Radó, bb5.org, and the Uncomputable

The Prompt

Explain the Busy Beaver problem to someone who has heard of Turing machines but not of uncomputability. Define BB(n); give the known values for n = 1 through 5; explain why BB is uncomputable (connect it to the halting problem). Cite Radó's 1962 paper, the 2024 bb5.org collaborative determination of BB(5), and Aaronson's work connecting BB(748) to the Goldbach conjecture. Conclude with a note on what it means for a well-defined function to have values that no algorithm can ever compute.

Completion Criteria

A short essay (three or four paragraphs) with at least three citations — Radó (1962), the bb5.org project (2024), and Aaronson — and a closing note on uncomputability.

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