Using warnings or launching perl with the -w switch would have told you that there is a problem:

> perl -w tmp.pl
Possible unintended interpolation of @gmail in string at tmp.pl line 5
+.
Name "main::gmail" used only once: possible typo at tmp.pl line 5.
Terminating on signal SIGINT(2)
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... and using strict would have prevented that error completely as it forces you to predeclare variables:

> type tmp.pl
#!/usr/bin/perl
use strict;

while (<>) {                   # take one input line at a time
    chomp;
    if (/(dmathis@gmail.\w+)/) {
        print "Matched: |$`<$&>$'|\n";  # the special match vars
    } else {
        print "No match: |$_|\n";
    }
}

> perl -w tmp.pl
Possible unintended interpolation of @gmail in string at tmp.pl line 6
+.
Global symbol "@gmail" requires explicit package name at tmp.pl line 6
+.
Execution of tmp.pl aborted due to compilation errors.
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You need to escape the @ because Perl interprets this as the start of the name of an array:

...
    if (/(dmathis\@gmail.\w+)/) {
...
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