| | Devlin's Angle |
Answer: None.
That's not a conclusion or a hypothesis. It's an observation. Many -- perhaps most -- of the CEOs of top companies have virtually no mathematical knowledge. If their company needs to have someone with mathematical expertise, such a person will be hired.
What can be extremely valuable in business, however, is the ability to dig beneath the surface of a problem to see what the real underlying issues are, and the capacity for clear and logical thought. And learning mathematics provides an excellent way to develop that capacity.
Just as the 1997 DOE Riley report showed that completion of a formal mathematics course in high school results in better performance at college whatever major the student chooses to pursue, so too completion of one or two college mathematics courses seems likely to confer benefits to practically anyone, regardless of their particular career. For the individual who goes into business, doubtless the main benefit of doing some college mathematics is the capacity for clear, precise thinking that is the bedrock of mathematics.
My own research having brought me into regular, close contact with a number of people in business over the past fifteen years, I have observed that nowhere do you find greater fuzzy thinking than when it comes to dealing with information.
To take just one example, the words data, information, and knowledge are often used interchangeably, and opinions differ as to whether knowledge management is about managing technology, managing people, or both.
Does this matter? You bet it can. How many times have you heard about a company that introduced a new computer system to improve its information management, only to discover that, far from making things better and more efficient, the new system led to scores of new problems that had never arisen with the old way of doing things. The new system is capable of providing vastly more information than was ever available before, but it is hard if not impossible to extract that information, or it's the wrong kind, or presented in the wrong form, at the wrong time, or delivered to the wrong person. Or there is simply too much of it for anyone to be able to use. What used to be a simple request over the phone becomes a lengthy battle with a seemingly uncooperative computer system, taking hours or even days, and eventually drawing in a whole host of people.
Why does this happen? The answer is that, despite all that we hear about living in the Information Age, what we are really living in is an age of information technology, or more precisely a collection of information technologies. We do not yet have an established science of information. As a result, we do not yet have the ability to properly design or manage the information flow that our technologies make possible.
The engineers who produce our buildings, bridges, automobiles, aircraft, household appliances, and communications technologies base their work on the solid foundation of decades and even hundreds of years of scientific progress in physics and other sciences. But the people who design and manage our information systems (which may comprise people or machines or a combination of the two) have to work with much shakier foundations.
Since 1987, I've been attached to Stanford University's Center for the Study of Language and Information, involved in a research project that sets out to analyze information as a theoretical concept. Though we are nowhere near having a "science of information" akin to, say, physics -- indeed, it's not clear there can be such a science -- the research work has led to some clarification of the basic issues involved.
For instance, here is a useful way of thinking about the difference between data, information, and knowledge:
Data is what newspapers, reports, and "computer information systems" provide us with. For example, a list of stock prices on the financial page of a newspaper is data.
When people acquire data, and fit it into an overall framework of previously acquired information, that data becomes information. Thus, when I read the list of stock prices in the newspaper, I obtain information about various companies. What allows me to acquire information from the data in the newspaper is my prior knowledge of what such figures mean and how the stock market operates.
When a person internalizes information to the degree that he or she can make use of it, we call it knowledge. For example, if I know how to buy and sell stocks and am familiar with some of the companies whose stock values are listed in the newspaper, the information I obtain by reading the figures can provide me with knowledge on which to trade stocks.
This simple analysis is not rocket science. Hey, it's not even science. Nor is it mathematics. What it is an application of clear thinking designed to establish exactly what a number of key terms mean. Mathematicians and scientists do this kind of thing as a matter of routine.
But, I'll tell you something: Many other people don't think that way. Even some very smart people. Indeed, many people find this way of thinking very alien.
After witnessing many times the enormous confusion that reigns in the world of information/knowledge management, and examined some of the problems that result from the installation of a new "information system", about a year ago I was motivated to set down on paper what I thought were some basic, common sense ideas about information. Those common sense ideas were based on some of the work that had been carried out at CSLI. But I deliberately cut out any of the deep philosophical issues or the mathematical modeling, and presented the basic ideas using simple, everyday examples, taken from the real business world.
The result -- the book InfoSense -- was just published by W. H. Freeman. If you are a regular MAA Online reader, you'll probably hate it -- at least, you will if you are expecting a mathematics book. If so, then don't think of buying it. It wasn't written as a mathematics book, nor was it written for people used to thinking mathematically.
Nevertheless, you might find it informative to glance at the book. Why? Well, when you do look through the pages (it's quite short), remember this one thing. Though many people have told me they like it, and find it very helpful, I have also been informed that it's "too technical" and "very heavy going in places". I am sure that no regular reader of MAA Online would make such a remark. Indeed, I doubt that anyone who had completed a high school geometry course could react that way.
And that's my point.