## Publication Peculiarities: Papers

I read a lot of papers. I also glance at many papers in journal contents pages and Google search results. From time to time I notice a paper that has an interesting title, author list, abstract, or some other notable feature. This post is the first in a series collecting such publication peculiarities. It concerns papers with striking features other than the title, author list, or abstract. The rules of the game are that I prefer examples from mathematics and related areas and that I must be able to provide a link to the article in question.

If you know of other good examples, please add them in the comments box at the end of this post.

## The Letter W

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.

## A Computer Program

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!

## Latin

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”.

## Shortest Paper

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.

## Order of Authors

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.”

## First Word

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.

## Remnant

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)”.

Posted in writing | 2 Comments

## Numerical Linear Algebra Group 2014

The Manchester Numerical Linear Algebra group was very active in 2014. This post summarizes what we got up to. Publications are not included here, but many of them can be found on MIMS EPrints under the category Numerical Analysis.

A new venture for several of us this year was to make our software available on GitHub: Deadman, Higham, Relton, Sego, Zhang.

## PhD Students

Three students successfully defended their theses:

Sam and Leo are now postdoctoral Research Associates in the group. Ramaseshan is a Senior Engineer at Arup, working in the Manchester office.

Weijian Zhang joined the group in September as a PhD student working with Nick Higham.

Sam Relton and Mary Aprahamian served as President and Treasurer, respectively, of the Manchester SIAM Student Chapter.

## Postdoctoral Research Associates (PDRAs)

Jennifer Pestana joined the group in January, from Oxford University, to work with Françoise Tisseur.

Javier Perez joined the group in September, to work with Françoise Tisseur.

Tim Butters joined the group in January to work as a postdoctoral Knowledge Transfer Associate with Stefan Guettel and Nick Higham, in a project with Sabisu.

Lijing Lin (2007-2014) left the group in September to take up a Research Associate position in the Faculty of Life Sciences at The University of Manchester.

Amal Khabou (2013-2014) left in September to take up a Maître de conférences position at Université Paris Sud.

Meisam Sharify (2013-2014) left in May to take up a post as Assistant Professor in the Department of Computer Science, Shahid Beheshti University, G.C. Tehran, Iran.

## Presentations

Members of the group gave presentations at the the following conferences and workshops.

IMA Conference on the Mathematical Challenges of Big Data, London, December 16-17, 2014 (Higham).

Structured Numerical Linear and Multilinear Algebra: Analysis, Algorithms and Applications, Kalamata, Greece, September 8-12 2014 (Noferini).

Spectral Theory Workshop to celebrate the 70th birthday of Brian Davies, King’s College London, 30 October 2014 (Tisseur).

4th IMA Conference on Numerical Linear Algebra and Optimisation, Birmingham, September 3-5, 2014 (Aprahamian, Berljafa, Khabou, Pestana, Relton, Strabić, Tisseur).

11th World Congress on Computational Mechanics, Barcelona, 20-25 July 2014 (Kannan).

International Workshop on Operator Theory and Applications, Amsterdam, July 14-18, 2014 (Tisseur).

SIAM Annual Meeting, Chicago, July 7-11, 2014 (Aprahamian, Deadman, Guettel, Lotz, Zhang).

First Joint International Meeting RSME-SCM-SEMA-SIMAI-UMI, Bilbao, June 30-July 4, 2014 (Noferini).

Householder Symposium XIX on Numerical Linear Algebra, Spa, Belgium, June 8-13, 2014 (Deadman, Guettel, Higham, Khabou, Lin, Noferini, Pestana, Taslaman, Tisseur).

10th International Workshop on Accurate Solution of Eigenvalue Problems (IWASEP10), Dubrovnik, Croatia, June 2-5 (Sego, Strabić).

Structured Matrix Days, XLIM, Université de Limoges, France, May 26-27, 2014 (Noferini).

Advances in Numerical Algorithms and High Performance Computing, University College London, April 14-15, 2014 (Deadman, Higham, Relton).

Napier 400th Anniversary Celebrations: Computation in Mathematics Workshop, ICMS, Edinburgh, April 2, 2014 (Higham: Video podcast).

Workshop on Nonlinear Eigenvalue Problems, The University of Manchester, April 23-25, 2014 (organized by Tisseur, Pestana, Kressner and Michiels and attended by the whole group).

Annual Meeting of the International Association of Applied Mathematics and Mechanics, Erlangen, March 10-14, 2014 (Guettel).

International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing March 7-9, 2014 Tsukuba, Japan (Guettel, Tisseur).

2014 SET for BRITAIN exhibition at the House of Commons (Mary Aprahamian presented a poster).

## Conference and Workshop Organization

The group organized three events in Manchester.

Several minisymposia were organized:

## Visitors

Vedran Sego visited the group throughout 2014.

Zhi-Gang Jia from Jiangsu Normal University, China, visited the group August 2013-July 2014.

Philip Gill (UC San Diego) and Margaret Wright (New York University) both visited for two weeks in March.

Jan Papež, a PhD student at the Academy of Sciences of the Czech Republic, Prague, visited for a week in November.

Marcel Schweitzer, a PhD student at the Universit of Wuppertal, visited the group for one week in September 2014.

Vladimir Druskin (Schlumberger-Doll Research Center, Cambridge, USA) visited the group for one week in June 2014.

Daniel Ruprecht (Università della Svizzera Italiana) and Robert Speck (Jülich Supercomputing Centre) visited the group for one week in February 2014.

Massimiliano Fasi, an M.Sc. student at the University of Bologna, Italy, visited for a week in November. He will join the group as a PhD student in September 2015, funded by a University of Manchester President’s Doctoral Scholarship Award.

Caterina Fenu, a PhD student at the University of Cagliari, Italy, visited for a week in November.

## Knowledge Transfer

In The Knowledge Transfer Partnership with Sabisu, involving KTP Associate Tim Butters, Stefan Guettel, Nick Higham, and Jon Shapiro (School of Computer Science), an alarm management system has been developed and launched as a product.

## Recognition and Service

Françoise Tisseur was awarded a Royal Society Wolfson Research Merit Award (2014-2019) to support her work on the numerical solution of nonlinear eigenvalue problems.

Former PDRA Yuji Nakatsukasa (2011-2013) was awarded the Householder Prize 2014 for his PhD thesis “Algorithms and Perturbation Theory for Matrix Eigenvalue Problems and the Singular Value Decomposition” (2011), written at the University of California, Davis.

Nick Higham served on Subpanel 10, Mathematical Sciences, in the Research Excellence Framework (REF) 2014.

Françoise Tisseur served as

• Vice-President of the UK & Republic of Ireland SIAM Section,
• Program Director of the SIAM Activity Group on Linear Algebra,
• Member of the Householder Prize Committee 2014.
Posted in research | 1 Comment

## More Tips on Book and Thesis Writing

Following my earlier post Top Five Tips on Book Writing, here are seven more tips. These apply equally well to writing a thesis.

## 1. Signpost Citations

In academic writing we inevitably include a fair number of citations to entries in the bibliography. In a book, even more so than in a paper, we do not want the reader to have to turn to the bibliography every time a citation is reached in order to understand what is being cited. So a sentence such as

The matrix logarithm appears in a wide variety of applications
[2], [8], [14].


The matrix logarithm appears in a wide variety of applications,
such as reduced-order models [2], image registration [8],
and computer animations [14].


Versions of the algorithm have been developed by several authors
[1], [3], [7].


I would write

Versions of the algorithm have been developed by Chester [1],
Hughes [3, Sec. 2], and Smith and Jones [7].


Even that example lacks information about the date of publication. In my books I have used my own version of the $\LaTeX$ \cite macro that allows me to include the year:

Versions of the algorithm have been developed by Baker and
Chester [1, 2006], Hughes [3, 2001, Sec. 2],
and Smith and Jones [7, 2004].


The macro is

\def\ycite[#1#2#3#4#5]#6{\cite[$\mit{#1#2#3#4}$#5]{#6}}


(which puts the year in the distinctive math italic font) and the first two citations in the previous sentence would be typed as \ycite[2006]{bach06} and \ycite[2001, Sec.~2]{hugh01}.

## 2. Produce a Good Index

A good index is essential, since it is the main way that readers can find content. The vast majority of books that I read have an inadequate index, as I have noted in my post A Call for Better Indexes at SIAM Blogs. Usually the index is too small. Occasionally the index is of about right length but is flawed. The main problems are

• Items that should be indexed are absent from the index.
• An index entry does not point to all (significant) occurrences of the term.
• Related entries are not grouped properly.

Advice on producing an index can be found in Section 13.4 of my Handbook of Writing for the Mathematical Sciences and various other sources (try a Google search), and I intend to wrote a post on indexing soon.

$\LaTeX$, through its \index command, used in conjunction with the MakeIndex program, provides an excellent way to produce an index.

## 3. Use the Backref $\LaTeX$ package

Backref.sty is a $\LaTeX$ package that adds to each bibliography entry the text “cited on pages” and then lists the pages on which that item was cited. It costs nothing to use it, but it adds great value to the bibliography, which then functions as a separate index into the book. I started using backref with my book MATLAB Guide (2005). To a large extent it removes the need for an author index, and if I do a third edition of Accuracy and Stability of Numerical Algorithms I will probably use backref and drop the author index.

The backref package is not widely used, though a number of SIAM books have made use of it.

For a book provided in PDF form, hyperlinks from an equation reference to the equation, a citation to the bibliography entry, a URL to the web page, and so on, are a great aid to the reader. In $\LaTeX$ obtaining the hyperlinks is usually just a matter of adding \usepackage{hyperref} in the pre-amble.

## 5. Make Figures Readable and Consistent

It’s very easy nowadays to produce figures containing plots of functions or computational results. But it’s much harder to produce a set of figures that

• are clearly legible,
• have labels, legends, and annotations that are of similar size to the main text,
• are consistent in format (axes, line thicknesses etc.)

All too often I see figures in which the text is so small that I cannot read it at a normal reading distance. My experience (which is mainly with MATLAB, and with the $\LaTeX$ packages TikZ and PGFplots) is that it is a time-consuming process to produce high quality plots. But it is worth the effort.

## 6. Use Short Captions in the List of Figures/Tables

The general form of the $\LaTeX$ caption command is \caption[short caption]{long caption}. The short caption is what is printed in the List of Figures or List of Tables at the front of the book, if you are printing those lists. The short caption will be read in isolation from the figure or table so it should omit all unnecessary detail, such as explaining line or marker types. All too often, the short and long captions are the same, resulting in unnecessarily long and detailed lists of figures or tables.

Here is an example (simplified, with other macros removed) of the caption from a figure in my book Functions of Matrices:

\caption[Illustration of condition (b) of Theorem~11.4.]%
{Illustration of condition (b) of Theorem~11.4,
which requires every eigenvalue of $B$ to lie in the
open half-plane (shaded) of the corresponding eigenvalue
of $A^{1/2}$.}


## 7. Make the Header Contain the Section and Chapter Number and Title

I like to know where I am when I am reading a book, so I expect the page headers to tell me the section number and chapter number, and preferably their titles as well. I cannot understand why some books omit this information. Without it, phrases such as “as discussed in the previous chapter” become harder to follow up, and searching for a particular section is more difficult.

## Emacs and Org Mode: What People are Saying

For a couple of years I’ve been collecting tweets about Emacs and Org mode. With the Twitter app’s new ability to provide code to embed tweets I decided to create a post listing the collection. If you are not an existing user of Emacs or Org mode these tweets should give you a feel for whether you might want to explore further. If you are already a convert then many of the sentiments expressed here will be familiar. Note that the links and hashtags below are clickable. (Like all of this Blog, this post was written in Org mode.)

## Hans Schneider (1927–2014)

I first met Hans in 1984 at the Gatlinburg meeting IX in Waterloo, Canada, at which time I was a PhD student. When I discussed my work on matrix square roots with him he recalled a 1966 paper by Culver “On the Existence and Uniqueness of the Real Logarithm of a Matrix”, of which I was unaware. By the time I returned to Manchester, after visiting Stanford for a few weeks, a copy of the paper was waiting for me, with an explanation of how the results of that paper could be adapted to analyze real square roots of a real matrix.

As chair of the 2002 Householder symposium XV in Peebles, Scotland, I was delighted to invite Hans to deliver the after-dinner speech. (The Gatlinburg meeting was renamed the Householder symposium in 1990, in honour of Alston Householder, who organized the early meetings.) Having Hans speak was particularly appropriate as he had studied at the nearby University of Edinburgh. I believe this was the last Householder Symposium that Hans attended.

I kept a copy of my introduction of Hans at the banquet. It seems appropriate to reproduce it here.

Ladies and gentlemen, our after-dinner speaker this evening is Hans Schneider, who is James Joseph Sylvester Emeritus Professor of Mathematics at the University of Wisconsin.

There’s an old definition that an intellectual is somebody who can hear the William Tell overture and not think of the Lone Ranger. I don’t think there are many people who can hear the term “linear algebra and its applications” and not think of Hans Schneider. After all, Hans has been Editor-in-Chief of the journal of that name since 1972, and developed it into a major mathematics journal. Hans was also instrumental in the foundation of the International Linear Algebra Society, of which he served as President from 1987 to 1996.

Some of you may be surprised to know that Hans has a strong connection with Scotland. He studied here and received his Ph.D. at Edinburgh University in 1952 under the famous Alexander Craig Aitken. I understand that Aitken gave him two words of advice: “Read Frobenius!”.

Well, it’s a real pleasure to introduce Hans and to ask him to speak on “The Debt Linear Algebra Owes Helmut Wielandt”.

The reference to Frobenius is apposite, given my original conversation with Hans since, as I have only recently discovered, Frobenius gave one of the earliest proofs of the existence of matrix square roots in 1896. That result, and much more about Frobenius’s wide range of contributions to mathematics is discussed in a 2013 book by Thomas Hawkins, The Mathematics of Frobenius in Context. A Journey Through 18th to 20th Century Mathematics (of which my copy has the rare error of having the odd pages on the left, rather than the right, of each two-page spread).

The photo below was taken during Hans’s after-dinner speech (more photos from the meeting are available in this gallery).

Posted in people | | 1 Comment

## Top Five Tips on Book Writing

I’ve written four books, and am currently writing and editing a fifth (The Princeton Companion to Applied Mathematics). I am also an editor of two SIAM book series and chair the SIAM Book Committee. Based on this experience here are my top five tips about writing an (academic) book. These cover high level issues. In a subsequent post I will give some more specific tips relating to writing and typesetting a book or thesis.

Book publishers ask prospective authors to complete a proposal form, one part of which asks who is the audience for the book. This is a crucial question that should be answered before a book is written, as the answer will influence the book in many ways.

As an example, you might be contemplating writing a book about the numerical solution of a certain class of equations and intend to include computer code. Your audience might be

• readers in mathematics or a related subject who wish to learn about numerical methods for solving the equations and are most concerned with the theory or algorithms,
• readers whose primary interest is in solving the equations and who wish to have lots of sample code that they can run,
• readers in the previous class who also need to learn the language in which the examples are written.

The choice of content, and how the book is presented, will depend very much on which audience you are writing for.

## 2. Revise, Revise, Revise

Just like a paper, a book draft needs to go through multiple revisions, and you must not be afraid to make major changes at any stage. You may receive constructive criticisms from reviewers of your book proposal, but reviewers may not have time to read the complete manuscript carefully and you should not assume that they have found all errors, typos, and areas for improvement.

## 3. Take Time to Choose Your Publisher

Given the huge effort that goes into writing a book you should take the time to find the right publisher. Discuss your book with several publishers and compare what they can offer in the way of

• format (hardback, paperback, electronic) and, if more than one format, the timescale in which each is made available,
• if the publisher has branches in more than one country, how price and publication schedule will differ between the countries,
• whether you are allowed to make a PDF version of the book freely available on your website, if this interests you,
• willingness to allow you to choose the book design (page size, font, cover, etc.),
• use of colour (which increases the cost),
• royalties (including a possible advance),
• pricing,
• the publisher’s policy on translations,
• copy editing (see the next section),
• time from delivering a completed manuscript to publication,
• marketing (will the book be advertised at all, and if so how?), and
• how long your book is guaranteed to stay in print.

It is perfectly acceptable to submit a proposal to several publishers and see what they are willing to offer. However, it is only fair and proper to make clear to a publisher that you are talking to other publishers and, once you have set the wheels of a publisher’s review process in motion, to wait for an offer before making a decision to go with another publisher.

I am always surprised when I hear of authors who approach only one publisher, or who go with the first publisher to express an interest in the book. As in many contexts, it is best to make an informed choice from among the available options.

## 4. Ensure Your Book is Copy Edited

If you are an inexperienced writer, or your first language is not English, the benefits of copy editing are obvious. But even an experienced author finds it virtually impossible to think about all the little details that a copy editor will check for, such as correctness and consistency of spelling, notation, punctuation (notably the serial comma), citations, and references. For example, I sometimes mix US and UK spellings and don’t want to have to worry about finding and correcting my occasional lapses. A good copy editor will also suggest minor improvements of the text that might escape even the best writers.

Unfortunately, not all publishers copy edit all books nowadays. Notable exceptions that always do copy edit (and, as I know from experience, work to the highest standards in every respect) are Princeton University Press and SIAM.

If your publisher has a Style Manual it obviously makes sense to follow its guidelines in order to minimize changes at the copy editing stage. Here is a link to the SIAM Style Manual.

## 5. Think Twice Before Co-Authoring a Book

It might seem an attractive proposition to share authorship of a book: surely having $n$ co-authors reduces the work by a factor $1/n$? Unfortunately it often does not work out like that, despite best intentions. In fact, $n$ co-authors can easily take $n$ times as long to write a book as any one of them would. One of the biggest difficulties is timescale: one author may be willing and able to finish a book in a year but another may need twice that period to make their contribution. Indeed it is rare for the co-authors to be matched in the amount of effort they can put into the book; this is clearly problematic if initial expectations are not realized. Other potential problems are potentially differing opinions on content, notation, level, length, and almost anything else associated with a book.

Successful authorship teams often have a track record of co-authoring papers together. Although it is no guarantee that a much larger book project will run smoothly, experience with writing papers together will at least have given a good indication of where disagreements are likely to lie.

Posted in books, writing | | 1 Comment

## The Spotlight Factor

In my Handbook of Writing for the Mathematical Sciences I described the spotlight factor, originally introduced by Tompa in 1989. The spotlight factor is defined for the first author of a paper in which there are $n$ authors listed alphabetically, and it is assumed that the paper is from a community where it is the custom to order authors alphabetically.

The spotlight factor is the probability that if $n-1$ coauthors are chosen independently at random they will all have surnames later in the alphabet than the first author. This definition is not precise, since it is not clear what is the sample space of all possible names, so it is better to regard the spotlight factor as being defined by the formula given by Tompa, which is implemented in the MATLAB function below.

The smallest spotlight factor I have found is the value 0.0244 for Zielinski, for the paper

Pawel Zielinski and Krystyna Zietak, The Polar Decomposition—Properties, Applications and Algorithms, Applied Mathematics, Ann. Pol. Math. Soc. 38, 23-49, 1995

This beats the best factor of 0.0251 reported by Tompa in a 1990 follow-up paper.

Can you do better?

Here is a MATLAB M-file to compute the spotlight factor, preceded by an example of its usage:

>> spotlight('zielinski',1)
ans =
2.4414e-02

function s = spotlight(x, k)
%SPOTLIGHT   Tompa's spotlight factor of authorship.
%   SPOTLIGHT(X, K) is the spotlight factor for the author whose
%   last name is specified in the string X, with K coauthors.
%   Mixed upper and lower case can be used.
%   Smaller spotlight factors correspond to rarer events.

%   Reference:
%   Martin Tompa, Figures of Merit, SIGACT News 20 (1), 62-71, 1989

if ~ischar(x), error('First argument must be a string.'), end
if nargin < 2, error('Must give two arguments.'), end

x = double(upper(x)) - double('A') + 1;
x( find(x < 0 | x > 26) ) = 0;  % Handle punctuation and spaces.

s = 0;

% Ideally use Horner's rule, but the following is clearer.

for i=1:length(x)
t = x(i);
s = s + t/27^i;
end

s = (1 - s)^k;

Posted in writing | Tagged | 3 Comments

## The Life of James Joseph Sylvester

Following my previous post about the James Joseph Sylvester Bicentenary and my article Sylvester’s Influence on Applied Mathematics I now give a brief, very selective, overview of Sylvester’s life. Some of this material was used in an after-dinner speech that I gave at the Householder Symposium XIX on Numerical Linear Algebra at Spa, Belgium on June 11, 2014.

I’ve drawn on many sources for this post, but the most important is the 2006 biography by Karen Parshall, James Joseph Sylvester. Jewish Mathematician in a Victorian World. That title brings out two key points: that Sylvester was Jewish, which hindered his career, as we will see, and that he lived much of his life in Victorian England, when almost everything that today we take for granted when doing our research did not exist.

## Thumbnail Sketch of The Man

Sylvester was born in London in 1814. He was short, mercurial, absent-minded, temperamental, fluent in French, German, Italian, Latin and Greek, and loved poetry but was not very good at it. He was a man of remarkable tenacity, as his career on both sides of the Atlantic shows.

## Career Outline

I’ll give a brief outline of Sylvester’s unusual career, with its many ups and downs, then go on to discuss some specific events in his life.

### First Spell in UK

• Sylvester was a student at University College London (UCL) under De Morgan, age 14. He was withdrawn by his family after attempting to stab a fellow pupil.
• He was a student at Cambridge, but was not able to take the degree because he was Jewish.
• He held the chair of natural philosophy at University College London (UCL) for three years.

### First Sojourn in USA

Sylvester became Professor of Mathematics at the University of Virginia in 1841. He left after four months after an altercation with an unruly student, because he was felt that the faculty did not back him up in a subsequent inquiry.

While in New York he applied for a position at Columbia University. According to R. L. Cooke (quoted in James Joseph Sylvester. Life and Work in Letters)

After leaving Virginia he sought a position at Columbia University, with a recommendation from one of America’s leading scientists, Joseph Henry. In a wonderful irony … the selection committee informed him that his rejection was in no way connected with the fact that he was British, only the fact that he was Jewish.

### Rest of Career (age 29–).

• Sylvester Worked for the next decade as an actuary for the Equity and Law Life Assurance Society in London and trained for the Bar. He founded the Institute of Actuaries. This is when he met Cayley, who became his best friend. For this ten-year period he was doing mathematics in his spare time.
• He was appointed Chair at the Royal Military Academy, Woolwich and spent 15 years there.
• He was appointed Chair at the newly founded Johns Hopkins University, Baltimore, at the age of 61. He negotiated a salary of $5000 payable in gold, plus an annual housing allowance of$1000 also payable in gold.
• His final position was as the Savilian Professor of Geometry at New College, Oxford in 1883, which he took up at the age of 69.

## The Neologist

Sylvester introduced many terms that are still in use today, including matrix (1850), canonical form (1851), Hessian (1851), and Jacobian (1852). Another notable example is the term latent root, which Sylvester introduced in 1883, with two charming similes:

“It will be convenient to introduce here a notion (which plays a conspicuous part in my new theory of multiple algebra), namely that of the latent roots of a matrix—latent in a somewhat similar sense as vapour may be said to be latent in water or smoke in a tobacco-leaf.”

The term has fallen out of use in linear algebra and matrix theory, but it can still be found in use through “the latent root criterion” in, for example (to pick two articles found with a Google search) Differentiating with brand personality in economy hotel segment in Journal of Vacation Marketing (2014) and GHOSTS: A travel barrier to tourism recovery in Annals of tourism research (2011).

## Editor

Sylvester did a great deal of editorial work. He was an editor of the Quarterly Journal of Mathematics for 23 years. He founded the American Journal of Mathematics in 1878 when he was at Johns Hopkins University. This was the first mathematics research journal in the USA, and indeed Sylvester set up the first mathematics research department in the country. As Editor-in-Chief he experienced some of the problems that subsequent journal editors have suffered from.

• He had to work very hard to secure high quality contributions, e.g., from his friend Cayley and from students and colleagues at Johns Hopkins, in addition to his own papers.
• He solicited Alfred Kempe’s proof of the four color theorem. After Sylvester had accepted the paper his managing editor, William Story, realized there was a gap in the reasoning, due to overlooked cases, and wrote a note the accompany the paper in which he unsuccessfully tried to patch the proof. This all happened while Sylvester was in England and he was very unhappy with the incident.

## Author

Even though Sylvester was an editor himself, he was also the author from hell! He was notorious for what his biographer Parshall calls “an impatience with bibliographic research”—something that led him into disputes with other mathematicians.

MacFarlane states that

Sylvester never wrote a paper without foot-notes, appendices, supplements; and the alterations and corrections in his proofs were such that the printers found their task well-nigh impossible. … Sylvester read only what had an immediate bearing on his own researches, and did little, if any, work as a referee.

The title of one particular paper illustrates this point:

J. J. Sylvester, Explanation of the Coincidence of a Theorem Given by Mr
Sylvester in the December Number of This Journal, With One Stated by
Professor Donkin in the June Number of the Same, Philosophical Magazine
(Fourth Series) 1, 44-46, 1851

## Secular Equation Paper

Out of Sylvester’s hundreds of papers, one in particular stands out as notable to me: “On the Equation to the Secular Inequalities in the Planetary Theory”, Philosophical Magazine 16, 267-269, 1883, for the following reasons.

• The title has virtually nothing to do with the paper.
• This is the paper in which Sylvester defines the term latent roots—but as if a totally new concept, even though the concept of matrix eigenvalue was already known.
• He states a theorem about a sum of products of latent roots of a product $AB$ being expressible in terms of sums of products of minors of $A$ and $B$.
• He gives the first general definition of function of a matrix (later refined by Buchheim).
• He discusses the special case of $p$th roots.

The paper is short (3 pages), no proper introduction is given to these concepts, and no proofs are given. In short, a brilliant but infuriating paper!

## Baltimore Summer

In these days of ubiquitous air conditioning it is interesting to note one of the things that made it difficult for Sylvester to do research. Parshall writes, of Sylvester in Baltimore,

“He could not concentrate on his research on matrices in the debilitating summer heat and humidity”.

## Teaching

Sylvester’s enthusiasm for matrices is illustrated by his attempt to teach the theory of substitutions out of a new book by Netto. Sylvester

“lectured about three times, following the text closely and stopping sharp at the end of the hour. Then he began to think about matrices again. I must give one lecture a week on those,’ he said. He could not confine himself to the hour, nor to the one lecture a week. Two weeks were passed, and Netto was forgotten entirely and never mentioned again.” (Parshall, p. 271, quoting Ellery W. Davis).

Compare this with the following quote about E. T. Bell (famous for his book Men of Mathematics, 1937), from Constance Reid’s book about Bell:

Bell’s method of teaching was to read a sentence aloud and announce that he didn’t believe it. By the time we students convinced him that it was true,’ concedes Highberg, we pretty well understood it ourselves.’

## Inaugural Lecture at Oxford, 12 December 1885

There are many ways in which we are more fortunate today than mathematicians of Sylvester’s time. But there were some advantages to those times. From his inaugural lecture, published as On the Method of Reciprocants as Containing an Exhaustive Theory of the Singularities of Curves (Nature, 1886)

It is now two years and seven days since a message by the Atlantic cable containing the single word “elected” reached me in Baltimore informing me that I had been appointed Savilian Professor of Geometry in Oxford, so that for three weeks I was in the unique position of filling the post and drawing the pay of Professor of Mathematics in each of two Universities:

## Obstinacy

Emile Picard recounted how Sylvester, on a visit to Paris, asked him if in six weeks he could learn the theory of elliptic functions. Picard said yes, so Sylvester asked if a young geometer could be assigned to give him lessons several times per week. This began, but from the second lesson reciprocants and matrices started to compete with elliptic functions and in the ensuing several lessons Sylvester taught the young geometer about his latest research and they remained on that topic.

## What Can We Learn from Sylvester’s Life?

If I had to draw two pieces of advice from Sylvester’s life story I would choose the following.

• You are never too old to take on a major challenge (he took up the chair at Johns Hopkins University at the age of 61).
• If you want to be remembered, define some new terms and have some theorems named after you!

## Typewriter Art

In 1981 my mother showed me a magazine (Woman’s Realm) that had instructions for producing on a typewriter a portrait of Prince Charles. The instructions had been designed by Bob Neill, who had worked out how represent a photograph of Prince Charles as a 100-by-79 grid of characters, choosing the density of each character appropriately and exploiting the facility of a typewriter to issue a carriage return without line feed and thereby overwrite one character with another. The instructions looked like

(6) 26G 16@ 1& 36G
(6a) 22sp 2. 1: 95 1& 15 1& 3S 2& 3: 1.

which say that on the 6th line you should type the letter G 26 times followed by 16 @ symbols, etc., then overwrite the line with 22 spaces, 2 full stops, etc.

This is an example of ASCII art, though ASCII art does not usually involve overwriting characters.

At the time I had a Commodore Pet microcomputer and it struck me that the painstaking process of typing the image would be better turned into a computer program. Once written and debugged the program could be used to print multiple copies of the image. By switching the data set the program could be used to print other photos. So I wrote a program in Commodore Basic that printed the image to a Commodore 4022 dot matrix printer.

I sent the program to Bob. He liked it and printed the program in an appendix to his 1982 book Bob Neill’s Book of Typewriter Art (With Special Computer Programme). That book contains instructions for typing 20 different images, including other members of the royal family, Elvis Presley and Telly Savalas (the actor who played Kojak in the TV series of the same name, which was popular at the time), and various animals,. Bob Neill’s Second Book of Typewriter Art was published in 1984, which reprinted my original program. It included further celebrities such as Adam Ant, Benny from Crossroads, “J.R.” from Dallas and Barry Manilow

I recently came across some articles describing Bob’s work, including one by his daughter, Barbara, one by Lori Emerson that includes a PDF scan of the first book, and an article The Lost Ancestors of ASCII Art. The latter pointed me to a recently published book Typewriter Art: A Modern Anthology. This resurgence of interest in typewriter art prompted me to look again at my code.

I had revisited my original 1982 Basic code later in the 1980s, converting it to GW-Basic so it would run on IBM PCs with Epson printers. I had also added the data for The Tabby Cat from Bob’s second book. Here is an extract from the code, complete with GOTOs and GOSUBs (GW-Basic had few structured programming features).

10 REM TYPEART.BAS
20 REM Program by Nick Higham 1982 (Commodore Basic),
30 REM and 1988 (GW-Basic/Turbo Basic).  (c) N.J. Higham 1982, 1988.
40 REM Designs by Bob Neill.  (c) A.R. Neill 1982, 1984.
...
530 REM -----------------------------
540 REM ROUTINE TO PRINT OUT DATABASE
550 REM -----------------------------
560 DEV$= "LPT"+PP$+":"
570 OPEN DEV$FOR OUTPUT AS #1 580 PRINT #1, RESET.CODE$
590 WIDTH #1,255 ' this stops basic inserting unwanted carriage returns
600 GOSUB  800
610 L$="" 620 GOSUB 700:IF A$="/" THEN PRINT#1, NORMAL.LFEED$+L$: GOTO 610
630 IF A$="-" THEN PRINT#1, ZERO.LFEED$;L$: GOTO 610 640 A=ASC(A$):IF A>47 AND A<58 THEN A=A-48: GOTO 660
650 L$=L$+A$: GOTO 620 660 GOSUB 700:B=ASC(A$):IF B>47 AND B<58 THEN A=10*A+B-48: GOSUB 700
670 FOR I=1 TO A:L$=L$+A$:NEXT: GOTO 620 680 ' 690 REM -- SUBROUTINE TO TAKE NEXT CHARACTER FROM Z$
700 A$=MID$(Z$,P,1):P=P+1: IF A$<>" "  AND A$<>"" THEN 730 710 IF P>Z THEN GOSUB 800 720 GOTO 700 730 IF A$="]" THEN A$=" " 740 IF A$="#" THEN A$=CHR$(34)
750 IF A$="^" THEN A$=":"
760 IF P>Z THEN GOSUB 800
770 RETURN
780 '
790 REM -- SUBROUTINE TO READ NEXT LUMP OF DATA
800 READ Z$:Z=LEN(Z$):P=1
810 IF Z$="PAUSE" THEN FOR D=1 TO 20000:NEXT: GOTO 800 820 IF Z$="FINISH" THEN PRINT #1, CHR$(12)+RESET.CODE$: CLOSE #1:END
830 RETURN
840 '
850 REM -------------------------------------
860 REM * DATABASE1 - H.R.H. PRINCE CHARLES *
870 REM -------------------------------------
880 '
890 DATA "H.R.H. Prince Charles"
900 DATA  79G/79G/79G/79G
910 DATA  /79G-25]2.2^2&^L2^2&3^2.
920 DATA /26G16@&36G-22]2.^9]&S&3S2&3^.
930 DATA /22G23@34G-20].^10&]3&^6Y2C&^.
...
4710 '
4720 REM -- EXPLANATION OF DATA --
4730 REM / MEANS NEWLINE
4740 REM - MEANS CONTINUATION LINE
4750 REM 29G MEANS PRINT 29 LETTER G'S.
4760 REM @ MEANS PRINT ONE @ CHARACTER.
4770 REM CHARACTERS : " AND 'SPACE'
4780 REM ARE REPRESENTED BY ^ # AND ]
4790 REM IN THE DATA STATEMENTS.
4800 REM ALL OTHER CHARACTERS ARE
4810 REM PRINTED OUT AS THEMSELVES.
`

The full code is available, along with documentation.

Like typewriters, dot matrix printers could carry out a carriage return without line feed. Today’s inkjet and laser printers cannot do that. I pose a challenge:

convert the program to a modern language (MATLAB or Python are natural choices) and modify it to render the images in some appropriate format.

## References

• A. R. Neill. Bob Neill’s Book of Typewriter Art (With Special Computer Programme). The Weavers Press, 4 Weavers Cottages, Goudhurst, Kent, 1982, 176 pp. ISBN 0 946017 01 8.
• A. R. Neill. Bob Neill’s Second Book of Typewriter Art. The Weavers Press, 4 Weavers Cottages, Goudhurst, Kent, 1984. ISBN 0 946017 02 6.
Posted in software | Tagged , | 4 Comments

## James Joseph Sylvester (1814–1897) Bicentenary

This year (or more precisely September 3, 2014) is the bicentenary of the birth of James Joseph Sylvester, FRS, a prolific 19th century mathematician who led an eventful life, holding positions at five academic institutions, two of them in the USA.

My article Sylvester’s Influence on Applied Mathematics published in the August 2014 issue of Mathematics Today explains how Sylvester’s work continues to have a strong influence on mathematics. A version of the article with an extended bibliography containing additional historical references is available as a MIMS EPrint.

In the article I discuss how

• Many mathematical terms coined by Sylvester are still in use today, such as the words “matrix” and “Jacobian”.
• The Sylvester equation $AX + XB = C$ and the quadratic matrix equation $AX^2 + BX + C = 0$ that he studied have many modern applications and are the subject of ongoing research.
• Sylvester’s law of inertia, as taught in undergraduate linear algebra courses, continues to be a useful tool.
• Sylvester gave the first definition of a function of a matrix, the study of which has in recent years has become a very active area of research.
• Sylvester’s resultant matrix, which provides information about the common roots of two polynomials, has important applications in computational geometry and symbolic algebra.

Sylvester’s collected works, totalling almost 3000 pages, are freely available online and are well worth perusing: Volume 1, Volume 2, Volume 3, Volume 4.

In a subsequent post I will write about Sylvester’s life.