Broadly speaking, Bioinformatics can be defined as a collection of mathematical,
statistical and computational methods for analyzing biological sequences,
that is, DNA, RNA and amino acid (protein) sequences. Numerous projects for
sequencing the DNA of particular organisms constantly supply new amounts
of data on an astronomical scale, and it would not be realistic to expect that
biologists will ever be able to make sense of it without resorting to help from
more quantitative disciplines.
Many studies in molecular biology require performing specific computational
procedures on given sequence data, for example, simply organizing
the data conveniently, and therefore analysis of biological sequences is often
viewed as part of computational science. As a result, bioinformatics is
frequently confused with computational sequence analysis, which is somewhat
narrower. However, understanding biological sequences now increasingly requires
profound ideas beyond computational science, specifically, mathematical
and statistical ideas. For example, the protein folding problem incorporates
serious differential geometry and topology; understanding the evolution
of sequences is dependent upon developing better probabilistic evolutionary
models; analysis of microarray data requires new statistical approaches. Generally,
when one goes beyond algorithms and starts either looking for first
principles behind certain biological processes (which is an extremely difficult
task) or paying more attention to modeling (which is a more standard approach),
one crosses the boundary between computational science and mathematics/statistics.
These days many mathematicians are becoming interested
in bioinformatics and beginning to contribute to research in biology. This is
also my personal story: I am a pure mathematician specializing in several
complex variables, but now I work in bioinformatics as well