## Section 0.2 Manipulating Numbers

¶This section is included because “it's not crazy until someone says it's crazy”; and hence I would like now to point out that some beliefs about high school mathematics *are crazy.*

What's the upshot? Well, you might like to know that graduate students *also* have to go through similar “spirals of understanding”, so you're in good company. The mathematics question-answer site on stackexchange.com has even kept a running list `https://mathoverflow.net/questions/23478`

of such misconceptions, based off a post from the british mathematician Timothy Gowers in 2015.