A contender for the world record for the paper with the greatest number of authors is the 5,154-author paper

G. Aad, B. Abbott, J. Abdallah, O. Abdinov et al., Combined measurement of the Higgs boson mass in Collisions at and 8 TeV with the ATLAS and CMS experiments. Phys. Rev. Lett., 114, 191803, 2015.

It comprises 8.5 pages of text and 24.5 pages of author list and author addresses.

New Scientist magazine used the term nominative determinism for the tendency for authors to gravitate to fields of research related to their surname. (See this article for more background on the term.)

A. G. Cock, Genetical Studies on Growth and Form in the Fowl, Genetical Research 4, 167-192, 1963.

A. J. Splatt and D. Weedon, The Urethral Syndrome: Experience with the Richardson Urethroplasty, British Journal of Urology 49, 173-176, 1977.

Zhian Sun and Keith Shine, Studies of the Radiative Properties of Ice and Mixed-Phase Clouds, Q. J. R. Meteorol. Soc. 120, 111-137, 1994.

It’s not hard to find examples of husband-wife co-authors. Other relations are less common.

Brothers:

Nicholas J. Higham and Desmond J. Higham, Large Growth Factors in Gaussian Elimination with Pivoting, SIAM J. Matrix Anal. Appl., 10, 155-164, 1989.

Father (second author) and son (first author):

Alex Olshevsky and Vadim Olshevsky, Kharitonov’s Theorem and Bezoutians, Linear Algebra Appl., 399 (1), 285-297, 2005.

Michael Stewart and G. W. Stewart, On Hyperbolic Triangularization: Stability and Pivoting, SIAM J. Matrix Anal. Appl., 19, 847-860, 1998

Mother (Alicja) and daughter (Agata):

Alicja Smoktunowicz, Agata Smoktunowicz, and Ewa Pawelec, The three-term recursion for Chebyshev polynomials is mixed forward-backward stable, Numerical Algorithm, 69(4), 785–794, 2015.

Grandfather (Walter) and grandson (Daniel):

Walter Ledermann, Carol Alexander and Daniel Ledermann, Random Orthogonal Matrix Simulation, Linear Algebra Appl. 434, 1444-1467, 2011

G. E. P. Box and D. R. Cox, An Analysis of Transformations, Journal of the Royal Statistical Society. Series B (Methodological) 26, 211-252, 1964.

Pronounced the same but spelled differently:

Peter D. Burns and Roy S. Berns, Error Propagation Analysis in Color Measurement and Imaging, Color Research & Application 22, 280-289, 1997

The latter paper also has the distinction of having a DOI that I cannot get to parse correctly in this post: 10.1002/(SICI)1520-6378(199708)22:4<280::AID-COL9>3.0.CO;2-L

R. A. Brown and C. H. Green, Threats to Health or Safety: Perceived Risk and Willingness-To-Pay, Social Science & Medicine. Part C: Medical Economics 15, 67-75, 1981.

Esther Black and Craig White, Fear of Recurrence, Sense of Coherence and Posttraumatic Stress Disorder in Haematological Cancer Survivors, Psycho-Oncology 14, 510-515, 2005

The next article includes the unusual combination of Wright and Wrong.

S. Levi, C. T. Dollery, S. R. Bloom, J. Calam, T. M. Cox, H. J. F. Hodgson, M. S. Losowsky, M. B. Pepys, N. A. Wright, and O. M. Wrong, Campylobacter Pylori, Duodenal Ulcer Disease, and Gastrin, BMJ 299, 1093-1094, 1989.

Many years ago Ron Mitchell, of the University of Dundee, told me that there was a report or paper by Collar and Tie, the first author presumably being the engineer Arthur Roderick Collar. I have not being able to locate this publication.

There are a number of examples of fictitious authors with amusing names being included on papers. I will not try to document any here, but point to The true story of Stronzo Bestiale (and others scientific jokes) for some examples.

Thanks to Des Higham for pointing out Box and Cox, Brown and Green, and Cock, which are taken from Learning LaTeX (page 40) by D. F. Griffiths and D. J. Higham.

We are looking for authors who share the same surnames and preferably are not related. It would be hard to beat

Allen Goodman, Joshua Goodman, Lucas Goodman and Sarena Goodman, A Few Goodmen: Surname-Sharing Economist Coauthors, Economic Inquiry, 2014.

These four economists got together to write their paper about surname-sharing economist co-authors with the ulterior motive of beating the previous record of three.

A weaker requirement is surnames beginning with the same letter, for which we offer

Steven Mackey, Niloufer Mackey, Christian Mehl and Volker Mehrmann, Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations, SIAM J. Matrix Anal. Appl. 28 (4), 1029-1051, 2006

Since Nick Trefethen does not go by his first name, I claim that the following example is valid for three Nicks:

Nicholas Hale, Nicholas John Higham and Lloyd Nicholas Trefethen, Computing , , and Related Matrix Functions by Contour Integrals, SIAM J. Numer. Anal. 46, 2505-2523, 2008.

Ideally I would like a pair of authors for which the first name of each is the last name of the other. The closest I’ve found is:

Philippe Chartier and Bernard Philippe, A Parallel Shooting Technique for Solving Dissipative ODE’s, Computing 51, 209-236, 1993.

Here is a run of four surnames beginning with consecutive letters:

D. Bremner, T. M. Chan, E. D. Demaine, J. Erickson, F. Hurtado, J. Iacono, S. Langerman, and P. Taslakian. Necklaces, convolutions, and . In Y. Azar and T. Erlebach, editors, Algorithms–ESA 2006, volume 4168 of Lecture Notes in Computer Science, pages 160–171. Springer-Verlag, Berlin, 2006.

The next paper goes even better by starting at “A”:

J. I. Aliaga, J. M. Badía, M. Castillo, D. Davidovic, Rafael Mayo and Enrique S. Quintana-Ortí, Out-Of-Core Macromolecular Simulations on Multithreaded Architectures, Concurrency and Computation: Practice and Experience, 2014.

A famous example, for the Greek alphabet, is

R. A. Alpher, H. Bethe and G. Gamow, The Origin of Chemical Elements, Physical Review 73, 803-804, 1948

According to Freeman Dyson, “Bethe had nothing to do with the writing of the paper but allowed his name to be put on it to fill the gap between Alpher and Gamow.”

In contrast to the previous section, here we are looking for names that are spaced as far apart in the alphabet as possible. For two authors this is the most extreme case:

H. Ashley and G. Zartarian, Piston Theory—A New Aerodynamic Tool for the Aeroelastician, Journal of the Aeronautical Sciences 23, 1109-1118, 1956.

Can we find an author list in which the surnames repeat cyclically? I offer

A. S. Lin, C. H. Chen, H. G. Hwu, H. N. Lin and J. A. Chen, Psychopathological Dimensions in Schizophrenia: a Correlational Approach To Items of the SANS and SAPS. Psychiatry Research 77, 121-130, 1998.

If you’re going to write about the programming language R, it helps if your first name begins with “R”:

R. Ihaka and R. Gentleman, R: A Language for Data Analysis and Graphics, Journal of Computational and Graphical Statistics 5, 299-314, 1996

However, it would be hard to beat the next paper, whose author (Walter Russell Brain) not only got his name into the title, but also published the paper in a journal of the same name: a triple whammy!

Lord Brain, Some Reflections on Brain and Mind, Brain 86, 381-402, 1963

Finally, we have a long author list with the first and last surnames the same:

Ling Zhang, Zhongshan Li, Ting-Zhu Huang, Qing-Fang Zhu, Jian Hua and Lihua Zhang, Periodic, Reducible, Powerful Ray Pattern Matrices, Linear Algebra Appl. 444, 81-88, 2014.

The first group comprises examples where the acknowledgement doesn’t say what it was meant to say. The explanatory comments are aimed at those whose first language is not English or who are new to the publishing game.

“I would like to thank the unknown referees for their valuable comments.”

This is quite a common usage. Unknown should be replaced by anonymous in order to avoid the interpretation that the referee is someone who is not known in the community.

“I thank the anonymous referees, particularly Dr. J. R. Ockendon, for numerous suggestions and for the source of references.”

A referee is not anonymous if his name is known.

“I am grateful to the referee whose suggestions greatly improved this paper.”

Ambiguous. Were there other referees whose suggestions did not improve the paper? A comma after “referee” would avoid the ambiguity.

“I am also glad about some suggestions of the referee.”

Non-idiomatic and implies that the author did not like some other suggestions of the referee.

“The authors wish to thank the valuable suggestions of the referee.”

It’s the referee who should be thanked, not the referee’s suggestions.

Here are some more unusual acknowledgements. The first, from

Gregory Ammar and Volker Mehrmann, On Hamiltonian and Symplectic Hessenberg Forms, Linear Algebra Appl., 55-72, 1991

reports a speeding ticket:

“We thank Dr. A. Bunse-Gerstner for many helpful discussions (and the German police for a speeding ticket during one discussion). We also thank the referee for several insightful comments.”

What a shame that the discussion did not take place on an unrestricted autobahn.

Sometimes an acknowledgement is about help that has “oiled the wheels”. The authors of

Alan Feldstein and Peter Turner, Overflow, Underflow, and Severe Loss of Significance in Floating-Point Addition and Subtraction, IMA J. Numer. Anal., 6, 241-251, 1986

write

The authors wish to thank Mr. and Mrs. Peter Taplin of the Stone House Hotel, near Hawes, North Yorkshire whose helpful service and friendly hospitality eased the preparation of this paper considerably.

It seems that, thirty years later, the Stone House Hotel is still up and running with the same hosts. Let this serve as an unsponsored recommendation.

The paper

Caleb M. Brown and Donald M. Henderson (2015). A New Horned Dinosaur Reveals Convergent Evolution in Cranial Ornamentation in Ceratopsidae. Current Biology, 25(12), 1641–1648.

contains a marriage proposal in the acknowledgements, which end

“C.M.B. would specifically like to highlight the ongoing and unwavering support of Lorna O’Brien. Lorna, will you marry me?”

Earlier posts in this series can be found at publication peculiarities.

The language Algol 60 did not have complex numbers as a built-in data type, so it was necessary to write routines to implement complex arithmetic. The following sequence of papers appeared in Communications of the ACM in the 1960s and concerns writing an Algol 60 code to evaluate the logarithm of a complex number.

J. R. Herndon (1961). Algorithm 48: Logarithm of a complex number. Comm. ACM, 4(4), 179.

A. P. Relph (1962). Certification of Algorithm 48: Logarithm of a complex number. Comm. ACM, 5(6), 347.

M. L. Johnson and W. Sangren (1962). Remark on Algorithm 48: Logarithm of a complex number. Comm. CACM, 5(7), 391.

D. S. Collens (1964). Remark on remarks on Algorithm 48: Logarithm of a complex number. Comm. ACM, 7(8), 485.

D. S. Collens (1964). Algorithm 243: Logarithm of a complex number: Rewrite of Algorithm 48. Comm. CACM, 7(11), 660.

“Remark on remarks”, “rewrite”—what are the reasons for this sequence of papers?

The first paper, by Herndon, gives a short code (7 lines in total) that uses the arctan function to find the argument of a complex number as . Relph notes that the code fails when the real part is zero and that, because it adds to the , the imaginary part is on the wrong range, which should be for the principal logarithm. Moreover, the original code incorrectly uses log (log to base 10) instead of ln (the natural logarithm).

It would appear that at this time codes were not always run and tested before publication, presumably because of the lack of an available compiler. Indeed Herndon’s paper was published in the April 1961 issues of CACM, and the first Algol 60 compilers had only become available the year before. according to this Wikipedia timeline.

Johnson and Sangren give more discussion about division by zero and obtaining the correct signs.

In his first paper, Collens notes that the Johnson and Sangren code wrongly gives and has a missing minus sign in one statement.

Finally, Collens gives a rewritten algorithm that addresses the previously noted deficiencies. It appears to have been run, since some output is shown.

This sequence of papers from the early days of digital computing emphasizes that even for what might seem to be a trivial problem it is not straightforward to design correct, reliable algorithms and codes.

I am working on logarithms and other multivalued functions of matrices, for which many additional complications are present.

Edward Lorenz is well-known for introducing the Lorenz equations, discovering the Lorenz attractor, and describing the “butterfly effect”. His sequence of papers

E. N. Lorenz (1986). On the existence of a slow manifold. J. Atmos. Sci., 43(15), 1547–1557.

E. N. Lorenz and V. Krishnamurthy (1987). On the nonexistence of a slow manifold. J. Atmos. Sci., 44(20), 2940–2950.

E. N. Lorenz (1992). The slow manifold—What is it? J. Atmos. Sci., 49(24), 2449–2451.

seems to suggest a rather confused line of research!

However, inspection of the papers reveals the reasoning behind the choice of titles. The first paper discusses whether or not a slow manifold exists and shows that this question is nontrivial. The second paper shows that a slow manifold does not exist for one particular model. The third paper shows that the apparent contradiction to the second paper’s result by another author’s 1991 proof of the existence of a slow manifold for the same model can be explained by the use of different definitions of slow manifold.

Here are some contenders for the shortest title (the first and third of these are taken from page 146 of my Handbook of Writing for the Mathematical Sciences, SIAM, 1998, second edition). Note that the following titles are all clickable, even though they are not underlined.

Charles McCarthy, , Israel J. Math. 5(4), 249-271, 1967.

F. Brezzi, L. P. Franca, T. J. R. Hughes and A. Russo, , Comput. Methods Appl. Mech. Engrg. 145(3-4), 329-339, 1997.

Norman Meyers and James Serrin, , Proc. Natl. Acad. Sciences USA 51, 1055-1056, 1964.

Mitchell Feigenbaum and David Mermin, , American Journal of Physics 56, 18-21, 1988.

The last three titles have the virtue of forming a complete sentence with subject, verb and object.

Olivier Ledoit and Michael Wolf, Honey, I Shrunk the Sample Covariance Matrix, J. Portfolio Management 30(4), 110-119, 2004.

The next paper, referring to The Blair Witch Project (1999), uses a photo of Tony Blair to compare different colour maps:

Bernice E. Rogowitz and Alan D. Kalvin, The “Which Blair Project”: A Quick Visual Method for Evaluating Perceptual Color Maps, 183-556, in Proceedings of IEEE Visualization 2001, 2001.

It is quite rare for a title to contain a typo. Here is an example

S. W. Ellacott and E. B. Saff, On Clenshaws’s Method and a Generalisation to Faber Series, Numer. Math., 52, 499-509, 1988.

In the body of the paper (in particular on the last line of the first page) the correct usage “Clenshaw’s” appears.

In the next example “Lambert W” is correctly spelled in the body of the paper, though not in the title:

M. M. Sherrif, N. S. Ravindran and P. Krishnapriya, Stability Analysis For Tumour Growth Model Through the Lambertz W Function, Journal of Advances in Mathematics 7(1), 1140-1146, 2014.

This paper has an incorrect spelling of Riccati:

George E. Trapp, Jr., The Ricatti Equation and the Geometric Mean, pages 437-445, in B. N. Datta, e.d., Linear Algebra and Its Role in Systems Theory, Contemporary Math., 47, 1985.

The next paper has a common grammatical error in the title:

A. A. Gurjar, S. Ladhake and A. Thakare, Analysis Of Acoustic of “OM” Chant To Study It’s Effect on Nervous System, International Journal of Computer Science and Network Security 9, 363-367, 2009.

The original 1942 edition of

Paul Halmos, Finite-Dimensional Vector Spaces, viii+200, Springer-Verlag, 1958.

was titled Finite Dimensional Vector Spaces, without the hyphen. Halmos explained that he became convinced of the need for the hyphen by the time of 1958 edition.

Finally, one should be aware that there can be errors in metadata if not in a paper itself. The title of

B. Wie, H. Weiss and A. Arapostathis, Quaternion Feedback Regulator for Spacecraft Eigenaxis Rotations, Journal of Guidance, Control, and Dynamics 12, 375-380, 1989.

has no typos, but the journal’s metadata at the above link, including the title displayed on the web page, has the typo “quarternion”.

Authors like enumerating things. Here we count to ten in paper titles.

H. F. Baker, The Reciprocation of One Quadric into Another, Proc. Cambridge Philos. Soc. 23, 22-27, 1925.

Donald Knuth, Two Notes on Notation, Amer. Math. Monthly, 99, 403-422, 1992.

Thomas Quinn, Scott Tremaine and Martin Duncan, A Three Million Year Integration of the Earth’s Orbit, Astron. J. 101, 2287-2305, 1991.

K. Appel and W. Haken, Every Planar Map is Four Colorable. Part I: Discharging, Illinois J. Math. 21, 429-490, 1977.

David Anderson, Tom Kilburn: A Tale of Five Computers, Comm. CACM, 57, 35-38, 2014.

Ergin Elmacioglu and Dongwon Lee, On Six Degrees of Separation in DBLP-DB and More, SIGMOD Rec. 34, 33-40, 2005.

Brian McCartin, Seven Deadly Sins of Numerical Computation, Amer. Math. Monthly, 105, 929-941, 1998.

E. C. Berkeley, Eight Hundred People Interested in Mechanical Brains, Amer. Statist., 4, 11-12, 1950.

Desmond Higham, Nine Ways to Implement the Binomial Method for Option Valuation in MATLAB, SIAM Review, 44, 661-677, 2002.

Gian-Carlo Rota, Ten Lessons I Wish I Had Been Taught, Notices Amer. Math. Soc., 44, 22-25, 1997.

As for continuing beyond 10, I will just pick out two specific cases.

Joseph Lee Rodgers and Alan Nicewander, Thirteen Ways to Look at the Correlation Coefficient, Amer. Statist., 42, 59-66, 1988.

Cleve B. Moler and Charles F. Van Loan, Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five years Later, SIAM Review, 45, 3-49, 2003.

This category refers to titles that are looking at a topic from a higher perspective.

Michael Berry, Why Are Special Functions Special?, Physics Today 54, 11-12, 2001.

Barbara Kitchenham, Pearl Brereton, David Budgen, Mark Turner, John Bailey and Stephen Linkman, Systematic Literature Reviews in Software Engineering—A Systematic Literature Review, Information and Software Technology 51, 7-15, 2009.

The final article is somewhat controversial: see The Tears of Donald Knuth.

Martin Campbell-Kelly, The History of the History of Software, IEEE Annals of the History of Computing 29, 40-51, 2007.

Now we are looking for titles that make reference to a Shakespearean play.

R. W. Bemer, Towards Standards for Handwritten Zero and Oh: Much Ado About Nothing (and a Letter), or a Partial Dossier on Distinguishing Between Handwritten Zero and Oh, Comm. ACM 10, 513-518, 1967.

William Kahan, Branch Cuts for Complex Elementary Functions or Much Ado About Nothing’s Sign Bit, in A. Iserles and M. J. D. Powell, eds, The State of the Art in Numerical Analysis, Oxford University Press, 1987, pages 165-211.

Peter Hall, A Comedy of Errors: The Canonical Form for a Stable Characteristic Function, Bull. London Math. Soc. 13, 23-27, 1981

Joel David Hamkins, Destruction or Preservation as You Like It, Annals of Pure and Applied Logic 91, 191-229, 1998

Someone whose titles I have often admired is William (Velvel) Kahan (he has already appeared in the previous section). I particular like his alliterative

William Kahan, Conserving Confluence Curbs Ill-Condition, Technical Report number 6, Computer Science Department, University of California, Berkeley, 1972.

and the pun in

William Kahan and Beresford N. Parlett, Can You Count on Your Calculator?, Memorandum No. UCB/ERL M77/21, Electronics Research Laboratory, College of Engineering, University of California, 1977.

If you know of further interesting titles please add them to the comments below.

The paper

Brian Hayes, Why W?, American Scientist 93, 104-108, 2005,

which is about the Lambert W function, has the remarkable feature that every sentence contains at least one instance of the letter “w” (as the author admits in the final section). There does not appear to be a word for the result of this constrained writing, but it is a kind of opposite of a lipogram: a text in which a certain letter is avoided entirely.

Charles Lindsey was a Senior Lecturer in the Department of Computer Science at the University of Manchester and was one of the designers of the language Algol 68. I took a course on programming languages from him when I was a student. His paper

Charles H. Lindsey, ALGOL 68 with fewer tears, Comput. J. 15 (2), 176-188, 1972

is a syntactically valid Algol 68 program. Nowadays we would call this literate programming!

The paper

Clifford Truesdell, Solutio Generalis et Accurata Problematum Quamplurimorum de Motu Corporum Elasticorum incomprimibilium in Deformationibus valde Magnis, Arch. Rational Mech. Anal. 11, 106-113, 1962

has been described by Ball and James (in The Scientific Life and Influence of Clifford Ambrose Truesdell III) as “perhaps the only serious scientific paper published in Latin in the 20th century”.

A contender for shortest paper is

L. J. Lander and T. R. Parkin, Counterexample to Euler’s Conjecture on Sums of Like Powers, Bull. Amer. Math. Soc. 72, 1079, 1966,

which consists of just two sentences. However, brevity is taken to extremes in the next paper, for which writer’s block led to an empty body:

Dennis Upper, The Unsuccessful Self-Treatment of a Case of “Writer’s Block”, Journal of Applied Behavior Analysis 7, 497, 1974.

This experiment has been successfully replicated:

Geoffrey Molloy, The Unsuccessful Self-Treatment of a Case of “Writer’s Block”: A Replication, Perceptual and Motor Skills 57, 566, 1983,

Robert Didden, Jeff Sigafoos, Mark O’Reilly, Giulio Lancioni and Peter Sturmey, A Multisite Cross-Cultural Replication of Upper’s (1974) Unsuccessful Self-Treatment of Writer’s Block, J. Appl. Behav. Anal. 40, 773, 2007.

Most fields have conventions about the order in which author names appear. The authors of the paper

M. P. Hassell and R. M. May, Aggregation of Predators and Insect Parasites and its Effect on Stability, Journal of Animal Ecology 43, 567-594, 1974

state that “The order of authorship was determined from a twenty-five-game croquet series held at Imperial College Field Station during summer 1973.”

The first word of the first article in the journal Nature was, appropriately, “Nature”:

T. H. Huxley, Nature: Aphorims by Goethe, Nature 1(1), 9-11, 1869.

Occasionally, a paper contains something the authors meant to remove before publication. The originally published version of the paper

Zachary W. Culumber, Christian E. Bautista-Hernández, Scott Monks, Lenin Arias-Rodriguez and Michael Tobler, Variation in Melanism and Female Preference in Proximate but Ecologically Distinct Environments, Ethology 120, 1090-1100, 2014

contained the sentence

Although association preferences documented in our study theoretically could be a consequence of either mating or shoaling preferences in the different female groups investigated (should we cite the crappy Gabor paper here?),

Some time after the paper was published it was updated, with the parenthetical phrase replaced by “(Gabor 1999)”.