I just finished reading Steven Strogatz' book Sync. It's a fascinating story of the use of mathematics to understand our world, and he tells the story without a single equation, as far as I recall.
What sticks with me now are two impressions.
First, his work re-emphasizes the utility of computer simulation as a way of gaining understanding. Its application isn't limited to the physical world; simulation can help explain issues we face in the business world, too. That's not news, but it's good to see the reminder, and it's good to see it from a variety of mathematical domains.
Second, it was interesting to read of his application of such techniques to a problem I mentioned in a prior entry: of what use are networking tools such as LinkedIn? As he and Duncan Watts explain by means of a simulation in Collective dynamics of 'small-world' networks , it takes only a small number of "short circuits" between otherwise loosely-connected parts of a large network to turn it into a "small world" in which the distance between any two nodes (people, companies, etc.) is greatly reduced from the purely random case. This relates to how we can improve word-of-mouth selling (and, on a less upbeat note, how communicable diseases spread). So, maintain your contacts with friends and close acquaintances, but be sure to keep in contact with at least a few who aren't in your day-to-day network; you might be surprised where they lead.