When trying to understand a mathematical proof or argument, I often use what I call “backtracking” and “momentum.”

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Consider a proof outline

Axiom

Statement 1

Statement 2

Statement 3

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Backtracking: If I am stuck on Statement 2, I don’t usually stay there for long. Instead, I backtrack to Statement 1. After having ensured that I do – truly – understand Statement 1, I then return to Statement 2. I often then do better with Statement 2.

Backtracking might sound like common sense, but, when I was starting, I had a tendency to linger where I got stuck. This would burn energy. Now, I prefer backtracking, and taking 2 easy steps instead of 1 hard jump.

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Momentum: If I get stuck at Statement 3, rather than backtracking to Statement 2, I often backtrack all the way to Statement 1. Then I run through Statement 1, Statement 2, and Statement 3.

This feels to me like building up momentum—a running start—which increases the chances that I break through Statement 3.

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