Book VII · 2026-09-19 · A commissioning list with its gaps marked
The Mathematicians History Overlooked
Different places, different languages, the same quiet persistence — largely uncredited. And when the credit goes, the mathematics quietly changes status: it stops looking made and starts looking found. Nineteen cards, kept exactly as supplied, then read the way this corpus reads anything carrying four claims at once.
People are passed over a lot, and then the mathematics gets another status. That is the thesis this volume is built on, and it is stronger than the one printed at the foot of the cards. Work that has lost its author stops reading as something made by somebody and starts reading as something found — ownerless, timeless, and therefore not arguable. Nineteen cards are set out below exactly as supplied, and then audited, because a card carries four claims and a handsome card carries them invisibly.
c. 350 – 415
Philosopher and astronomer in Alexandria. Taught and preserved Greek geometry and edited works on conics.
Apollonius, On Conics
Geometry
chapter ✓
tagAryabhata
c. 476 – 550
Indian astronomer-mathematician. Gave a refined value of pi and built early sine tables.
π ≈ 3.1416
Number Theory
no chapter
Liu Hui
c. 225 – 295
Commentator on the Nine Chapters on the Mathematical Art. Devised a polygon method for pi.
π ≈ 3.14159
Geometry
no chapter
Brahmagupta
c. 598 – 668
Formalized rules for zero and negative numbers; gave general solutions to quadratics.
ax² + bx + c = 0
Algebra
no chapter
Virahanka
c. 700 – 800
Studied Sanskrit poetic metre; described the recurrence later known as the Fibonacci sequence.
F(n) = F(n-1) + F(n-2)
Number Theory
no chapter
Al-Khwarizmi
c. 780 – 850
Father of algebra. Gave systematic methods for solving linear and quadratic equations.
al-jabr
Algebra
no chapter
Al-Biruni
973 – 1050
Polymath who measured Earth's radius and advanced trigonometry and geodesy.
sin² θ + cos² θ = 1
Applied Mathematics
no chapter
1048 – 1131
Solved cubic equations geometrically by intersecting conic sections; reformed the Persian calendar.
x³ + ax = b
Algebra · Geometry
chapter ✓
Bhaskara II
1114 – 1185
Wrote the Lilavati and Bijaganita; the chakravala method solved a hard class of equations.
x² - N y² = 1
Algebra · Number Theory
no chapter
Al-Karaji
c. 953 – c. 1029
Freed algebra from geometric proof; worked on the binomial theorem and arithmetic series.
1+2+3+...+n = n(n+1)/2
Algebra
no chapter
Abu'l-Wafa al-Buzjani
940 – 998
Advanced trigonometry and spherical geometry; compiled tangent-function tables.
sin θ, cos θ, tan θ
Trigonometry
no chapter
Gangesa Upadhyaya
c. 14th century
Founder of the Navya-Nyaya school; built a rigorous formal theory of inference.
∧ ∨ ¬
Logic
no chapter
formulaNarayana Pandita
c. 14th century
Wrote on magic squares, combinatorics, and algebraic identities.
(a+b)² = a² + 2ab + b²
Algebra
no chapter
c. 1340 – 1425
Founded the Kerala school; found infinite series for pi and trig functions, anticipating calculus.
π/4 = 1 - 1/3 + 1/5 - 1/7 ...
Analysis
chapter ✓
tagJamshid al-Kashi
c. 1380 – 1429
Computed pi to sixteen decimal places and advanced decimal fractions and astronomical tables.
π = 3.1415926535
Number Theory
no chapter
formulaSeki Takakazu
c. 1642 – 1708
Founder of wasan, Japan's native mathematical tradition; pioneered work on determinants.
ax² + bx + c = 0
Algebra
no chapter
1776 – 1831
Worked under a male pseudonym; advanced elasticity theory and a special case of Fermat's Last Theorem.
p, 2p+1 both prime
Number Theory
chapter ✓
status1928 – 2014
Rebuilt algebraic geometry from its foundations with schemes, sheaves, and topos theory.
Spec(R)
Algebra · Geometry
chapter ✓
statusShinichi Mochizuki
born 1969
Number theorist working in arithmetic geometry; proposed inter-universal Teichmuller theory toward the ABC conjecture.
c > rad(abc)^(1+ε)
Number Theory
no chapter
Corner marks: tag — the subject label does not match the stated contribution. formula — the formula slot does not carry this person's work. status — a card where the person and the standing of the work moved together; the argument's sharpest cases, not its weakest. Green chapter — this corpus already holds a chapter on the person; red no chapter — it does not.
1 · Five of nineteen already have a chapter
Hypatia, Omar Khayyam and Madhava are in Volume IX; Sophie Germain and Grothendieck are in this volume. The other fourteen have nothing, and that is the useful output of the gallery: it is a commissioning list with the gaps already marked, in a corpus whose Volume VII rule is that a chapter exists when there is a person whose encounter with an object is the point.
2 · What being passed over does to the mathematics
An earlier version of this page marked Grothendieck and Mochizuki as failing the gallery's premise, on the reading that the gallery was about obscurity and neither man is obscure. That reading was imported, not given. The thesis is not that these nineteen were forgotten. It is that people are passed over a lot, and then the mathematics gets another status — and the two are the same event seen from either end.
A result with a person attached is contingent. Somebody wanted something, tried something, was working in a place at a time, and could have been wrong. A result whose person has been stripped off reads as if it were found rather than made: ownerless, timeless, above the ordinary business of being argued with. The promotion is unearned and it is invisible, because nothing on the page says a name was removed.
Why this volume exists, stated in one line
Volume VII's rule is that a chapter exists when there is a person whose encounter with an object is the point. That rule is not a courtesy to the dead. It is the same instrument this corpus uses everywhere else — a claim resolves at the path cited, a number arrives with the script that computed it, a proof names its file and its axioms. Anonymity is what lets a claim get promoted without being checked, in mathematics exactly as in a citation.
Read that way, the two modern cards are not exceptions. They are the two ends of the range, and they are the most instructive cards on the wall.
| card | what happened to the person | what happened to the status |
|---|
| Grothendieck | Removed himself. Left the institution, then the subject, and asked for his work to be withdrawn from circulation. | The mathematics carried on under his name without him. The most cited case in the century of work outliving, and being detached from, the person who made it. |
| Mochizuki | Inseparable from the work. Acceptance turns on who will read it, on what terms, and in which language. | The mathematics has not been granted the ownerless status. It is still a claim by a person, which is why it is still argued with. |
One is a man whose work became authorless while he lived; the other is work that cannot become authorless and is therefore still contested. Between them sits every other card: seventeen people whose names had to be recovered before anyone could ask what they actually did.
Correction, 2026-09-19
The “fails the premise” finding was this page auditing the gallery against a thesis it attributed to the author rather than one the author held. The flag on those two cards is now status — the person and the standing of the work moved together — and it marks the cards as the argument's sharpest cases rather than its weakest.
3 · Two subject tags do not match the contribution
Aryabhata's refined value of π and al-Kashi's sixteen decimal places are both tagged Number Theory. They are approximation and computation. Liu Hui's polygon method for the same constant is tagged Geometry, which is right — and the disagreement between the three cards is how the error shows.
4 · Two formula slots carry someone else's work
Seki Takakazu's card credits him, correctly, with pioneering work on determinants — and then prints ax² + bx + c = 0, the same formula as Brahmagupta's card eleven places earlier. Nārāyaṇa Paṇḍita's card prints (a+b)² = a² + 2ab + b², which belongs to nobody in particular and certainly not to a man remembered for magic squares and combinatorics.
Why a filler formula is worse than a blank one
A formula slot on a card of this kind reads as a claim: this is the thing this person gave us. Filling it with a standard identity because the design needs a line of monospace is a small dishonesty that compounds — the reader who does not know Seki learns something false about him, and the card looks exactly as authoritative as the one next to it that is right. An empty slot says “not summarised in one line”, which is true of most real mathematics.
5 · The epigraph is attested and unsourced
“Algebra is but written geometry and geometry is but figured algebra” is given to Sophie Germain. It appears on MacTutor's Germain quotations page — and with no source attached, while the letter to Gauss on the same page carries a date, 1807. The line is attested in a reference work and not traced to a document. That is a real state, and different from both “sourced” and “spurious”.
6 · What this page does not claim
- That the biographical notes are wrong. Nothing in them was contradicted by what was checked; what was checked is listed above and it is not all of them.
- That the dates are settled. Several are c. for good reason — Virahanka's century is argued over, and the gallery's ranges are within the usual spread.
- That fourteen missing chapters is a criticism of the gallery. It is the gallery's contribution.
7 · Sources
- MacTutor History of Mathematics, Sophie Germain, quotations page. mathshistory.st-andrews.ac.uk/Biographies/Germain/quotations/
- Card data as supplied, kept verbatim in gallery-overlooked-data.tsv so the audit can be re-run against it.
- Chapter presence checked against this repository by gallery-overlooked-verify.py.