Mr. O’Neill

Mr. O’Neill, known to the boys as Dotty, is the fourth-class master whose Euclid lessons briefly open a space for mathematical curiosity inside a school ruled by intimidation. Small enough to earn his nickname, he teaches from a raised platform, threatens pupils with an ash plant, and peels an apple before the class; his lessons bring geometry into uneasy contact with the boys’ fear of the war and with a rival master’s claim over the subject.

Identity and Classroom Authority

Mr. O’Neill is the master of the fourth class. The boys call him Dotty because he is small “like a dot.” His classroom places him physically above them: he stands on a platform, where he can threaten the pupils with his ash plant and peel an apple for all to see. The arrangement makes authority conspicuous, but his presence in the classroom is not defined by punishment alone. He teaches ideas that the boys do not understand, and his response to a question from Brendan Quigley is notably gentler than they expect from a master.

At the start of the school year in September, Mr. O’Neill writes three words on the blackboard: “Euclid, geometry, idiot.” He warns the boys not to interfere with the words, threatening that a culprit will go through the rest of his life with one hand. He then makes the class repeat that anyone who does not understand Euclid’s theorems is an idiot. The exercise turns a mathematical subject into a test of rank and shame, in a school where the boys already know the word idiot from the masters’ repeated use of it against them.

Euclid and the Boys’ Questions

When Brendan raises his hand to ask what a theorem and Euclid are, the boys expect Mr. O’Neill to lash out at him. Instead, the master gives him a little smile and recognizes that he has asked not one but two questions. He asks Brendan’s name, then later uses the boy’s knowledge that Euclid was Greek to distinguish him from Clohessy, whom he calls a half-wit. The smile and the lesson make Brendan’s questioning an exception within the classroom’s usual hierarchy: for a moment, a pupil’s question is welcomed as a beginning rather than punished as insolence.

Mr. O’Neill draws two parallel lines and explains that they never meet, even if extended to infinity—or to God’s shoulders, which, he observes, are a long way off. He adds that a German Jew is upsetting the world with ideas about parallel lines. The boys, however, are preoccupied with Germans marching and bombing. Unable to ask the master directly what geometry has to do with the world around them, they enlist Brendan, whom they regard as the master’s pet, to put the question on their behalf.

Brendan does not want the role. He says he did not ask to be the master’s pet and fears that Mr. O’Neill will attack him if he asks what use Euclid’s endless lines are while the Germans are bombing everything. The other boys threaten to attack him if he refuses. Under this pressure, Brendan asks the question the following day. The exchange exposes a second kind of coercion in the classroom: the boys turn their fear of the master into pressure on the one pupil they think can safely approach him.

The Geometry Dispute

Mr. O’Neill answers the boys’ challenge by returning to the question of parallel lines and God’s shoulders. When asked whether God has shoulders, Brendan says no; Mr. O’Neill replies that he knows and dismisses him as an idiot, ordering him home. The earlier indulgent smile gives way to a sharp rebuke. The episode does not resolve the boys’ practical question about the war; instead, it makes the teacher’s authority and the limits of their permission to question him newly visible.

The next day, a commotion at the classroom door brings a conflict between masters into the open. Mr. O’Dea calls Mr. O’Neill a “chancer” and a “poltroon,” while the new headmaster, Mr. O’Halloran, tries to prevent an argument in front of the pupils. Mr. O’Dea insists that geometry belongs to the fifth form and is his subject. He wants Mr. O’Neill to teach long division instead, claiming that it will stretch Mr. O’Neill’s intellect, and complains that the geometry lessons are destroying the boys’ minds. His objections also seize on the apple peels, which he says cause diarrhea.

Mr. O’Neill refuses to yield quietly. He tells Mr. O’Halloran that he might as well ask him to stop eating his daily apple. The headmaster insists that there can be no more Euclid. The dispute therefore ends not through an answer to the boys’ question or a resolution between the teachers, but through an order that removes geometry from Mr. O’Neill’s classroom. His intellectual enthusiasm meets the school’s hierarchy of subject, form, and authority.

The Apple and the Interrupted Lessons

After the order, Mr. O’Neill returns to the classroom with watery eyes. He tells the boys that little has changed since the time of the Greeks because the barbarians are within the gates and their names are legion, then asks what has changed since the Greeks. His remark turns the interruption of his lessons into a broader image of a besieged world. It resonates with the boys’ attention to wartime bombing, though the record does not identify the barbarians he means.

The apple remains a daily feature of his teaching. Its peel is long and red or green, and pupils close enough to the platform can smell its freshness. A boy who behaves well and answers Mr. O’Neill’s questions may receive the apple and eat it at his desk, where he can keep it from classmates who would otherwise demand pieces in the yard. The reward is small, but in a classroom shaped by threat and scarcity it offers a brief, private pleasure.

On days when the questions are too hard, Mr. O’Neill drops the peel into the wastebasket, leaving the boys to watch the lost food go away. He sometimes has a pupil from another class carry the basket to the furnace to burn the papers and peel; at other times it is left for Nellie Ahearn, the charwoman, to remove in her large canvas sack. The boys would like her to save the peel for them before the rats get it, but she is exhausted from cleaning the whole school alone and refuses. The apple thus connects Mr. O’Neill’s classroom ritual to the boys’ hunger, while the route of its discarded peel shows how even a small remainder becomes an object of desire.

Character and Narrative Significance

Mr. O’Neill is presented through contrasts rather than a fully supplied biography: he threatens pupils yet smiles at a sincere question; he makes learning theatrical, yet his chosen subject is displaced by school rules; his apple is both a reward and, when questions go unanswered, a visible denial. The boys’ first-person-plural account keeps his motives at a distance. It gives the reader his gestures, words, and classroom practices, but does not establish why he is so committed to Euclid or how he feels about losing the lessons.

The sequence also shifts between repeated classroom habits and distinct confrontations. The blackboard’s three words, the daily peeling, and the recurring questions establish a routine; Brendan’s challenge and Mr. O’Dea’s dispute interrupt it. Through that pattern, Mr. O’Neill becomes the focus of a conflict over what education is for: abstract geometry cannot answer the boys’ immediate fear of war, but neither can the school’s power struggle make their questions disappear. His return to class after the ban preserves the mathematical lesson as an image of intellectual resistance, even as the order ensures that Euclid can no longer be taught there.