21 April 2004On the Importance of Technique
On 27 November 2003, I was using a free desk at deCODE Genetics in Reykjavík, ready to deliver a talk based on the paper The Complexity of Checking Consistency of Pedigree Information and Related Problems. After browsing through the slides, and while waiting for lunch time to arrive, I idly looked at the bookshelf next to me, and picked up a copy of the book Random Graphs (second edition) (CUP, 2001) by Béla Bollobás. While skimming through the preface of the book I was struck by the following sentence on page xv:
"....proofs are often more important than results; not infrequently the reader will derive more benefit from knowing the methods used than from familiarity with the theorems."
This sentence reminded me of what Matthew Hennessy sometimes told me when I was one of his doctoral students at COGS, viz. that often the importance/contribution of a paper lies in the technicalities. (I hope that Matthew does not mind me quoting freely from my chest of memories of our conversations!)
An often quoted passage from G.H. Hardy's A Mathematician's Apology also reads:
"Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics."
In contrast to these views, I have the feeling that when we write in our referee reports that a paper is "technical", this opinion is often used to debase its contribution for the community. I, for one, would like to think that technical contributions to our field deserve a place in the literature, and should be respected. More and more, as hinted at in the aforementioned quotation from Béla Bollobás's preface, I find myself using the techniques used in the proofs of unique prime decomposition introduced in process algebra by Robin Milner and Faron Moller, proof strategies from very early papers by Matthew Hennessy on split-2 bisimilarity, and no doubt many others. Reductions on which the proofs of complexity results like the one I was talking about in Reykjavík are very much based on technical mastery --- which I have not developed to the degree I should have.
Yes, sometimes proof techniques are more important than the results they prove. I'll do my best to remember this when writing my next referee report tomorrow.
Last modified: Wednesday, 21-Apr-2004 16:05:48 CEST.