There are no precise criteria for accepting a word, but we would say
that a word should be added if:
(A) the coinage is known;
(B) it WAS or IS used by prominent mathematicians in outstanding
papers or books;
Although the lexicon is dedicated mainly to FIRST occurrences of
TERMS, we think that, in certain cases, the CONCEPTS behind them and
the mathematical context involved deserve also a brief discussion in
order to avoid ambiguities. For instance, what Hausdorff called
"topological space" is now called a "Hausdorff topological space";
Andre' Weil used "Lefschetz's principle" as a sort of conjecture but
the term was "reintroduced" in logic in many precise versions; and so
on. Moreover, many words are, so to speak, "polymorphic" in that their
meanings vary when we pass from one field to another. Thus we have
"duality" in projective geometry (Gergonne), Boolean algebra
(Hausdorff), category theory, etc.; "distribution" in probability and
in functional analysis; and so on. On the other hand, there are also
extreme cases of terminological variation in a single field (as in
graph theory and combinatorics).
Attention should also be paid to terminological variations between
countries. Some Russian authors, for example, insist on reserving the
term "topological space" for spaces that satisfy the first separation
axiom (T1-spaces). If possible, additional information about
translations in other languages should be provided. This task is
extremely difficult with "blends" like "poset" and "clopen" (for
"closed and open"), but, as a way of example, we mention that "clopen"
has corresponding terms in French (ouferme'), Portuguese (feberto) and
German (geschloffen).
Nontechnical expressions like "working mathematician", "civilized proof"
and "the mathematician in the street" are also welcome.
Anyway, we think that an uncontroversial sampling of relevant
aspects of a word would include (if possible):
(1) the name of the mathematician who introduced the word;
(2) a reference to the paper or book in which it first appeared (title,
the name of the journal, the volume number, the year, first and last
page numbers etc.);
(3) its present-day meaning (in case of variation in time);
(4) illuminating comments by eminent mathematicians, physicians and
logicians (pros and cons);
(5) relating notational issues (when pertinent).
We present now some words as suggestions for lexicological research:
1. Baire space (probably due to Bourbaki)
2. Bornology (bornological vector space)
3. Cartesian product (Cantor's Verbindungsmenge; later generalized to an
infinite number of factors by N. Whitehead; consider also products of
structures)
4. Congruent number
5. Convolution
6. Distribution
7. Dummy (mute, blind) variable (probably used long before "bound variable"
– after Hilbert -, now common in logic; remember Peano's "apparent")
8. Equivalence class
9. Ergodic
10. Fewnomial ("malochen"; probably due to Kushnirenko)
11. Hamel basis
12. Handshaking lemma
13. Hauber's principle (by the way, who was Hauber?); also known in Brazil
as "general reciprocity principle".
14. Intractable (as used in complexity theory)
15. Multifunction (now common in set-valued analysis)
16. Noetherian induction
17. Nomography (probably due to d'Ocagne;)
18. Pseudocompact
19. Pseudo-prime (pseudoprime)
20. Pingeohole principle (Dirichlet's box-in principle, Dirichlet's
Schubfachprinzip; circa 1896)
21. Primitive recursive (Peter)
22. PV-number (also known as Pisot number)
23. Recursive (recursion)
24. Schauder basis
25. Separation axiom (trennungsaxiom; in topology, probably due to Tietze)
26. Strong induction (course of values induction etc.)
27. Subbase (probably due to Kelley in his General Topology; the concept
is apparently due to Bourbaki)
28. Unitial algebra (that is, an algebra with unit; for some "unitial"
is considered barbaric)
29. Urelement (axiomatic set theory; other terms: individual – not
exactly in Russell's sense-, atom; note the German prefix ur-)
30. Syzygies (in invariant theory)
31. Weak induction
Credits will be appropriately given to all who want to contribute.
Carlos Cesar Araujo