Both Uses of

correspond
in
Outliers

At the age of twelve, he began corresponding with local geologists about rock formations he had seen in Central Park, and he so impressed them that they invited him to give a lecture before the New York Mineralogical Club.
Chpt 4 *

corresponding = exchanging letters or messages

They can hold more numbers in their heads and do calculations faster, and the way fractions are expressed in their languages corresponds exactly to the way a fraction actually is, and maybe that makes them a little more likely to enjoy math, and maybe because they enjoy math a little more, they try a little harder and take more math classes and are more willing to do their homework, and on and on, in a kind of virtuous circle.
Chpt 8 *

corresponds = matches

Definitions:

(1) (correspond as in: corresponding time period)
connect or fit together by being equivalent, proportionate, or matched

(Two things are equivalent if they have the same or very similar value, purpose, or result.)
(2) (correspond as in: corresponding by email)
communicate -- typically by writing letters or email

A corresponding secretary is an officer of an organization who is responsible for managing the organization's correspondence and keeping a record of it.
(3) (correspondence as in: a correspondence course)
done from afar

For example, a corresponding member or a correspondence course.

This sense of corresponding arose because people who lived in distant cities and could not be present for meetings, could communicate by sending written communications.
(4) (correspondent as in: foreign correspondent of the paper)
a reporter or other representative -- typically from a foreign country or with a particular expertise