Other reviewers, both academics and nonacademics, have quite forcefully deprecated his use of ideas without context, the irrelevancy of various sections, an unreadably poor organization, and a purposely opaque stream-of-consciousness that prohibits understand [sic] rather than encourages it.… Others consider the work to be profound, insightful and innovative, heaping emoluments which, as Harris himself notes, can be found on the back cover of the book itself. They commend the author for providing a kaleidoscopic lens into the social and theoretical implications of mathematics itself.
Rather than declaring the correctness of either of these polarized viewpoints, perhaps I would offer the possibility that all of them are correct, but that the perspectives say just as much about the reader than the author himself.… Harris’s work may appeal more to readers who enjoy a more impressionistic approach than those who prefer a more direct, linear engagement.
From the review by Stanley Chang in Society, August 2018
“This book appeals to contemporary academic thought and culture. It is engaging and provocative, challenging and deconstructing the usual narratives of the discipline. Harris describes mathematical research as not so much about solving problems but as challenging perspectives and raising more questions. And his book surely does so.”
But after an unusually close reading, the reviewer concludes:
“Harris’s Romantic ideal is appealing. It provides an individual authentic ity and seeming purpose, while still allowing individuality and freedom. One’s imagination can roam free without being bound to the necessities of existence. It is a life which emphasizes dignity over importance. Unfortunately, it ultimately lacks purpose and responsibility. It may be part of human flourishing, but Harris may fall prey to the same critiques he makes of philosophers. The actual practice of mathematicians may not line up with his claims. Being human, mathematicians’ desires often go beyond noble ones.” (my emphasis)
From the extended review by Jeremy Scott Case in the Summer 2017 issue of Christian Scholars’ Review
“Many mathematicians succumb to the temptation to parade their non-mathematical learning (I plead guilty) but I don’t think I’ve ever come across so unchecked a proliferation of references before.… If you can read past the authorial noise there is plenty here that is illuminating and thought-provoking; I particularly enjoyed Harris’s distinguishing between four different usages of inverted commas, and his chapter on what constitutes a “trick”(usage 3). It is also modestly priced. However, there are other books currently available that offer similar insights.”
From the review by Owen Toller in the Mathematical Gazette, 14 March 2016.
Winner of the 2016 PROSE Award in Mathematics, Association of American Publishers
One of Choice‘s Outstanding Academic Titles for 2015 (list behind paywall)
[Mathematics without Apologies] is rambling, sardonic (the term “fuck-you money” appears in the index), and witty. It contains fascinating literary digressions, such as an analysis of the occult mathematical structure of Thomas Pynchon’s novels, and lovely little interludes on elementary math, inspired by Harris’s gallant attempt to explain number theory to a British actress at a Manhattan dinner party.… The book takes an intimate look at the deepest developments in contemporary mathematics, especially the visionary work of the recently deceased Alexander Grothendieck. And it successfully conveys what Harris calls the “pathos” of the mathematician’s calling.
From the review by Jim Holt in The New York Review of Books, December 3, 2015
Mathematics without apologies is a wide-ranging and significant work of cultural criticism.… While his answers typically fall short of his provocations, Harris nonetheless conjures a fruitful array of suggestive and challenging interventions that richly reward the reader who brings the background, curiosity, and patience to follow them.… Playful, erudite, probing, and difficult, Mathematics without apologies is not an ordinary contribution to any of the familiar genres of writing about mathematics that fill Mathematical Reviews. For better and occasionally for worse, Harris’s unusual approach makes mathematics out to be a discipline at once pervasive and elusive, superficially graspable yet impossible to hold in place: in a word, problematic.
From the review by Michael J. Barany in Mathematical Reviews (MathSciNet)
It is high time for Michael Harris’s book, mathematics without apologies.…By mixing memory and desire with mathematics, Harris has provided fresh responses to all the standard questions… I learned something new on almost every page.
From the review by Avner Ash in Harvard Magazine, September-October 2015
This book is a rich tapestry interweaving various aspects of culture and tradition–social, economic, religious, aesthetic–in an attempt to explicate the three basic philosophical questions underlying mathematics as a human endeavor: the What, Why and How of it. However, the feel of the book is far from being philosophically heavy and didactic.… A reader hoping for clear-cut answers to such philosophical questions will not find them in this book. What she or he will find is a thoroughly enjoyable, at times refreshingly irreverent, account of a ‘proof by demonstration’: ‘See this is what it is’ by pointing to how actual practitioners do it.…
From the review by Swami Vidyanathananda in Prabuddha Bharata, July 2015
This book is an addition to the genre of insider-reports on the mathematical life written by distinguished mathematicians. It’s much more than that, though, because Michael Harris is more than a mathematician; he is a Parisian intellectual. His suspicion of high-falutin’ talk might cause him to resist that title, but he makes good jokes about Lacan, explores philosophical themes through literary analysis, treats popular culture as seriously as he does high culture, fills his book with references and allusions, argues by telling stories, reflects on the narrative conventions of those stories and is deeply suspicious of high-falutin’ talk. If it walks like a duck and playfully explores the motives hidden beneath highly serious quacking like a duck, it’s a duck. What must be maddening for all the other Parisian intellectuals is that he does it rather well.
from the review by Brendan Larvor in the London Mathematical Society Newsletter
This extraordinary, extravagant Apologia pro Vita Sua—the title more deliberately echoes G. H. Hardy’s renowned 1940 memoir A Mathematician’s Apology—heads off in many directions and is all the more admirable for it. … the work offers erudition, panache, and an intriguing authorial voice.… Harris is polyglot, deeply learned. Threading through his remarkable book, unifying it, is Hardy’s lament regarding whether a pure mathematician can make a claim that the vocation has a philosophically “useful” purpose. Harris’s reply is multivalent, persuasive, and profound. A book to be read and then read again.
from the review by M. Schiff in Choice (July 2015)
Although applied mathematics is discussed at some places, mathematics in this book is mainly understood as pure mathematics. But above all, this is a very broad approach to human culture as seen by a mathematician. More than a systematic exposition and demonstration of clear and well defined positions, it is a collection of etches, and sketches, i.e., portraits forming an exhibition, evoking the life of a mathematician living in a social, cultural, philosophical, and historical context. The erudition displayed by Harris in this book is amazing. It’s not easy reading but the satisfaction it gives is more than rewarding.
from the review on Adhemar Bultheel’s blog (May 18, 2015)
…a refreshing look into a mysterious field; for me, large swaths of the book were mysterious because the mathematics was dense, but that’s the “problematic” part of the subtitle. As a picture of what drives mathematicians, and what it is like being a professional one, this proves an entertaining, if necessarily complex, explanation. … If you are stuck with a mathematician at a dinner party, his sometimes rollicking volume will convince you that Harris is the one to pick.
From Rob Hardy’s review in The Dispatch (April 21, 2015)
“Das Buch ist in der oben geschilderten Vielfältigkeit sicherlich sehr offen und demokratisch hinsichtlich der Darstellung der verschiedensten Ideen; aber ich würde den Autor nicht so schnell aus seiner Verantwortung entlassen, aus einer faszinierenden Materialsammlung ein Werk, mit so etwas wie einem ‘roten Faden’, zu destillieren.”
(rough translation: “In the diversity described above, the book is certainly quite open and democratic with respect to the representation of a great variety of ideas. But I wouldn’t be so quick to let the author off the hook; he ought to provide some kind of guiding theme in order to turn a fascinating collection of material into a work.”)
The last paragraph of a four-star customer review by Mr. T. on amazon.de (March 22, 2015).
“…[a] relaxed and illuminating set of reflections on the life of a professional mathematician…an ingratiating guide to life as lived by the world’s top mathematicians…”
But there’s also this:
“his [taste] is somewhat hip and hucksterish…a tolerance towards male-identified competitiveness that may shock some readers”
and in conclusion:
“Michael Harris paints a persuasive picture of what it is like to be a mathematician in the 21st century. But it is not as flattering as he seems to think, and readers may come away with a distinct impression that the world would be a better place with less mathematics in it rather than more.”
From Jonathan Rée’s review in Literary Review (March 2015)
“Mathematics Without Apologies [together with Cédric Villani’s Birth of a Theorem] provide[s] an unmatched perspective on life in this ‘problematic vocation’… a kaleidoscope of philosophical, sociological, historical and literary perspectives on what mathematicians do, and why.”
From Amir Alexander’s review in Nature (5 March 2015)
“Overall… I can’t remember when I last read a book that was as “unapologetically” self-satisfied and self-congratulatory.”
From Ernest Davis’s review in SIAM News (March 2, 2015)
Naturally, I disagree, and I explain why here, on this very blog.
UPDATE: The reviewer has generously added a link to my reply. More information here.
“I don’t recommend you all read this book once… I recommend you read it, indeed savor it, 2-3 times….”
From the MathTango review (February 15, 2015)
“Harris’ reflections on the role of mathematics in the recent financial crisis raise important questions, and this chapter should be required reading for anyone studying or teaching financial mathematics.”
From Tony Mann’s review in the Times Higher Education Supplement (February 12, 2015)
“If you are interested at all in what mathematics really is and what the best mathematicians really do (and you’re up for an intellectual challenge), I highly recommend that you get a copy and set some time aside for delving into this unusual book. . . . Harris manages to move back and forth between the deepest ideas about mathematics at the frontiers of the subject, insightful takes on the sociology of mathematical research, and a variety of topics pursued in a sometimes gonzo version of post-modern academic style.”
From Peter Woit’s review in Not Even Wrong (January 27, 2015)
“Harris is the kind of mathematician one hopes to meet at an intimate dinner party. . . . Recommended for curious readers in any subject wishing to answer problems in creative ways.”