The Mathematical Hacker (2012)
&gt; Rather, mathematics is a tool for understanding phenomena in the world: the motion of the planets, the patterns in data, the perception of color, or any of a myriad things in the world that might be understood better by manipulating equations.<p>OK, so on one hand I love this point, and I&#x27;d love for it to be more broadly understood and appreciated, especially since my educational background is Mathematics and my CS has been practical, half self-taught, and frankly patchier than I&#x27;d like.<p>But:<p>&gt; Fortran-school programmers view the computer as an advanced tool for doing mathematics.<p>If we&#x27;re understanding &quot;mathematics&quot; as numerical&#x2F;analytical work + engineering (<i>maybe</i> applied mathematics) I can see this.<p>But the Lisp programmer talking in terms of recursive fibonnaci definitions is doing something that can quite adequately be described as mathematics, though it&#x27;s also mathematics to figure out the closed form and understand why you might or might not use it. Not sure if it&#x27;s mathematics to simply know a given closed form, though it&#x27;s something mathemeticians sometimes do.<p>And I&#x27;m more skeptical that Lisp programmers <i>don&#x27;t</i> do all this stuff: recursive demonstrations of fibonacci numbers are usually in textbooks <i>to teach recursion</i> rather than present an optimal way of computing fibonacci numbers, because it&#x27;s simpler than starting with dynamic programming, and you&#x27;re gonna need recursion to effectively solve <i>some</i> problems.<p>Not only that but a higher level, I think that a lot of developers (Lisp included) are already reaching into the very mathematical skills of domain modeling at one level or another -- often first with a different set of tools than a mathematician might bring, but a similar kind of work. If Miller&#x27;s overall point is that we all could do a better job with more of a mathematician&#x27;s tools, I agree, but then again as someone who came into industry with a math undergrad&#x27;s tools the utility of those might be overemphasized here.<p>Or maybe I just don&#x27;t appreciate what I already have.