When I was 11 y.o. I was screamed at by a teacher and thrown out of class for pointing this out when he claimed the false belief stated (it wasn't class material, but the teacher wanted to show he was smart). I found the counterexample later at home. I didn't let the matter drop either... I knew I was right and he was wrong, and really had a major fallout with that math teacher and the school; and flunked math that year. – Daniel Moskovich May 5 2010 at 1:19I guess I had the good luck to not ever have such a completely horrible math instructor, because I think any of these cases would have made me completely lose my mind. (As an aside, I will say that it's routine in my classes that I'll have to disabuse people of the idea that pi = 22/7... perhaps this is more common in Israel, as Prof. Kalai above is, and many of my students are from.) Have you ever seen someone punished, yelled at, or thrown out of class for actually expressing true basic math facts?
@Daniel: Sorry to hear that. When my daughter Meena was the same age (11), her teacher asserted that 0.999... was not equal to 1. Meena supplied one or two proofs that they were equal, but her teacher would not budge. Maybe this is another example of a common false belief. – Ravi Boppana May 5 2010 at 2:59
@Daniel: I've heard a worse story. A college instructor claimed in Number Theory class that there are only finitely many primes. When confronted by a student, her reply was: "If you think there are infinitely many, write them all down". She was on tenure track, but need I add, didn't get tenure. – Victor Protsak May 5 2010 at 5:38
This false belief leads to a proof of the Twin Prime conjecture: For every n, (p1p2⋯pn−1,p1p2⋯pn+1) are twin primes, right? – David Speyer May 6 2010 at 15:50
Daniel, about the same age, I was asked to leave class for claiming that pi is not 22/7. The math teacher said that 3.14 is an approximation and while some people falsly believe that pi=3.14 but the true answer is 22/7. Years later an Israeli newspaper published a story about a person who can memorize the first 2000 digits of pi and the article contained the first 200 digits. A week later the newspaper published a correction: "Some of our readers pointed out that pi=22/7". Then the "corrected" (periodic) 200 digits were included. Memorizing digits of pi is a whole different matter if pi=22/7. – Gil Kalai May 11 2010 at 5:45
Monday, May 27, 2013
Punished for True Math
Reading some Mathoverflow the other day, I ran into some truly blood-boiling recollections in a discussion of "Examples of common false beliefs in mathematics" (mostly at the research level, but the comments diverged), such as that "Many students believe that 1 plus the product of the first n primes is always a prime number". Recollections such as these (link):