I've run across this cute little story before, and now for the life of me I can't find it anywhere. It goes something like:

Two people are looking out onto a mathematical landscape, and there are these hills/towers that represent problems. Some are unsolved, but some are solved and have little staircases that lead up to their tops---proofs. As they watch, a mathematician comes along, considers one of the unsolved problems, and leaps to the top of it! Then the mathematician builds a staircase down from off the top of the hill/tower and walks away. The onlookers marvel at what they have witnessed.

My Google searches are just not turning this up, and I'd really like to find where I found this, or some other source. Maybe you know where to find it, or maybe your Google fu is better than mine? Thanks!

  • $\begingroup$ this is the closest thing i can think of (grothendieck) mathoverflow.net/a/7156/29776 $\endgroup$ – citedcorpse Jun 30 '13 at 18:36
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    $\begingroup$ i must add that as a baker, i find the following scenario more realistic: it is known that slow food is the tastiest food. specifically, sourdough bread has the most flavour. to produce it takes a long time, and you can either knead the dough a lot, or else let it rest, knead it for literally 15 seconds, let it rest, and repeat. in either case, you end up with the same product. which approach sounds more productive? note that sobriety is required in only one of these... $\endgroup$ – citedcorpse Jun 30 '13 at 18:42
  • $\begingroup$ This looks more like a question of interpretation, and I would think this is applicable when you are trying to disprove something by contradiction. Leaping to the rooftop is assuming that the problem is already settled, and building the stairs down is actually solving the problem by showing it leads to a contradiction. $\endgroup$ – Ovi Jul 8 '13 at 4:05

You can find it in the beginning of the chapter Why Study Mathematics? in Hayward's Unabridged Dictionary (don't be fooled by the title) by C. J. S. Hayward.


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