What fraction of Leonhard Euler's output actually came after he went blind? Two Tier-2 sources conflict ('half of his output' vs '≈a third in the first seven years') — new findings on the figure's origin and an unresolved denominator

This capture follows up question-verify-euler-post-blindness-output-fraction, which was raised against claim-euler-produced-large-share-of-output-after-going-blind — an existing seedling note recording that two Tier-2 sources disagree on the fraction of Euler's ~850 works produced after he lost his sight: Allyn Jackson's 2002 AMS Notices piece ("half of his output") versus Mele & Sicignano's 2021 figure via Calinger ("almost a third of his results in the first seven years"). New searching this run did not locate the Eneström-catalogue count, MacTutor chronology cross-tabulation, or Calinger primary text that the existing question named as the way to resolve it. It did surface three findings that bear directly on the conflict without resolving it: the "half" figure has an identifiable, much older textual ancestor; the very total against which any fraction would be computed is itself not agreed upon across sources; and the "seven years" language used in different accounts of Euler's late output does not consistently refer to the same seven years. The core numeric question stays [unverified — could not confirm or deny after search].

Claim: The "half of his output after blindness" figure traces to an 1883 lecture, not to an independent modern tally

Claim type: quantitative (a fraction) with historical framing. Sourcing floor: Tier 1–2 required; the sources available are Tier 3, so this is recorded as [unverified-quant — needs primary].

Ferdinand Rudio, professor at the Federal Polytechnic in Zurich, delivered a centenary tribute to Euler at the Zurich Town Hall on 6 December 1883. In it, discussing Euler's return to St Petersburg in 1766 and total loss of sight by 1771, Rudio said: "Thus, Euler was completely blind during the last 17 years of his life. However, now Euler's unusual mental abilities truly showed themselves: henceforth, the totally blind old man developed an almost frenetic activity; almost half of his entire production dates to the years when Euler was bereft of a scholar's most valuable organ." This 1883 statement — translated by Stefanie Eminger and hosted verbatim by MacTutor — is the earliest occurrence of the "half" figure found in this search, predating Allyn Jackson's 2002 AMS Notices wording ("Amazingly, half of his output came after his blindness") by 119 years. MacTutor's own separate biography page repeats the same fraction independently in the narrative voice: "Amazingly after his return to St Petersburg (when Euler was 59) he produced almost half his total works despite the total blindness." None of the three appearances (Rudio 1883, the MacTutor biography, Jackson/AMS 2002) cites a bibliographic count or shows its method — Rudio states it as rhetorical color in a public address, and MacTutor's biography does not attach an inline citation to that specific sentence. This does not make "half" wrong, but it means the "half" side of the conflict may be one claim propagating across a century of retellings rather than several independent computations converging on the same number — relevant to the vault's single-source-concentration concern, since apparent agreement across named sources here may not be corroboration in the load-bearing sense.

Claim: Euler's total lifetime work count has no single agreed figure, so the fraction's own denominator is unsettled

Claim type: quantitative. Sourcing floor: Tier 1–2 required; sources below are Tier 1–2, but they conflict with each other, so the resulting range is recorded rather than a single number.

At least four different totals for Euler's output circulate in sources that would otherwise clear the sourcing floor. The AMS's Allyn Jackson quotes historian Dirk Struik's A Concise History of Mathematics: "During his life 560 books and papers appeared; at his death he left many manuscripts, which were published by the St. Petersburg Academy during the next forty-seven years" — 560 being only what was published during Euler's lifetime, excluding the posthumous material. Dora Musielak's arXiv preprint states "Euler wrote about 800 books and papers," and separately that "the 'official' number of entries in Eneström's index is 866, including a number of letters and unfinished manuscripts," while "the Euler Archive currently has 834 works." So depending on whether posthumously-published items, letters, and unfinished manuscripts are counted, the reported total ranges from 560 to 866 — a roughly 50% spread on the denominator alone, before any numerator (post-blindness count) is even attempted. Neither the existing claim-note's ~850 figure nor the "half"/"a third" fractions specify which of these baselines they are computed against.

Claim: The "seven years" cited in different accounts of Euler's post-blindness output do not describe the same seven years

Claim type: quantitative / comparative. Sourcing floor: Tier 1–2 required; the MacTutor figure below is Tier 3 and is recorded flagged.

The existing claim-note's Mele & Sicignano figure covers "the first seven years after completely losing his sight at the age of sixty" — i.e., a window opening around Euler's near-total blindness on returning to St Petersburg in 1766 (age 59–60) or, on Rudio's dating, his final loss of sight after the failed 1771 cataract operation. Separately, MacTutor's biography states that Nicolaus Fuss "became his assistant in 1776" and that "Fuss helped Euler prepare over 250 articles for publication over a period on about seven years in which he acted as Euler's assistant" — i.e., 1776 until Euler's death in 1783, the last seven years of his life, not the first seven years of blindness. [unverified-quant — needs primary: the "250 articles" figure carries no inline citation in the MacTutor text beyond a general reference to Yushkevich's Dictionary of Scientific Biography entry]. These are two different seven-year spans within Euler's roughly seventeen blind years — one immediately following the onset of blindness, one ending at his death a decade later — so a reader assembling "seven years" statistics from different secondary sources should not assume they are describing the same period, which compounds rather than resolves the original AMS-vs-Mele&Sicignano conflict.

Further leads

• The Euler Archive (eulerarchive.maa.org, directed by Dominic Klyve, Lee Stemkoski, Erik Tou) hosts a dated, searchable listing of works keyed to Eneström numbers — in principle the direct resource for computing the pre/post-1766 split by hand; not attempted this run. Scholarly-commons mirror: https://scholarlycommons.pacific.edu/euler-works/
• Ed Sandifer's MAA column "How Euler Did It" (eulerarchive.maa.org/hedi/) is cited by Musielak as the source for the "~800 books and papers" figure and reportedly analyzes Euler's output rate in detail; not fetched this run.
• Emil A. Fellmann's Leonhard Euler (Birkhäuser, 2007) is cited repeatedly by Musielak for biographical specifics (e.g., the dating of the eye-loss events) and is flagged as an authoritative secondary biography worth checking directly.
• A dating discrepancy surfaced but not resolved: Rudio (1883) and Struik (via AMS) date Euler's first eye loss to the 1735 fever from an astronomical-calculation marathon; Musielak's arXiv paper dates it to 1738, citing Euler's own 1740 letter to Goldbach ("I have lost an eye"). Not pursued here as it is tangential to the output-fraction question, but it touches the same "which biographical detail is contemporaneous vs. secondhand" problem.

Entity candidates

• Ferdinand Rudio — person — 19th-century mathematician-historian whose 1883 centenary lecture appears to be the textual origin of the "half of his output" figure that later sources (MacTutor, AMS/Jackson) repeat; foundational to this whole conflict and currently un-flagged anywhere in the vault.
• Gustaf Eneström — person — Swedish mathematician who compiled the Eneström index (E-numbers), the closest thing to a primary bibliographic catalogue of Euler's works; the person whose own count would actually resolve this question.
• Dirk Struik — person — historian of mathematics; author of A Concise History of Mathematics, quoted by AMS for the "560 books and papers" lifetime-publication figure, one of the four competing totals.
• Nicolaus Fuss — person — Euler's grandson-in-law and final amanuensis (assistant from 1776); the "250 articles in seven years" figure describes his specific tenure, distinct from the "first seven years of blindness" window used elsewhere.
• Dora E. Musielak — person — physicist/historian (UT Arlington) whose arXiv preprint is the source for the 800/866/834 total-count figures used above; unrefereed preprint, so any promoted claim resting on it should track the single-source concentration cap.
• Ronald Calinger — person — author of the 2019 Princeton biography that Mele & Sicignano cite for the "almost a third in seven years" figure; already named in the existing claim-note as the unread primary that would resolve the conflict, worth flagging again since it remains unread.
• Eneström index — concept — the E-number catalogue itself; a future note on what it is and how it's structured (chronological ordering, letter/translation suffix conventions) would be useful scaffolding for anyone attempting the actual count.