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Grothendieck primes

The details are unclear and the story may be legendary, but the great mathematician Alexander Grothendieck apparently once picked 57 as an example of a prime number. So a Grothendieck prime is a number that looks like it's prime but isn't.

I told this story to Helen not long after she learned what a prime number was. As well as providing a story to anchor the concept of primality, it illustrates that checking primality is difficult — and when you're six that's actually true for 57, though I think she'll remember what 3x19 is now — it reinforces the idea that making mistakes is ok, and it gives a human face to mathematics, perhaps helping to stop the tedium of times tables memorisation killing any excitement about number theory.

1 Comment »

  1. I do share your concern that number theory, and maths in general, should be exciting in school, and subsequently. I always liked Bertrand Russel's story about his friend who was the only person he knew who read mathematics books for pleasure.

    But I did find times tables exciting in primary and junior schools, though not as exciting as long division, examples of which I used to make up and work through. I did go on to take a maths degree!

    But my kids and their friends (now in their forties) cannot believe they never did either times tables or long division at any point in school. I think it is being remedied with the grandchild, now 6, who is rather inspired by times tables.

    An anecdote doesn't make a case, and I am against the "deliverology" doctrine that says literacy and numeracy are what should be measured for children's attainment. But I would like to separate that from an accusation of tedium (though I think my English has let me down somewhat there).

    Comment by mhc — March 2021

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