True False Proofs...or Poofs
The MathLint for this week shares an interesting proof (or poof) that... Perhaps you want more of this....
These websites are just teasers. Many other websites include false proofs...just do a search and explore...anmd enjoy.
- In the late 1990's, the University of Toronto produced a webpage with multiple false proofs. There you will find proofs that 1=2 using either algebra or complex numbers, a math induction proof that all people in Canada are the same age, a calculus proof that a ladder will fall infinitely fast when pulled, and a subtle proof that all natural numbers can be unambiguously described in 14 words or less.
- MathOverflow.net offers a discussion of "interesting-but-false" proofs. be forewarned that the level of mathematics is at the college level for most of the proofs, though many of them are still accessible for secondary students (e.g. the bathroom-wall proof that ei = 1).
- Larry Freeman, a software engineer, offers the blog False Proofs, with the goal of "seeking to analyze 'incoherent' ideas from the perspectives of mathematics." Make sure you read about the E. E. Escultura hoax regarding an error in Wiles proof.
- The great CutTheKnot website offers a discussion of multiple false proofs of the Pythagorean Theorem. And, if you have never visited this website before, take some time to browse its rich and high-quality ideas.
- SkullsInTheStars offers a fun "Spot the Math Errors." Just as revealing is the interesting reader dialogue that was generated.