With Shapiro-Wilk and Pearson’s rho in statistics, how was it developed? Like constantly? How do we determine the right formulas for a certain statistics, certain calculus, etc?

In: 1

Math is developed in roughly two different ways:

1. Math is useful because it helps us solve real-world problems. Sometimes math is developed because someone has an interesting problem they don’t know the answer to – they can express the problem using math but they don’t know how to solve for the right answer. That often leads to new areas of discovery.

2. Other times, mathematicians ask questions about the math we already have, like “how could we generalize X to all real numbers, or negative numbers?” – that often leads to interesting problems and solutions that don’t have real-world applications right away. But sometimes the real-world applications come later (and sometimes they don’t.)

In both cases, mathematicians write proofs that their new techniques work. Other mathematicians adopt these techniques and ideas if they believe the proof and if it works in practice.

Sometimes ideas are flawed; if it turns out a new technique doesn’t always give the right answer, other mathematicians will point out the flaws and fix it.

Ideas mostly spread through mathematicians publishing papers and giving talks at math conferences. There are enough mathematicians in the world that new discoveries are pretty “constant”, but any given mathematician probably only writes one or two papers a year.

Math builds upon itself. First there was basic addition. Then multiplication and division. Zero was developed at some point. Algebra came along and allowed for a whole bunch of new types of math. From there we got calculus, which also opened up whole new doors. At this point, new math was often developed/discovered to be able to explain new, more complicated things, like big discoveries in the field of theoretical physics. Math continues to this day to build on all the math that came before it.