A Cambridge logician didn't invent overlapping circles — and said so. But he used them so well that his name stuck. He also built a machine that bowled out an Australian star.
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Ten items. Say your answer out loud before you reveal it.
Read the sentence, guess the meaning of the word in bold, then reveal.
The three words are: intersection · exclusive · category. Read each meaning, say the word, then reveal.
One missing word fits every phrase in the group. Say it, then reveal.
Read each part. After it, answer the quick check from memory, then discuss one question.
John Venn was born in Hull, in the north of England, in 1834, into a family of evangelical churchmen. His grandfather, also called John Venn, had been rector of Clapham and a leader of the Clapham Sect, the group that campaigned against slavery. Everyone expected young John to become a priest too.
In 1853 he went to Gonville and Caius College, Cambridge, and in 1857 he graduated as sixth Wrangler — sixth among the best mathematics students of his year. Two years later he was ordained as a priest.
But in 1862 he returned to Cambridge to teach moral sciences — subjects that included logic and probability. Teaching changed the direction of his life. He needed ways to make difficult arguments clear to his students.
1. What did his family expect him to become?
2. What does “sixth Wrangler” mean?
3. Why did he return to Cambridge in 1862?
1. A priest.
2. He was ranked sixth among the best mathematics students of his year.
3. To teach moral sciences, including logic and probability.
In July 1880, Venn published a paper with a long title: “On the Diagrammatic and Mechanical Representation of Propositions and Reasonings”. In it, he used overlapping circles to show logical statements. With three circles, every possible combination — in A and B but not C, in all three, in none — has its own space.
He never claimed the idea was his own. Circles had been used for logic before, most famously by the mathematician Leonhard Euler in his Letters to a German Princess of 1768, and Venn called his diagrams “Eulerian circles”. He later wrote: “Of course the device was not new then, but it was so obviously representative of the way in which any one, who approached the subject from the mathematical side, would attempt to visualise propositions, that it was forced upon me almost at once.”
What Venn added was a system: his diagrams show every possible overlap, even the empty ones. The name “Venn diagram” came later; the philosopher Clarence Irving Lewis used it in 1918.
1. When did Venn publish his paper?
2. What did Venn call his diagrams?
3. What did Venn add to the older circles?
1. In July 1880.
2. “Eulerian circles”.
3. A system that shows every possible overlap, even the empty ones.
In 1883 Venn left the clergy, having concluded that his beliefs were incompatible with the Church of England. In the same year he was elected a Fellow of the Royal Society. Later in life he turned to history, and with his son compiled an enormous register of past members of the university.
He also had a rare talent for building machines. One of them bowled cricket balls. When the Australian team visited Cambridge in 1909, the machine reportedly bowled out one of their star batsmen, Victor Trumper. In 2024, the university's engineering department built a new version of it.
Venn died in 1923. Today he is remembered in a stained-glass window at his old college, on a bridge in Hull, and in almost every classroom in the world. Not bad for a man who borrowed his most famous idea — and was honest enough to say so.
1. Why did Venn leave the clergy?
2. What happened when the Australian team visited Cambridge?
3. Give two ways Venn is remembered today.
1. He concluded that his beliefs were incompatible with the Church of England.
2. His bowling machine reportedly bowled out their star batsman, Victor Trumper.
3. Any two: a stained-glass window at his college, a bridge in Hull, Venn diagrams in classrooms.
Each circle is a group. Where the circles overlap, things belong to both groups; outside the circles are things that belong to neither. Here, two job offers are compared.
Two friends are choosing a holiday: the mountains or the coast. Where on the diagram does each feature go?
1. Both — both places have it — the overlap.
2. Mountains only — only the mountains offer this.
3. Neither — neither place has one — outside both circles.
4. Coast only — only the coast has a harbour.
5. Both — shared by both — the overlap.
6. Coast only — only possible by the sea.
Size isn't shown. A big area on the page might hold two tiny features; a Venn diagram doesn't measure importance.
Too many circles. Beyond three, the diagram quickly becomes hard to read.
Things aren't always in or out. Real categories are fuzzy: is a tomato a fruit or a vegetable?
Venn diagrams are about what things share. English has a small family of words for exactly that — and a quick way to say “me too” and “me neither”.
Use both, either, neither, nor or or.
1. my brother and my sister live abroad.
2. You can pay by card in cash.
3. of the two jobs offers a company car.
4. The flat is neither cheap close to the station.
5. of my parents was born here — they're both from Poland.
1. Both
2. either … or
3. Neither
4. nor
5. Neither
Respond with So … I or Neither … I.
1. “I studied maths at university.” →
2. “I don't like crowded beaches.” →
3. “I've never been to Cambridge.” →
4. “I'm going to compare the two offers tonight.” →
1. So did I.
2. Neither do I.
3. Neither have I.
4. So am I.
Now compare yourself with your teacher: find two things you both like and one thing neither of you does — and react with So do I / Neither do I.
Draw circles out loud. Choose a task, start the timer, and talk.
Compare two options you are thinking about — two jobs, two phones, two places to live. What is unique to each, and what do they share?
Draw three circles for three people in your life. What sits in the middle — the thing all three share?
Venn made a borrowed idea famous. Tell the story of someone else who became famous for an idea that wasn't completely new.