Three times – but still not true!

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Three times just recently I have been told that mathematicians do not need to know about citation and referencing because they do not cite other people’s work.

Three times is more than coincidence.  But, for mathematicians as for any other academic discipline, this is just not true! Mathematicians do cite. A look at any mathematics journal shows that mathematicians cite their sources. Papers with 50 and more references are common, and they all cite the sources in the text.

But these looks at mathematics journals do reveal something curious. Mathematicians do not always cite their sources, by name, in the text.  Is this where the myth originates?  What mathematicians commonly use is a (non-superscript) numbered referencing system.  And it often results in nearly unreadable prose.

…  Recently a “leaky waveguide” with a small parameter breaking the symmetry was considered in [31]. For the similar problems in the one-dimensional case see [10,29,36,41]. The analogous results for quantum graphs were obtained in [16,17,35].  See also recent developments for Pauli operators [25]. …
(Kondej & Lotoreichik 1418)

The reference list, and the citations which derive from them, cannot be easy to compile – at least, I suspect, not without software.

The list is alphabetical by surname, initials first. Once the list is complete, a reference number is assigned to each of the entries. This is why I suspect software is involved – if a new reference is introduced, then the numbering is thrown out!  Memories of essays and dissertations written on a manual typewriter, carbon paper copies and all.  Software would solve that problem.

The number forms the in-text citation, signalling that this is not the present author’s original idea, it derives from elsewhere; the number links to a full reference at the end of the paper.

It is not a style which is helpful to the writer, and it is not helpful to the reader either.  It’s a style which lends itself to practical difficulties, for when the print journal runs to several hundred pages, one can run out of fingers and thumbs, trying to keep one’s place in the paper while searching out a reference or five somewhere further on in the journal.

The text does not read well. It can be ironic too.

….  Its theory has subsequently been developed and used by many authors working in various areas of mathematics and physics (see [13,18] for applications to quantum mechanics); a non-exhaustive list of contributions is (in alphabetical order) [4,6,11,17,22], and the references therein.
(de Gosson & Lueff 948)

if the reference list is in alphabetical order and numbered in the order in which entries appear in the list, then numerical order is the same as alphabetical order; that parenthetical note, “in alphabetical order,” is, perhaps, both unneeded and redundant?  But wouldn’t it read better if those 5 references were actually named?

Referencing systems have evolved from the needs of the subject or discipline and the styles of writing commonly used in those subjects.  Could it be that, because mathematics deals with constants and truths, it does not matter who first voiced an idea; it is always true; it is “fact”?  And thus, perhaps, there is no need to name sources in the text, in turn, leading to the notion – mistaken –  that mathematicians do not cite sources in the text.

It must be pointed out that unreadability of text is not a requirement of this citation style. It is just as possible to name sources (and to improve readability and to stress authority) in a math paper as it is in other styles.

Koblitz [9] suggested a NAF τ-and-add algorithm for a family of supersingular curves in characteristic 3; this method was later improved by Blake, Murty and Xu [4]. Avanzi, Heuberger and Prodinger [2] exploited the existence of the 6-th roots of unity in Z[τ ] = {a + bτ | a, b ∈ Z} to create a sixpartite digit set that decreased memory consumption by a factor three; Avanzi and Heuberger [1] also provided a precomputationless factored digit set. A similar study was undertaken by Kleinrahm [7], examining a curve in characteristic 5 where the 4-th roots of unity belong to Z[τ].
(Heuberger & Mazzoli 19).

But, readablity or otherwise, I think the lie is laid to rest: for mathematicians as for academics in other subjects, sources count.

(To be continued)


de Gosson, M. & Luef, F. (2014). Metaplectic group, symplectic Cayley transform, and fractional Fourier transforms. Journal of Mathematical Analysis and Applications 416 (2), 947–968. DOI: 10.1016/j.jmaa.2014.03.013 (Open access article used here under CC BY-NC-ND license).

Heuberger, C. & Mazzoli, M. (2014) Symmetric digit sets for elliptic curve scalar multiplication without precomputationTheoretical Computer Science 547, 18–33.  (Open access article used here under CC BY-NC-ND 3.0 license).

Kondej, S. & Lotoreichik, V. (2014).  Weakly coupled bound state of 2-D Schrödinger operator with potential-measure. Journal of Mathematical Analysis and Applications 420 (2), 1416–1438. DOI: 10.1016/j.jmaa.2014.06.053 (Open access article used here under CC BY-3.0 license).

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