In theory, there's no difference between theory and practice, but in practice there is.
The Pure/Applied dichotomy in mathematics has had a strange history with some germane lessons for programmers. From Plato's Academy right through to the emergence of the "modern" universities in 19th century Europe, mathematics was free from such argufying divisions. The great mathematicians of this period were likely to have chairs in Natural Philosophy (such as Newton) or Astronomy (such as Gauss). Whether the mathematics had immediate practical applications or not, the general feeling was that the sums related to the real world and that useful deployments were not far away.
The Pure/Applied "split" appeared in the early 1900s for three basic reasons [1]. First, many branches of mathematics had expanded rapidly in "abstract" directions that seemed forever beyond the "commonsense" of daily life. (Non-Euclidean Geometry and Topology, for example.) Second, separate university mathematical departments were being formed where the donnish pecking order was "lofty non-trivial Pure" over "lowly trivial Applied." Thirdly, mainly under the influence of G. H. Hardy and the widespread revulsion to the horrors of World War I, the very inapplicability of these abstract domains was lauded (nay, lorded) over the deadly branches such as ballistics. Sciences such as engineering, with its boring calculations, and the chemistry, which had produced explosives and mustard gas, were beyond the pale.
To many, it was really a "pure/impure" dichotomy, although Felix Klein urged a less black/white approach. When a reporter asked Klein if he saw any conflict between pure and applied mathematics, he replied "No, the two are complementary." The reporter then approached David Hilbert and told him "Klein sees no conflict between pure and applied mathematics." Hilbert replied "Yes, he's right...the two have absolutely nothing in common." [2]
Then, quite suddenly, the walls started crumbling and the disputatious "us/them" attitudes were mollified. Again, the simplifying historians can point to key events behind this transformation. General Relativity borrowed heavily from Riemann's "impractical" non-Euclidean geometry to describe the real world, and Quantum Theory developed around the "purest" of group and operator theories. Perhaps the biggest crisis was Goödel's attack on the very foundations of mathematics. What? The simplest sets of axioms supporting arithmetic were forever either incomplete or inconsistent, and true theorems could be proved to be unprovable! Dave (Hilbert) and Johnny (von Neumann) were dazed, and the daze lingers on. Further, World War II was clearly a "just" war for the Allies, and the Hardy pacifist generation was replaced by scientists and mathematicians less squeamish about "applying" their skills in the anti-Fascist cause. In particular, and of interest to our fair trade, the ineffably abstract work of the 1930s in recursive enumerability and computability was harnassed by Turing and his Ultra-secret Bletchley team to break the unbreakable German Enigma codes. (Churchill claimed that this miraculous achievement shortened the war by 18 months.) Since then, the supreme irony, even Hardy's most aloof Number Theory (the Virgin Queen of all Queens) has become an every day tool for grubby encryptionists. One could also cite the use of topology in molecular biology and cosmological string theory.
So we seem to be back to the pre-dichotomy days when "pure" would surely become "applied" sooner or later. Yet, in the computing arena, we still hear of heated conflicts between academe and the "trenches." Many conferences devoted to "Software Engineering" (a term surely intended to tip the scale from pure to applied computing science) have failed to placate the "practitioner." One dealine-haunted programmer left such a meeting complaining "Far too academic!" Academic as an insult? Way to go Dijkstra, Knuth, Wirth, ... Just think (reader exercise) of the concepts, operating systems, languages, and tools, now taken for granted, that started life as arcane papers in obscure academic journals.
And finally consider this pure/applied, life-after-tenure bridge: Tony (Quicksort) Hoare, recently retired from academia, is joining the Microsoft Research Centre at Oxford.
References
[1] Solomon W. Golomb. "Mathematics After Forty Years of the Space Age," The Mathematical Intelligencer, Vol 21, No. 4, Fall 1999 (Springer-Verlag).
Stan Kelly-Bootle has been computing on and off since 1953 when he graduated from Cambridge University in Pure Mathematics and hacked on EDSAC I (the first true stored-program computer). He is a contributing editor for UNIX Review/Performance Computing, and a Jolt Judge for Software Development Magazine. His many books include 680x0 Programming by Example, Mastering Turbo C, Lern Yerself Scouse, The Devil's DP Dictionary, The Computer Contradictionary, and Unix Complete. Under his nom-de-folk, Stan Kelly, his songs have been recorded by Cilla Black, Judy Collins, the Dubliners, and himself. Stan welcomes email via skb@crl.com and his website http://www.crl.com/~skb/.