When I was taught math, the focus was mostly on the “how”:

**How**to multiply numbers.**How**to work with fractions.**How**to use calculus.- etc..

But even more useful is to know the **when**:

**When**to multiply numbers.**When**to work with fractions.**When**to use calculus.- etc..

Knowing how to do something is useful, but it’s just knowledge of one tool.

For example, take a hammer. It’s nice to know how to bang in a nail without sending yourself to the hospital, but not all situations require a hammer. To select the best tool for the job, we need to know “when” each tool should (or shouldn’t) be used.

Especially nowadays, where computers can solve so many mathematical problems for us, knowing “when” allows us to navigate choice, and select between multiple tools. Once we select the right tool, then it’s easy to find the resources to teach us the “how” part.

## Math catalog

I ran a bunch of Google searches for “when should I use x?”, and collected them into a list:

### Addition

Joining multiple items together.

### Subtraction

Removing items from a set.

### Multiplication

Repeating a set of items.

### Division

Breaking a set of items into parts.

### Fractions

Working with partial units.

### Exponents

Abbreviating large numbers.

### Equation & Formulas

Describing how multiple variables relate to each other.

### Geometry

Visualizing math with drawings.

### Logarithms

Scaling numbers.

### Linear algebra

Working with sets of equations.

### Logic

A language for reasoning.

### Combinatorics

Finding all possible outcomes.

### Number theory

Discovering relationships between numbers.

### Calculus

Finding aproximate solutions to equations.

### Statistics

Gathering, reviewing, analyzing, and drawing conclusions from data.

### Machine learning

Extracting algorithms from data.