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Craft and StructureVery hardFunction of a shift in a mathematics profile

Craft and Structure practice question

For seven years the proof would not close. She filled notebooks with approaches that collapsed: the induction that broke at a single stubborn case, the geometric translation that obscured more than it revealed, the borrowed technique that almost — but only almost — carried over. When the argument finally came together, colleagues called it sudden. The notebooks say otherwise: every abandoned route had charted exactly where the final proof could not afford to go.

Which choice best describes the function of the final sentence in the text as a whole?

  1. A. It reframes the mathematician's failed attempts as the source of the eventual breakthrough.Correct
  2. B. It concedes that the problem remains unsolved despite decades of work.
  3. C. It introduces a rival mathematician's competing proof.
  4. D. It questions whether the problem was worth seven years of effort.

Answer: A. It reframes the mathematician's failed attempts as the source of the eventual breakthrough.

After cataloging the dead ends, the final sentence recasts them: each failure mapped the terrain the successful proof would need — failure reframed as foundation.

Why the other answers are wrong

B. It concedes that the problem remains unsolved despite decades of work.
The text says the proof succeeded; nothing remains unsolved.
C. It introduces a rival mathematician's competing proof.
No rival or competing proof appears.
D. It questions whether the problem was worth seven years of effort.
The sentence honors the long effort rather than questioning it.

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