The Vietnamese mathematical record

No figure here is a world census, nor do published summaries share units. Certain studies count texts or documents, while others count volumes, images, or pages. For this reason, a larger number frequently measures another metric entirely. Where two sources cannot be reconciled, this page gives both and notes the difference, and where no defensible figure exists it gives none. That restriction applies in particular to the share of the Hán-Nôm corpus that has been digitized, which available sources cannot answer.

Nguyễn Xuân Diện of the Institute of Hán-Nôm Studies and Tạ Duy Phượng of the Institute of Mathematics conducted the survey. They found twenty-two Hán-Nôm mathematical books located between the Institute of Hán-Nôm Studies and the National Library of Vietnam, with thirteen written in Hán and nine mixing Hán and Nôm.1 This figure remains a count of two named libraries at a single date. Their subjects are administrative and practical, covering abacus reckoning, farmland area calculation, measurement, construction, astronomy, tides, alongside Nguyễn dynasty tax rules.1

Very few of these volumes carry a date. Specific dated texts include a work from 1820 by Phan Huy Khuông, an 1829 text by Nguyễn Hữu Thận, and two items from 1909 written by Nguyễn Cẩn and Đỗ Đức Tộ. Phạm Hữu Chung appears as author of Cửu chương lập thành tính pháp, though without any date attached.2

Requesting a treatise by shelfmark provides the practical test of whether a text exists as a physical object. At the Institute of Hán-Nôm Studies, Lập thành toán pháp bears shelfmark VHv.497.14 It is an anonymous, undated manuscript in Hán that opens with traditional introductions to arithmetic operations and multiplication tables before expanding into a long section on plane figure areas.2 Meanwhile, Cửu chương lập thành toán pháp survives in two printed copies: AB.173, containing fifty-six pages printed in 1713, and AB.563, containing forty-four pages.15 Finally, cataloguers listed Nguyễn Hữu Thận's 1829 work Ý trai toán pháp nhất đắc lục under A.1336, VHv.1184, A.982, and A.1336/a.16

The most widely known treatise also remains the least settled. Preserved as manuscripts A 2931 and VHv 1152, Toán pháp đại thành features Lương Thế Vinh's name written on the opening page of each copy.3 Alexei Volkov's finding is that "the text of the treatise does not contain any information proving that the manuscript found in the Han-Nom Institute in Hanoi was indeed authored by Lương Thế Vinh".3 That attribution remains traditional yet contested. Details on how his name came to be attached to the text appear in our summary of the history of Vietnamese mathematics.

On 13 September 1979, Decision 326/CP of the Government Council established the Institute of Hán-Nôm Studies, building upon the Ban Hán Nôm that had operated since 1970.4 Today its library holds roughly 20,000 units of general books, over 48,000 units of inscription rubbings, alongside about 20,000 old printing blocks.5 Because these figures count storage units rather than distinct titles, they exceed any tally of individual works.

The 2013 survey assigned eighteen of the twenty-two mathematical items to the Institute and four to the National Library of Vietnam, with three of those four digitized at that time.1 Someone seeking to inspect this mathematical corpus in person need visit only one reading room. Further details about the institutions that study these texts appear in our article on mathematics research in Vietnam.

Outside Vietnam, holdings are thinner and less documented. In Paris, the library of the École française d'Extrême-Orient holds sixty-six Hán-Nôm manuscripts and printed works.8 The Bibliothèque nationale de France maintains a France-Vietnam digital library containing over 2,000 accessible items. That mixed collection offers no distinct tally for Hán-Nôm material or mathematical texts.9

One frequently repeated episode requires careful scrutiny. In 1938, the Chinese mathematician and historian of science Zhang Yong examined the old Vietnamese holdings at the École française d'Extrême-Orient in Hanoi, an investigation Li Yan summarised in 1954.13 Volkov notes that Han Qi later "used the partial copies of Vietnamese treatises made by Zhang Yong in Vietnam, while the original texts preserved in Vietnamese and French libraries remained unexplored".13 That observation reflected the state of scholarship when Volkov wrote it. Because statements placing a set of Vietnamese mathematical books in a Chinese institution today exceed what library catalogues confirm, this page makes no claim about where Zhang Yong's materials are now.

Reporting on an Institute stocktake dated 29 March 2023, Thanh Niên stated that 121 Hán-Nôm volumes were missing or unlocated, with another 110 listed as seriously damaged.6 Police were investigating twenty-five items that staff formally reported missing. The remaining ninety-six volumes were classified as unlocated rather than stolen, as administrators still expected to retrieve them from internal shelving.6

Two specific qualifications apply to those figures. These numbers derive from the Institute's own press-reported inventory, standing apart from an external audit or court finding. Investigating twenty-five items differs from establishing twenty-five confirmed thefts. As of July 2026, searches yielded no published conclusion to that police inquiry.

The stocktake report lists none of the twenty-two mathematical books among the missing or damaged volumes.6 This silence requires clear interpretation: the lack of a specific mention neither proves that the mathematical texts remain safe nor demonstrates that damage occurred.

A major partnership drove the largest scanning effort. In April 2006, the Vietnamese Nôm Preservation Foundation signed a memorandum with the National Library of Vietnam to construct a digital library for the institution's Hán-Nôm special collection of over 4,000 texts.10 The Foundation states that it "digitized and catalogued some 4,000 Hán-Nôm texts" alongside the Library.11 In 2015, a paper recorded that technicians had scanned over 5,200 historical documents, placing roughly 1,907 documents comprising 133,495 pages online at the Library's Hán-Nôm portal.12 Columbia University Libraries subsequently published its Vietnamese Hán-Nôm Digital Collection of approximately 1,100 texts gathered from the National Library, Thắng Nghiêm Temple in Hanoi, and Phổ Nhân Temple in Hưng Yên.17

A clarification regarding institutional repositories is necessary here. Under project EAP219, titled "Assessment and preservation of the old Vietnamese École française d'Extrême-Orient archive in ancient ideographic Nôm script", the British Library's Endangered Archives Programme scanned materials at the Institute of Social Sciences Information in Hanoi rather than the Institute of Hán-Nôm Studies.7 That project catalogued 105 files from a total of 2,055 books within an unregistered, unclassified Hán-Nôm collection dating between about 1624 and about 1954, generating 19,039 TIFF images with subject matter described simply as mixed.7 While the resulting catalogue lists no mathematical treatises, it leaves their presence open.

Significant hurdles remain in automated text processing. Introduced at RIVF in 2022, NomNaOCR is what its authors call the first dataset for optical character recognition on Hán-Nôm script, constructed using 2,953 handwritten pages from the Vietnamese Nôm Preservation Foundation along with 38,318 annotated patches.18 Writing in a 2020 issue of Pattern Recognition Letters, Kha Cong Nguyen, Cuong Tuan Nguyen, and Masaki Nakagawa argue that owing to "the gradual degradation of Nom documents and a decrease in the number of scholars who can understand them, a system to digitalize Nom documents is urgently necessary". These same researchers note that among the vast surviving Nôm corpus, "most of them have not yet been digitized".19 Neither publication claims coverage of mathematical treatises, notation, or diagrams.

Although scanning has proceeded at scale, a 2020 assessment concluded that the bulk of the Nôm corpus remains unscanned.19 Physical records for mathematical works show even less progress: as of the 2013 survey, three of the four books at the National Library were digitized.1 Searches revealed no public digitization initiative for the eighteen volumes at the Institute of Hán-Nôm Studies. A raw page image remains distinct from machine-readable text, and neither OCR study details methods for processing mathematical notation in this script. Current holdings of Vietnamese-language mathematics datasets involve a separate, modern effort.

Named Cadmus, this processing pipeline converts Vietnamese mathematical source material into verified, structured records across eleven stages. Machine reading of Hán-Nôm script is another topic of research. In testing, the dual-view normalization-chunking stage preserved 100% of mathematical tokens compared to 0.03% for a normalization-only baseline; this distinction separates a searchable document from one with its equations silently erased. Meanwhile, the deterministic post-OCR corrector achieved 99.913% precision over 2,288 automatic edits, recording zero catastrophic errors and zero source-file mutations.

Cadmus operates on modern curriculum materials today, leaving archival manuscripts for a future project phase. That limit is stated directly because a report on historical holdings published by an active engineering lab can easily imply unearned scope.