This will probably not be considered a serious mistake, but maybe it counts:

According to [Dray, Manogue](http://math.oregonstate.edu/bridge/ideas/functions/) if you ask the following question to scientist:

> Suppose the temperature on a rectangular slab of metal is given by
> $T(x,y)=k(x^2+y^2)$ where $k$ is a constant.
> 
> What is $T(r,\theta)$?
> 
> A: $T(r,\theta)=kr^2$  
> B: $T(r,\theta)=k(r^2+\theta^2)$  
> C: Neither

most mathematicians choose B while most other scientists choose A. 

(I don't know if this experiment was ever done on a large scale. I do know some people who studied mathematics and have tried to argue that A is the right answer.)

This question is called Corinne's Shibolleth in [this article](https://doi.org/10.1007/s11191-015-9749-7) of Redish and Kuo, where it is discussed further.