Delete comment from: Computational Complexity
Gil, the total MathSciNet database has (apparently) 2723609 entries, of which 874 reviewer texts include the word "breakthrough". Thus (very roughly) about one review in 3000 uses the term "breakthrough".
My own (informal) opinion is that "breakthrough" is *not* a devalued term, that is, the mathematics community really is producing breakthrough results at an accelerating pace, precisely as one would hope and expect from an increasing population of mathematicians drawing inspiration from an increasing body of literature.
On the other hand, as one might expect, some articles suggest that having more mathematical breakthroughs may not be an unalloyed good. For example, Natali Hritonenko and Yuri Yatsenko argue in "Technological innovations, economic renovation, and anticipation effects" (MR2739540) that foreknowledge of impending breakthroughs can act to inhibit rational economic investment.
Hmmmm … does the Hritonenko-Yatsenko mechanism create a mathematical tragedy of the commons? If mathematicians were to cease advertising "breakthroughs" — and scientists, engineers and physicians followed suit — would the global recession swiftly end, as investors regained their confidence in existing business models? ;)
Obviously the relation between breakthroughs, enterprise, and investment is more subtle than *that*!
Dec 9, 2011, 1:06:03 PM
Posted to What is a Breakthrough?