Here are some possible ways for finding the email / contact information for a potential reviewer (or any researcher, really):

 1. Just try looking them up in a search engine. Of course, this is less effective if they have a common name, in which case it might not be obvious that you found the right person. Also, sometimes you can find out-of-date information.
 2. Look up their latest publications or preprints. If they're recent, there's a good chance the affiliation information is up-to-date. If they provide a correspondence address within the paper you're already done. If not, look them up at the website of the institution/department they're affiliated with. Often you'll find their email that way. You can also try seeing if a search engine finds anything when searching for their name and institution. Perhaps their group page is not yet linked from their department.
 3. Since your field is math, there is a good chance they have a preprint on arXiv. Under the "Submission history" there is a "view email" button where you can check which address the preprint was submitted from, which may be of use. (Other preprint repositories may have corresponding functionality.)
 4. Ask others, e.g. their colleagues and coauthors. This can be the only way of finding some researchers who have retired or otherwise left academia. Whether these researchers are willing to accept review invitations is another question.
 5. As suggested by Richard Erickson, you could also consult professional society directories. Many such societies provide contact information of members through online portals. However, note that this information is sometimes only accessible to other members.

Finally, given that many editors prefer not blindly trusting author-provided contact information for suggested reviewers (or even inviting author-suggested reviewers) in the first place, leaving the field blank might be a better option than spending a lot of time looking up someone's email address. On the other hand, some journals make providing this information mandatory, so it varies.