clipped from: www.maa.org   
doing mathematics makes use of nine basic mental abilities

1. Number sense

Child psychologists have demonstrated conclusively that we are all born with number sense

2. Numerical ability

The Sumerians are the first people we know of who used abstract numbers

3. Spatial-reasoning ability

ability to recognize shapes and to judge distances

4. A sense of cause and effect. Much of mathematics depends on "if this, then that" reasoning, an abstract form of thinking about causes and their effects.


5. The ability to construct and follow a causal chain of facts or events. A mathematical proof is a highly abstract version of a causal chain of facts.


6. Algorithmic ability. This is an abstract version of the fifth ability on this list.


7. The ability to handle abstraction

8. Logical-reasoning ability

9. Relational-reasoning ability

Much of mathematics deals with relationships among abstract objects