Andrew’s Favorite Mathematical Writing Tip
One of my favorite math writing tricks is to keep big chunks of math on their own lines. It can be hard to read math when it’s in-line with English prose. Plus, when the math is on its own lines, it’s easy to scan down the page and see how equations and formulas evolve.
As an example, here’s a narrative description of solving a quadratic equation, involving both mathematical symbols and also English sentences, but with the math and the English all in-line:
We have the equation \(x^2+5=7x\). To solve it, we’ll first move everything to one side, so we get \(x^2+5-7x=0\), or just \(x^2-7x+5=0\). Then we can apply the quadratic equation. Without simplifying, this gives us \(x=\frac{-(-7)\pm \sqrt{(-7)^2 -4\!\cdot1\cdot5}}{2\!\cdot\!1}\). We can simplify this a bit. \((-7)^2\) is \(49\), and \(4\cdot5\) is \(20\), so this becomes just \(x=\frac{7\pm \sqrt{49 - 20}}{2}\), or just \(x=\frac{7\pm \sqrt{29}}{2}\).
Here’s the same exact text, but written so that the really big chunks of math are on their own lines:
We have the equation: \[x^2+5=7x\] To solve it, we’ll first move everything to one side, so we get: \[x^2+5-7x=0\] Or just: \[x^2-7x+5=0\] Then we can apply the quadratic equation. Without simplifying, this gives us: \[x=\frac{-(-7)\pm \sqrt{(-7)^2 -4\!\cdot\!1\!\cdot\!5}}{2\!\cdot\!1}\] We can simplify this a bit. \((-7)^2\) is \(49\), and \(4\cdot5\) is \(20\), so this becomes just: \[x=\frac{7\pm \sqrt{49 - 20}}{2}\] Or just: \[x=\frac{7\pm \sqrt{29}}{2}\]
See how much easier it is to read??? Again, the exact same text, just laid out differently on the page.