Keith Devlin writes: All the mathematical methods I learned in my university math degree becamse obsolete in my lifetime.
Dr Keith Devlin is a mathematician at Stanford University in Palo Alto, California. When I graduated with a bachelors degree in mathematics from one of the most prestigious university mathematics programs in the world (Kings College London) in 1968, I had acquired a set of skills that guaranteed full employment, wherever I chose to go, for the then-foreseeable future—a state of affairs that had been in existence ever since modern mathematics began some three thousand years earlier. By the turn of the new Millennium, however, just over thirty years later, those skills were essentially worthless, having been very effectively outsourced to machines that did it faster and more reliably, and were made widely available with the onset of first desktop- and then cloud-computing. In a single lifetime, I experienced first-hand a dramatic change in the nature of mathematics and how it played a role in society. The shift began with the introduction of the electronic calculator in the 1960s, which rendered obsolete the need for humans to master the ancient art of mental arithmetical calculation. Over the succeeding decades, the scope of algorithms developed to perform mathematical procedures steadily expanded, culminating in the creation of desktop packages such as *Mathematica* and cloud-based systems such as *Wolfram Alpha* that can execute pretty well any mathematical procedure, solving—accurately and in a fraction of a second—any mathematical problem formulated with sufficient precision (a bar that allows in all the exam questions I and any other math student faced throughout our entire school and university careers). So what, then, remains in mathematics that people need to master? The answer is, the set of skills required to make effective use of those powerful new (procedural) mathematical tools we can access from our smartphone. Whereas it used to be the case that humans had to master the computational skills required to *carry out* various mathematical procedures (adding and multiplying numbers, inverting matrices, solving polynomial equations, differentiating analytic functions, solving differential equations, etc.), what is required today is a sufficiently deep *understanding* of all those procedures, and the underlying concepts they are built on, in order to know when, and how, to use those digitally-implemented tools effectively, productively, and safely.
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