Anathem is set on and around the fictional planet Arbre. Thousands of years before the events in the novel, the planet's intellectuals entered concents (monastic communities) to protect their activities from the collapse of society. The avout – intellectuals separated from Sæcular society – retain extremely limited access to tools and are banned from possessing or operating most advanced technology and are supervised by the Inquisition, which answers to the outside world. The avout are allowed to communicate with people outside the walls of the concent only once every year, decade, century, or millennium, depending on the particular vows they have taken.
The narrator and protagonist, Fraa Erasmas, is an avout at the Concent of Saunt Edhar. His primary teacher, Fraa Orolo, discovers that an alien spacecraft is orbiting Arbre – a fact that the Sæcular Power attempts to cover up. Orolo secretly observes the alien ship with a video camera, technology that is prohibited for the avout. Erasmas becomes aware of the content of Orolo's research after Orolo is banished (in a rite called Anathem) from the Mathic World for his possession and use of proscribed technology within the concent. But the presence of the alien ship soon becomes an open secret among many of the avout at St. Edhar. The alien ship eventually declares its presence by shining a laser upon the Millenarian Math of Saunt Edhar, the bastion of those avout who have taken a thousand-year vow not to interact with the outside world. Shortly after that, the Sæcular Power evoke many avout from Saunt Edhar, including Erasmas, as well as one Millenarian – Fraa Jad.
Erasmas and several companions, on Fraa Jad's suggestion, decide to seek out Orolo. After a dangerous journey over the planet's frozen pole, undertaken to reach another continent without passing through national borders, Erasmas and his comrades eventually arrive at a concent-like establishment called Orithena – which is on the site of the ancient source of the Mathic world – where they reunite with the no-longer Fraa Orolo (he being Anathematized). Orolo holds discussions with Erasmas about the nature of the cosmos and consciousness, and how he believes that the aliens are not simply from another planet, but from another cosmos that is influenced by Arbre. During the discussions between Orolo and Erasmas, a small spacecraft lands in Orithena, on the very site of the ancient Mathic world's Analemma, which is visible from space. A female alien is on board, but dead of a recent gunshot wound. She has brought with her four vials of blood – presumably that of the aliens – and much evidence about their technology. Shortly thereafter, the aliens propel a massive metal rod at a nearby volcano, triggering an eruption that destroys Orithena. Orolo sacrifices his life to ensure the safety of the dead alien's remains and her blood samples, an event that leads to his canonization as Saunt Orolo.
Erasmas then travels to the concent of Saunt Tredegarh - where he was expected to have gone when evoked - to attend the Convox. This is a joint conference of the avout and the Sæcular Power, dedicated to dealing with the military, political, and technical issues raised by the existence of the alien ship in Arbre's orbit. Tredegarh is where the Sæcular Power had brought the evoked avout of Saunt Edhar and from many other concents from all around the world to work on methods of interpreting the limited information regarding the alien spacecraft, as well as investigating possible military options. Much research is done on the samples Orolo sacrificed his life to save, and the aliens are found to come from planets in four parallel and distinct cosmos: Urnud, Tro, Laterre and Fthos. The mulitple-worlds interpretation of the cosmos is discussed in great detail by the high-level avout at successive evening meals to which Erasmus performs the duties of a servant. In this section of the novel, it slowly becomes plain that Laterre is our own Earth, which serves as a 'higher plane of existence' for Urnud and Tro, and Arbre is itself a 'higher plane' for Laterre. Through observation and experiment, Erasmas and his companions determine that the conference is infiltrated by the aliens, and unmask a French speaking Laterran linguist by the name of Jules Verne Durand. He explains that the aliens are experiencing internal conflict between two factions. The currently ruling faction (the less evolved and more militaristic Urnud and Tro, as well as some Laterrans) intends to attack and raid Arbre for its resources in order to repair their spaceship, while the opposing faction (the more enlightened Fthos and most Laterrans) favors open negotiation. Jules Durand offers to assist the avout of Arbre in resisting the ruling faction of the aliens, believing that they can bring the situation to a peaceful conclusion.
Fearing alien attack after Durand has been exposed, the avout evacuate Saunt Tredegarh and all the other concents on Arbre simultaneously. Erasmas and his comrades are taken to a distant sanctuary, where they receive training for a mission to board the alien ship and disable its weaponry. They are launched into space - on ballistic missiles built for planetary nuclear warfare - unknowingly bringing with them "Everything Killers" (miniaturized Neutron Bombs) that the Sæcular Power intends to use as a last resort should the primary goal of the mission fail. Three people – including Fraa Jad – are issued detonators.
Upon arrival at the alien ship it is obvious that they are preparing the ship's main weapon. The Ringing Vale avout head off to destroy the ship's main weapon, ultimately successful, but also perishing in their attack. The narrative now parallelizes (across multiple variations of the multiple cosmos of Arbre) as the avout team boards the ship and pass out from breathing the alien oxygen. In one Narrative, Fraa Jad awakens Erasmus and leads him through the ship toward the command center. Jad opens the accessway to the command center on the first try and, upon being attacked by alien soldiers, triggers the Everything Killers killing himself, Erasmus and everyone in that area. The Narrative immediately jumps back to the same accessway but this time Jad doesn't guess the lock code, and instead the soldiers take them captive and bring them to parley with the leader of peaceful faction, where it emerges that the Millenarian avout of hundreds of years in the past may have used their "incanting" powers to summon the ship to their cosmos from another universe.
In the final Narrative (the one that continues forward) Erasmas awakens in a hospital on the starship to the perplexing news that Fraa Jad had died immediately after their launch, contradicting his obvious presence and Raz's memories up to that point. It remains unclear which (or how many) of these contradictory narratives is real, and what may have happened in different worldtracks that have crossed and overlapped. However, Fraa Jad had hinted that the Incanters (and possibly Rhetors) were capable of operating simultaneously in parallel universes, so Jad is likely to have survived in other versions of the world.
Erasmas learns that the aliens have brought up a delegation of diplomats from Arbre. A funeral ceremony for those lost on both sides of the attack forms part of the signing of a peace treaty between the aliens and the Arbrans. On Arbre itself, the Sæcular Powers and the avout have agreed to cooperate as equal powers. The people of Arbre inaugurate a second "Reconstitution", revising many of the rules that had restricted the work and lifestyle of the avout. Erasmas and friends set about the task of building a new concent, dedicated to Saunt Orolo.
In the novel, avout follow a life path called the Discipline, sometimes referred to as Cartasian Discipline, after Saunt Cartas, the founder of the mathic world. It is a set of rules governing what is (and is not) allowed for avout to know and/or do, and was codified centuries before the time of the story in the Second New Revised Book of Discipline.
Chief among these is that the avout are separated, both mentally and literally, from the Sæculum, or outside world. There are different levels of separation. For example, within a concent, there are different terms of residency. There are 1-, 10-, 100-, and 1,000-year orders. Each of these celebrates "Apert", a festival opening the concent to the outside world and allowing the flow of information between them, on an interval determined by that number. For example, a 10-year order would celebrate Apert once every ten years, remaining isolated otherwise. Likewise, a 100-year order would only celebrate Apert every hundred years, and a 1,000-year order once every 1,000 years. It is an essential part of this that at any time an order celebrates Apert, all orders below it also celebrate Apert. For example, a Millenarian (1,000-year) order would celebrate in the year 3000. Because 3000 is also a multiple of 100, 10, and 1, Centenarian, Decenarian, and Unarian orders would also celebrate. Exceptions to this rule include "hierarchs" (those who administer the concent) who are required to confer with the Sæcular Power on decisions of weight.
The main secondary aspect of the Discipline is that the avout are allowed to own only their "bolt, chord, and sphere". These objects are made with "newmatter" (matter made with a modified atomic structure to be more versatile), and can be made to alter their shape, texture and other physical properties without the use of tools or other outside technologies. The bolt is a length of newmatter fabric and is used as clothing; the chord is a newmatter rope used to secure the bolt; and the sphere is a newmatter balloon of adjustable size, shape and hardness, and serves as a multipurpose tool.
There are several restrictions governing, for example, the use of "sequencing" (genetic engineering), "syntactic devices" (computers), or other "praxis" (technology). Due to the restrictions, avout can only work on an entirely theoretical basis de jure.
Large portions of the book involve detailed discussions of mathematics, physics, and philosophy. Most of these discussions use fictional Arbran terminology, but treat ideas from actual science and philosophy. Stephenson acknowledges the work of author Julian Barbour as the source for much of this material.
A major theme of the novel is the many-worlds interpretation of quantum mechanics based on a directed acyclic graph, which accounts for the various "worldtracks" and "narratives" explored by Fraa Orolo and manipulated by Fraa Jad. Another major theme is the recurring philosophical debate between characters espousing mathematical Platonic realism (called "Halikaarnians" in the novel and associated with Incanters) and characters espousing nominalism (called "Procians" in the novel and who are the Rhetors).
Stephenson cites the work of Roger Penrose as a major influence on the novel. Specific ideas from Penrose's work include: the idea that the human mind operates in certain fundamental ways as a quantum computer, espoused in Penrose's The Emperor's New Mind; Platonic realism as a philosophical basis for works of fiction, as in stories from Penrose's The Road to Reality; and the theory of aperiodic tilings, which appear in the Teglon puzzle in the novel. Stephenson also cites as an influence the works of Kurt Gödel and Edmund Husserl, whom the character Durand both mentions by name in the novel.
Much of the Geometers' technology seen in the novel reflects existing scientific concepts. The alien ship moves by means of nuclear pulse propulsion.
As an appendix to the novel, Stephenson includes three "Calca", discussions among the avout of purely philosophical or mathematical content. The first is a discussion of a cake-cutting procedure corresponding to the geometric problem of "doubling the square" presented in Plato's Meno. The second presents configuration spaces (called "Hemn spaces" in the novel) as a way of representing three-dimensional motion. The third discusses a "complex" Platonic realism, in which several realms of Platonic ideal forms (called the "Hylaean Theoric Worlds" in the novel) exist independently of the physical world (called the "Arbran Causal Domain" in the novel). The mathematical structure of a directed acyclic graph is used to describe the way in which the various realms can influence one other, and even the physical world can function as part of the realm of ideal forms for some worlds "downstream" in the graph.Erasmas (nickname "Raz"): The protagonist of Anathem; a Decenarian fraa from the Concent of Saunt Edhar. The neglected son of slines, he was collected by the concent at the age of eight.
Orolo: A Decenarian fraa from the Concent of Saunt Edhar. He is an eminent cosmographer and Erasmas's mentor at the concent, but he's later Thrown Back for using forbidden technology to observe the Geometers in violation of the Discipline's isolation requirements.
Arsibalt: A Decenarian fraa from the Concent of Saunt Edhar and one of Erasmas's friends. The estranged son of a Bazian prelate, he seeks to reconcile religion with theorics.
Lio: A Decenarian fraa from the Concent of Saunt Edhar and one of Erasmas's friends. He's known as an absent-minded eccentric and is interested in military history, Vale-lore(martial arts), and unusual gardening techniques.
Jesry: A Decenarian fraa from the Concent of Saunt Edhar and one of Erasmas's friends. Unlike Erasmas, Jesry comes from a prosperous burger family, and is bored with the routine of mathic life preceding the arrival of the Geometers. He becomes famous for going into space with the Warden of Heaven (a religious leader of the Sæcular Power) to investigate the Geometers' ship.
Ala: A Decenarian suur from the Concent of Saunt Edhar and later a major organizer of the Convox. Although they disliked each other as children, she and Erasmas become romantically involved in the course of the story.
Jad: A Millenarian fraa from the Concent of Saunt Edhar. Jad is evoked in the same aut as Erasmas and accompanies him to Bly's Butte in search of Orolo. He later reappears at the Convox.
Cord: Erasmas' half-sister and a machinesmith who lives extramuros near the Concent of Saunt Edhar. She accompanies Erasmas on his search for Orolo.
Sammann: An Ita (a social caste of computer experts) from the Concent of Saunt Edhar who accompanies Erasmas on his search for Orolo.
Yulassetar Crade (nickname "Yul"): An extramuros wilderness guide, member of the expedition to find Orolo.
Ganelial Crade (nickname "Gnel"): An Counter-Bazian deolater (and Yul's cousin) who volunteers to drive the avout to the Convox, member of the expedition for Orolo
Jules Verne Durand: An alien linguist who infiltrates the convox to gather information for the Geometers.
The novel was partly inspired by Stephenson's involvement with the Clock of the Long Now project, to which he contributed three pages of sketches and notes. A separate compact disc, entitled IOLET: Music from the World of Anathem, containing eight experimental vocal compositions by David Stutz, will be sold separately through CD Baby and the Long Now Foundation, with profits going to The Clock of the Long Now project.
To create the world of Arbre, Stephenson constructs new vocabulary. In order to familiarize the reader with the new words, many of which are analogous to English, Latin or Greek words and ideas, he put a glossary at the end of the book. Each chapter begins with a definition of one of these words, which usually relates to the chapter in some way. In addition, the Orth language spoken by the characters was created by Jeremy Bornstein at the author's request, and has been documented. The word anathem was invented by Stephenson, based on the word anthem and the Greek word anathema. In the book, an anathem is a mathic ritual by which one is expelled from the mathic world.
Anathem received mostly positive reviews. Paul Boutin wrote in The Wall Street Journal that "the lasting satisfaction of Anathem derives … from Mr. Stephenson's wry contempt for today's just-Google-it mindset. His prose is dense, but his worldview contagious." On Salon.com, Andrew Leonard described the book as "a page turner and a philosophical argument, an adventure novel and an extended existential meditation, a physics lesson, sermon and ripping good yarn."
Michael Dirda of The Washington Post disagreed, remarking that "Anathem will certainly be admired for its intelligence, ambition, control and ingenuity", but describing it as "fundamentally unoriginal", "grandiose, overwrought and pretty damn dull." The novel entered The New York Times Best Seller list for Hardcover Fiction at number one and achieved the rare distinction for a novel of being reviewed in Nature.
Anathem won the Locus Award for Best Science Fiction Novel in 2009 and collected nominations for the Hugo, Arthur C. Clarke, and John W. Campbell Memorial Awards the same year. In 2008, the novel received a nomination for the British Science Fiction Award.