This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

Authorship attribution supported by statistical or computational methods has a long history starting from the 19th century and is marked by the seminal study of Mosteller and Wallace (1964) on the authorship of the disputed “Federalist Papers.” During the last decade, this scientific field has been developed substantially, taking advantage of research advances in areas such as machine learning, information retrieval, and natural language processing. The plethora of available electronic texts (e.g., e-mail messages, online forum messages, blogs, source code, etc.) indicates a wide variety of applications of this technology, provided it is able to handle short and noisy text from multiple candidate authors. In this article, a survey of recent advances of the automated approaches to attributing authorship is presented, examining their characteristics for both text representation and text classification. The focus of this survey is on computational requirements and settings rather than on linguistic or literary issues. We also discuss evaluation methodologies and criteria for authorship attribution studies and list open questions that will attract future work in this area. © 2009 Wiley Periodicals, Inc.

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A survey of modern authorship attribution methods

Authorship attribution, the science of inferring characteristics of the author from the characteristics of documents written by that author, is a problem with a long history and a wide range of application. Recent work in "non-traditional" authorship attribution demonstrates the practicality of automatically analyzing documents based on authorial style, but the state of the art is confusing. Analyses are difficult to apply, little is known about type or rate of errors, and few "best practices" are available. In part because of this confusion, the field has perhaps had less uptake and general acceptance than is its due.

This review surveys the history and present state of the discipline, presenting some comparative results when available. It shows, first, that the discipline is quite successful, even in difficult cases involving small documents in unfamiliar and less studied languages; it further analyzes the types of analysis and features used and tries to determine characteristics of well-performing systems, finally formulating these in a set of recommendations for best practices.

Authorship Attribution

With the rapid proliferation of Internet technologies and applications, misuse of online messages for inappropriate or illegal purposes has become a major concern for society. The anonymous nature of online-message distribution makes identity tracing a critical problem. We developed a framework for authorship identification of online messages to address the identity-tracing problem. In this framework, four types of writing-style features (lexical, syntactic, structural, and content-specific features) are extracted and inductive learning algorithms are used to build feature-based classification models to identify authorship of online messages. To examine this framework, we conducted experiments on English and Chinese online-newsgroup messages. We compared the discriminating power of the four types of features and of three classification techniques: decision trees, backpropagation neural networks, and support vector machines. The experimental results showed that the proposed approach was able to identify authors of online messages with satisfactory accuracy of 70 to 95p. All four types of message features contributed to discriminating authors of online messages. Support vector machines outperformed the other two classification techniques in our experiments. The high performance we achieved for both the English and Chinese datasets showed the potential of this approach in a multiple-language context. © 2006 Wiley Periodicals, Inc.

A framework for authorship identification of online messages: Writing-style features and classification techniques

Inference and Disputed Authorship: The Federalist

This paper is a companion to my 'Questions of authorship: attribution and beyond', in which I sketched a new way of using the relative frequencies of the very common words for comparing written texts and testing their likely authorship. The main emphasis of that paper was not on the new procedure but on the broader consequences of our increasing sophistication in making such comparisons and the increasing (although never absolute) reliability of our inferences about authorship. My present objects, accordingly, are to give a more complete account of the procedure itself; to report the outcome of an extensive set of trials; and to consider the strengths and limitations of the new procedure. The procedure offers a simple but comparatively accurate addition to our current methods of distinguishing the most likely author of texts exceeding about 1,500 words in length. It is of even greater value as a method of reducing the field of likely candidates for texts of as little as 100 words in length. Not unexpectedly, it works least well with texts of a genre uncharacteristic of their author and, in one case, with texts far separated in time across a long literary career. Its possible use for other classificatory tasks has not yet been investigated.

‘Delta’: a Measure of Stylistic Difference and a Guide to Likely Authorship

Word-Patterns and Story-Shapes: The Statistical Analysis of Narrative Style

This article describes the operation of two new tests of authorship and offers some results. Both tests rely on controlled contrasts of word-frequency and both exclude the very common words, which have been put to such good use in recent years. One test treats of words used with some consistency by a target-author but more sporadically by others. The second treats of words used sporadically by the target-author but not by most others. (The inclusion of words that some other authors use avoids the strict constraint that has impoverished this form of evidence.) In suitable cases, both tests prove very accurate. The fact that evidence of authorship can be detected in these three distinct frequency-strata helps to explain why such tests should work at all and so encourages the development of even better ones.

All the Way Through: Testing for Authorship in Different Frequency Strata

L'A. intervient a l'occasion de la reception du prix Roberto Busa 2001 qui lui est decerne pour sa contribution dans le domaine de l'informatique et des sciences humaines. Il fait un bilan de son parcours et presente une nouvelle methode d'identification de l'auteur d'un texte. Son interet pour ce domaine de recherche a debute dans les annees 1970, avec l'analyse d'un texte de Jane Austen. Il nous presente aujourd'hui une nouvelle approche basee sur une liste hierarchique des frequences des mots communs a l'ensemble des textes. Il decrit alors les procedures et les resultats de cette methode, en donne quelques developpements possibles pour l'avenir et fait le point sur l'etat de l'art dans ce domaine de la recherche assistee par ordinateur

Questions of Authorship: Attribution and Beyond A Lecture Delivered on the Occasion of the Roberto Busa Award ACH-ALLC 2001, New York

The statistical analysis of literary texts has yielded valuable results, not least when it has treated of the frequency patterns of very common words. But, whereas particular frequency patterns have usually been examined as discrete phenomena, it is possible to correlate the frequency profiles of all the very common words, to subject the resulting correlation matrix to eigen analysis, and to present the results in graphic form. The specimens offered here deal, first, with differences among Jane Austen's characters and, secondly, with differences between authors. The most striking general differences among the authors studied relate to historical eras and authorial gender.

John Burrows

Papers

‘Delta’: a Measure of Stylistic Difference and a Guide to Likely Authorship

Word-Patterns and Story-Shapes: The Statistical Analysis of Narrative Style

All the Way Through: Testing for Authorship in Different Frequency Strata

Questions of Authorship: Attribution and Beyond A Lecture Delivered on the Occasion of the Roberto Busa Award ACH-ALLC 2001, New York

‘An ocean where each kind. . .’: Statistical analysis and some major determinants of literary style