mathiness", i.e. math with dubious assumptions and ideological aims, in particular in models with perfect competition. Writting about "Prescott is No Solow, No Becker", he points out:
"Remember that the motivation for the theory is that for these authors, perfect competition is the ultimate non-negotiable, more sacred even than micro-foundations. If this were a Hotelling model of location or a Krugman model of spatial location, I’d have some way to try to make sense about how “some measure of people defines a market.” But in the formal mathematical model of perfect competition that the authors are using, this sentence means nothing"
I confirm that all the story in Hotelling and Krugman is indeed in the link between population and market (I really don't know concerning McGrattan and Prescott (2010), I will work on that) but if mathiness is about crazy assumptions and lack of rigor in results then Hotelling and Krugman are not exempt of review. The initial model of Hotelling is wrong - see d'Aspremont, Gabszewicz and Thisse (1979, Econometrica) - and the model of Krugman on location choices is a "toy model" with "aggressively unrealistic assumptions" according to Fujita, Krugman and Venables (1999). Furthermore this model is not totally satisfactory on the mathematical side, for instance the analysis on existence and stability of equilibria in Krugman (1991, JPE) is lacking (see Robert-Nicoud (2005, JEG) for rigorous proofs). BUT assumptions and results in Hotelling and Krugman are just great. Imperfect competition and transportation costs are the heart and soul of the tradeoff that leads to agglomeration.
From that point, I think that what matters for Romer is not the use of math per se, but the meaning of these math. By promoting models written by Hotelling, Krugman but also by Solow and Becker, he demonstrates its preference for toy models with clear messages (this clearly written in Romer (1992, P66) see also Chris House). I also love these models.
But to get a job, a Ph-D student has to publish papers. I just put here the tweet of Jon Hersh illustrating this pressure.
Mathematics produces, not only (and not always), knowledge in economics, it is also a signaling tool.
Maybe I am wrong (and I hope I am), but I am not sure that the job market (at least in my field) is still looking for simple models like those developed by Hotelling, Becker, Solow or Krugman. For instance, the New Economic Geography of Krugman is dying, it is just impossible to publish a paper in a top-5 journal with the basic assumptions of this literature. Quantified models are wanted and it is often asked to both develop multi-country models and to provide analytical results. Quite logically, this (sometimes) leads to consider models with perfect competition because they are more tractable. An example of this "come back to perfect competition" is the paper of Allen and Arkolakis (2014, QJE) where authors use old tricks but "determine the spatial distribution of economic activity on any surface with (nearly) any geography".
To conclude, diversity of ideas and methodologies must be represented in top journals and there is some journals where it is the case (the JEG is a good example of diversity with publications by economists and geographers). Because it is hard to identify mathiness, and thus to fight against this bad equilibrium, we must consider multiple equilibria where many ecosystems emerge. Obviously the other solution regarding the market of lemons described by Romer is to remove informational problems by employing reviewers that detect and denounce more systematically the ideological devil... the organization of the delegated expertise must be improved (if you want to play with a model on that topic, start with Gromb and Martimort (2007, JET)). Good luck!
PS: The timing of this welcomed rage against mathiness is an enigma for me. Romer has discussed the paper of Prescott in 2007, this paper has been published in 2010 and we are in 2015...
Edit [22/05/15]: A huge number of researchers and journalists have discussed the "mathiness" of Romer (DeLong 1 & 2, Farmer, Williamson, Smith, Fox, Wren-Lewis, Andolfatto, Gans and PK has presented a similar point of view here before Romer) but the best piece comes from Dietz Vollrath who clearly explains what are the implications to assume monopolistic or perfect competition in growth models.