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tparker
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This is not in any way a comprehensive answer to your question, but it may be worth pointing out that while there are certainly several disadvantages to "erasing the trail" up to a result, there is also (at least) one major advantage: it lessens the "path dependence" and encourages others to think about possible applications of the result that would not have occured to the original discoverer.

For example, many people discover a result by thinking very carefully about one specific example. But the beauty of abstract math is that the same general result often applies to a huge range of concrete examples that differ hugely in their details, but share the minimal mathematical structure necessary for the result. The original discoverer may be so used to thinking about the result in the context of one type of example that they miss applications to other classes of examples. Presenting the detailed example that they worked through to motivate the result risks similarly locking other readers into the same mode of thoughthought. Whereas if a reader approaches a new result with a completely different example/application in mind, then they may be able to more easily extend the result to new corollaries that the original discoverer didn't think of.

This is not in any way a comprehensive answer to your question, but it may be worth pointing out that while there are certainly several disadvantages to "erasing the trail" up to a result, there is also (at least) one major advantage: it lessens the "path dependence" and encourages others to think about possible applications of the result that would not have occured to the original discoverer.

For example, many people discover a result by thinking very carefully about one specific example. But the beauty of abstract math is that the same general result often applies to a huge range of concrete examples that differ hugely in their details, but share the minimal mathematical structure necessary for the result. The original discoverer may be so used to thinking about the result in the context of one type of example that they miss applications to other classes of examples. Presenting the detailed example that they worked through to motivate the result risks similarly locking other readers into the same mode of though. Whereas if a reader approaches a new result with a completely different example/application in mind, then they may be able to more easily extend the result to new corollaries that the original discoverer didn't think of.

This is not in any way a comprehensive answer to your question, but it may be worth pointing out that while there are certainly several disadvantages to "erasing the trail" up to a result, there is also (at least) one major advantage: it lessens the "path dependence" and encourages others to think about possible applications of the result that would not have occured to the original discoverer.

For example, many people discover a result by thinking very carefully about one specific example. But the beauty of abstract math is that the same general result often applies to a huge range of concrete examples that differ hugely in their details, but share the minimal mathematical structure necessary for the result. The original discoverer may be so used to thinking about the result in the context of one type of example that they miss applications to other classes of examples. Presenting the detailed example that they worked through to motivate the result risks similarly locking other readers into the same mode of thought. Whereas if a reader approaches a new result with a completely different example/application in mind, then they may be able to more easily extend the result to new corollaries that the original discoverer didn't think of.

Source Link
tparker
  • 1.3k
  • 16
  • 26

This is not in any way a comprehensive answer to your question, but it may be worth pointing out that while there are certainly several disadvantages to "erasing the trail" up to a result, there is also (at least) one major advantage: it lessens the "path dependence" and encourages others to think about possible applications of the result that would not have occured to the original discoverer.

For example, many people discover a result by thinking very carefully about one specific example. But the beauty of abstract math is that the same general result often applies to a huge range of concrete examples that differ hugely in their details, but share the minimal mathematical structure necessary for the result. The original discoverer may be so used to thinking about the result in the context of one type of example that they miss applications to other classes of examples. Presenting the detailed example that they worked through to motivate the result risks similarly locking other readers into the same mode of though. Whereas if a reader approaches a new result with a completely different example/application in mind, then they may be able to more easily extend the result to new corollaries that the original discoverer didn't think of.

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