Euclid, geometry, idiot

Mr. O’Neill is the master in the fourth class at school. We call him Dotty because he’s small like a dot. He teaches in the one classroom with a platform so that he can stand above us and threaten us with his ash plant and peel his
apple for all to see. The first day of school in September he writes on the blackboard three words which are to stay there the rest of the year, Euclid, geometry, idiot. He says if he catches any boy interfering with these words that boy will go through the rest of his life with one hand. He says anyone who doesn’t understand the theorems of Euclid is an idiot. Now, repeat after me, Anyone who doesn’t understand the theorems of Euclid is an idiot. Of course we all know what an idiot is because that’s what the masters keep telling us we are.
     Brendan Quigley raises his hand. Sir, what’s a theorem and what’s a Euclid?
     We expect Dotty to lash at Brendan the way all the masters do when you ask them a question but he looks at Brendan with a little smile. Ah, now, here’s a boy with not one but two questions. What is your name, boy?
     Brendan Quigley, sir.
     This is a boy who will go far. Where will he go, boys?
     Far, sir.
     Indeed and he will. The boy who wants to know something about the grace, elegance and beauty of Euclid can go nowhere but up. In what direction and no other can this boy go, boys?
     Up, sir.

Detail from the statue of Euclid. Joseph Durham (1814–1877), Oxford University Museum of Natural History.
Photo: rodtuk, 2009, CC BY-NC-SA 2.0. Source:

    Without Euclid, boys, mathematics would be a poor doddering thing. Without Euclid we wouldn’t be able to go from here to there. Without Euclid the bicycle would have no wheel. Without Euclid St. Joseph could not have been a carpenter for carpentry is geometry and geometry is carpentry. Without Euclid this very school could never have been built.
     Paddy Clohessy mutters behind me, Feckin’ Euclid.
     Dotty barks at him. You, boy, what is your name?
     Clohessy, sir.
     Ah, the boy flies on one wing. What is your Christian name?
     Paddy what?
     Paddy, sir.
     And what, Paddy, were you saying to McCourt?
     I said we should get down on our two knees and thank God for Euclid.
     I’m sure you did, Clohessy. I see the lie festering in your teeth. What do I see, boys?
     The lie, sir.
     And what is the lie doing, boys?
     Festering, sir.
     Where, boys, where?
     In his teeth, sir.
     Euclid, boys, was a Greek. What, Clohessy, is a Greek?
     Some class of a foreigner, sir.
Clohessy, you are a half-wit. Now, Brendan, surely you know what a Greek is?
     Yes, sir. Euclid was a Greek.

Egyptian papyrus with Greek inscription: fragment from Euclid’s Elements (II, 5). Oxyrhynchus, 3rd–4th century AD.
Penn Museum, E2748 © Penn Museum 2020, source:

     Dotty gives him the little smile. He tells Clohessy he should model himself on Quigley, who knows what a Greek is. He draws two lines side by side and tells us these are parallel lines and the magical and mysterious thing is that they never meet, not if they were to be extended to infinity, not if they were extended to God’s shoulders and that, boys, is a long way though there is a German Jew who is upsetting the whole world with his ideas on parallel lines.
     We listen to Dotty and wonder what all this has to do with the state of the world with the Germans marching everywhere and bombing everything that stands. We can’t ask him ourselves but we can get Brendan Quigley to do it. Anyone can see Brendan is the master’s pet and that means he can ask any question he likes. After school we tell Brendan he has to ask the question tomorrow, What use is Euclid and all those lines that go on forever when the
Germans are bombing everything? Brendan says he doesn’t want to be the master’s pet, he didn’t ask for it, and he doesn’t want to ask the question. He’s afraid if he asks that question Dotty will attack him. We tell him if he doesn’t ask the question we’ll attack him.
     Next day Brendan raises his hand. Dotty gives him the little smile. Sir, what use is Euclid and all the lines when the Germans are bombing everything that stands?
     The little smile is gone. Ah, Brendan. Ah, Quigley. Oh, boys, oh, boys.
     He lays his stick on the desk and stands on the platform with his eyes closed. What use is Euclid? he says. Use?

Portrait of Euclid, engraving.
© Wellcome Collection, CC BY 4.0

    Without Euclid the Messerschmitt could never have taken to the sky. Without Euclid the Spitfire could not dart from cloud to cloud. Euclid brings us grace and beauty and elegance. What does he bring us, boys?
     Grace, sir.
     Beauty, sir.
     Elegance, sir.
     Euclid is complete in himself and divine in application. Do you understand that, boys?
     We do, sir.
     I doubt it, boys, I doubt it. To love Euclid is to be alone in this world.
     He opens his eyes and sighs and you can see the eyes are a little watery.

Frank McCourt: Angela’s ashes (excerpt)

Featured image: Detail of a page from the first printed edition og Euclid’s Elements (II, 5). Venice, Erhard Ratdolt, 1482. Munich, Bayerische Staatsbibliothek, Rar. 292. Source:

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