The scientific approach: you have a hypothesis and test it. Modeling: approximate reality by mathematical expressions. You are lucky if you can transform your model into a closed form solution. They are usually easy to interprete and compute. If not you apply numerical schemes. Advanced numerical schemes need to be accurate and robust related to noisy input. The other extreme. Extract models from data. We have sensors everywhere, "Infinite" storage, clouds of computers. Wired magazine takes an extreme position in The End of Theory The Data deluge makes the scientific method obsolete.
Far from that, IMO. But, in some sense one can understand mathematics as data compression (those who correctly state mathematics-is-a-culture-technique will disagree). And in the petabyte scale, information is often a matter of multi-dimensional order. But still you need analytical tools, which at least have "learned" from mathematics. However better data and better analytical tool together with plugged mathematics might win the day. Remember? The AND effect.
What we do in machine learning and data mining: mlf
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