Number forms are a fancy way of talking about how people imagine numbers in their minds. Imagine counting to five on your fingers. You probably picture the number one in a certain spot, maybe your thumb. Each number has its own special spot in your imagination.
Some people imagine numbers in a more complex way. For example, they may imagine numbers as shapes or objects in different locations. This happens naturally for some people, and they may not even realize they are doing it.
These patterns of imagining numbers are called number forms. Scientists are still trying to understand why some people have number forms, and what causes them. Some studies have shown that people with number forms tend to be better at math, but it is not clear if number forms actually help people do math better.
Overall, number forms are just one interesting way that people think about numbers!