The Guardian has a great article on a new startup that's using algebraic topology to analyze data sets. Just goes to show you that you never really know how theory will get brought into the real world. From the article:
Modern business intelligence methods allow analysts to drill down into complex databases and find the answers to predetermined questions, but the emergent field of data science is concerned with finding the questions that should be asked of huge and often unstructured data in order to yield otherwise invisible results.
Using topology, data scientists can do exactly this, running algorithms that carry out what is effectively blind analysis of a database to reveal the inherent patterns therein, rather than showing correlations between preselected variables.
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