HippoCampusMathematicsOpen-endedIntermediate3 chapters
Famous unsolved problems, explained for the curious
Explain famous unsolved problems in mathematics — the Riemann hypothesis, P versus NP, the Collatz and twin prime conjectures — at a level a curious non-mathematician can follow.
What you'll learn
3 chapters
- 1
Early Number Mysteries: Primes, Patterns, and the Twin Prime Conjecture
- Describe what prime numbers are and why they became central objects of mathematical study.
- Explain the statement of the twin prime conjecture in plain language.
- Summarize the historical roots of the conjecture and why simple-to-state problems can remain unsolved for centuries.
- Interpret partial progress, such as results about bounded gaps between primes, without confusing them with a full proof.
- 2
A 20th-Century Puzzle from Simple Rules: The Collatz Conjecture
- State the Collatz process clearly and follow it on sample starting numbers.
- Explain why a problem with very simple rules can produce behavior that is hard to prove.
- Distinguish between computational verification for many cases and a proof for all positive integers.
- Compare the Collatz conjecture with prime-number problems as a different kind of unsolved question.
- 3
Modern Giants: The Riemann Hypothesis and P versus NP
- Give an accessible statement of the Riemann hypothesis and its connection to prime numbers.
- Explain the basic idea behind P versus NP using the contrast between solving and checking problems.
- Identify why these two problems became iconic beyond specialist mathematics.
- Compare the kinds of consequences each solution would have for mathematics, computing, and society.
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