally deemed an innocent error, until Fiction pp.72-75 presented multiple evidences that it was fraud. When the original 1906 Peary diary finally became available in the 1980s, DR found that at the place and moment of the 6/24 alleged discovery, Peary had written “No land visible”. (Washington Post 1989/4/20; DIO 1.1  p.22; Peary Diary 1906/6/24 [U.S. National Archives], obverse of leaves 37&39.)
Cook later claimed he was 1st to reach the North Pole, 1908/4/21. DR found that his alleged observations, if taken as real, placed him on the planet Vesta. (Norsk Geografisk Tidsskrift 26  p.135 [Norwegian Geographical Society; Oslo University]; Fiction p.86.)
Peary also claimed priority at the N.Pole, 1909/4/6-7.
DR showed that his navigation claims were folly.
Many commentators (e.g., Sir Wally Herbert,
1st sledge-crosser of the Arctic Ocean) have skeptically noted
the remarkable 1909 speeds Peary claimed, once he was north of the camp
where he unloaded his last navigationally competent witness, R.Bartlett.
But DR was 1st to remark on his proportionally-sudden slow-down,
once he passed the same point when heading south during the return —
contrasts which made it obvious that Peary's reports had
just doubled the speeds (both ways) north of Bartlett Camp.
DR also noted that Peary's alleged zeroing-in observation of 1909/4/5
(one day before farthest) was not in the data-set submitted by him to
the International Geographical Congress. And that his failure to achieve
a sounding near his farthest-north was due to leaving half his
sounding wire back on land.
Polar Notes 10  Dartmouth College; U.S. Naval Institute Proceedings 1970 June; DIO 1.1  ‡4; DIO 10  p.5 note. New York Times Science 2009/9/8 and online with link to DIO.
Richard Byrd claimed to have flown to the N.Pole on 1926/5/9. When DR examined
his diary in 1996, he found that Byrd had unsuccessfully attempted
to erase his actual sextant solar data, sights which put him 150 mi
south of the latitudes indicated by the sights he concocted
later for his official 1926/6/22 typed report
to SecNavy. The 1" precision of these fabrications was impossible on
his sextant, anyway — a difficulty solved by re-writing the typed report
on 1926/11/24, stripping out all the original report's raw 1"-precision data,
and then hiding said original for 70 years
with National Geographic connivance:
New York Times
DIO 10 ,
co-published with Cambridge University's
Polar Record 2000 pp.25-50.
DR had been 1st (Fiction  p.280) to allege that the 1st three claims to the N.Pole were fakes and thus that the Amundsen-Ellsworth-Nobile Norge dirigible expedition had priority: 1926/5/12. This once-outré view is now the generally accepted one — entailing the shocking realization that the 1st explorer to the S.Pole (1911), R.Amundsen (and loyal companion O.Wisting), was also 1st to the N.Pole.
A weird footnote
to Peary … Fiction's publication:
In 1973, J.Eddie Weems, who wrote the 1963 Peary-family-approved biography of the explorer, partially funded by the American Philosophical Society (US equivalent of Britain's Royal Society) and Houghton-Mifflin, contributed three literally-dustjacket reviews to three different Texas newspapers, falsely claiming that DR's 1973 book Peary at the North Pole: Fact or Fiction had attacked Amundsen's 1926 N.Pole achievement. This occurred partly (the full story is even more discreditable than what follows) because Weems' reading of the confusingly-written dustjacket of DR's book didn't get even as far as the end of either of its first two paragraphs.
This is obvious from checking the jacket's first two paragraphs, which follow:
Frederick A. Cook, Robert E. Peary, Richard E. Byrd, Roald Amundsen: all these men claimed to have discovered the North Pole. History has awarded the distinction to Peary, while granting to Amundsen the secondary honor of being first to fly over the Pole.
Not so, says Dennis Rawlins. Although Peary appeared to have conquered the Pole, and was lauded and certified upon his return, his claim was disputed almost from the outset. Rawlins' thesis indicts not only Peary, but conman Cook and Richard E. Byrd, who claimed but could not prove he flew to the Pole a few days before Roald Amundsen's meticulously documented flight.
Weems' faked reviews appeared in:
Dallas Morning News 1973/7/8 p.8E;
Wichita Falls Times 1973/7/15;
and then, incredibly, a 3rd Weems fake appeared five months later: Houston Chronicle 1973/12/16.
An even weirder footnote to the foregoing footnote:
in the early 1970s, DR sent the ms of his nearly-completed Peary book to Houghton-Mifflin for consideration. At that stage, the final Amundsen-vindicating chapter had not yet been written, so H-M's declining referee (guess who) would not learn (from that version) what DR's view on Amundsen was, and might easily later (when rushing under a newspaper-review deadline: his Dallas review was 10d after Fiction's publication) try swiftly learning said info from the dustjacket, confident that he had already read the book when earlier reviewing it for H-M. So: did Houghton-Mifflin choose a certain patently-partisan reviewer without telling the author? Weems' 1973/7/8 Dallas book review volunteered that H-M had a decade earlier fiscally backed Weems' Peary-defense book with a helpful advance, claiming (who'd asked?) H-M wasn't taking sides: “interested in books and not in the specific claims of Arctic explorers”. Hmmm. Was this PUBLISHER's early-1960s behavior neutral, when it chose to fund a book promoting the dubious #1-hero of a fellow PUBLISHER (one of the richest & best-connected on Earth)? Was its 1970s choice of referee for Fiction a neutral one? If no&no, then: why?
And what was the integrity of the book H-M was Persuaded to publish? Check out Weems' selective use of his then-exclusive access to the Peary Papers: DIO 1.1  ‡ §D [pp.24-25].)
If the passage of over 30y makes a hoax historical, then it's OK to close
out this list with the notorious sTARBABY affair, in which
establishment-catering CSICOP (now CSI),
the Committee for Scientific Investigation of Claims of the Paranormal
bungled its 1st Scientific Investigation and then attempted
to get away with escaping from its
catastrophe via post-test sample-splitting, threat & banishment against
whistleblowing. The case is thoroughly recounted