From Bioinformatics.Org Wiki
Mathematical biology is easier to distinguish from bioinformatics than computational biology. Mathematical biology also tackles biological problems, but the methods it uses to tackle them need not be numerical and need not be implemented in software or hardware. Indeed, such methods need not "solve" anything; in mathematical biology it would be considered reasonable to publish a result which merely establishes that a biological problem belongs to a particular general class.
The distinction between bioinformatics and mathematical biology was illuminated by an email I received from Alex Kasman at the College of Charleston. According to his working definition, he distinguished bioinformatics which (under the tight definition at least)...
"...seems to focus almost exclusively on specific algorithms that can be applied to large molecular biological data sets..."
...from mathematical biology which...
"...includes things of theoretical interest which are not necessarily algorithmic, not necessarily molecular in nature, and are not necessarily useful in analyzing collected data."