What (Some) Mathematicians Create Alongside Wrong Proofs Inwards Journals

Paul Romer has a followup article close "post-Real" economics. I only wanted to launch a digression roughly his comments close mathematicians in addition to wrong proofs. Although at that topographic point powerfulness hold upwards some useful conclusions for academic economics, the problems faced past times the acre are to a greater extent than hard than the number of wrong proofs.

Romer writes:

This is only post-real Calvinball used equally a shield from criticism. Imagine someone maxim to a mathematician who finds an mistake inward a theorem that is false,  “you can’t criticize the proof until y'all come upwards up alongside valid proof.” 

(As an aside, I should regime notation that concord that DSGE macro stinks, in addition to I accept used the Calvinball metaphor myself.)

My academic sense was inward Control Systems Theory, a branch of applied mathematics. I ran into a example where I was an anonymous referee for a submitted paper. The novel newspaper contained Theorem B, in addition to Theorem B cited Theorem A within its proof. Meanwhile, Theorem A was contained inward some other newspaper that was published inward the #2 mag inward the field.

The outcome looked dubious, in addition to I managed to disprove Theorem A within 10 seconds of picking upwards the book that held it. (Luckily, the book opened unopen to the page alongside the alleged "proof.") That was a personal speed record, in addition to it was the most entertaining minute of my academic career.

I was able to write a brusque reply rejecting the paper, explaining that the cited theorem was inward fact incorrect; thus at that topographic point was no ask to pursue the novel newspaper without a full re-write. Since it was someone else who made the master copy error, I was able to hold upwards quite gracious to the authors. (Although I doubtfulness that made them whatsoever happier.)

And that was effectively the halt of it. I did non write an anguished populace missive of the alphabet to the editors of the #2 journal, telling them that they published a clunker of a paper. I only ignored its being when I did literature surveys. (I discovered that at that topographic point was a modest sub-literature built roughly Theorem A.) If anyone objected to my ignoring that paper, I would accept quietly sent them the explanation.

I would non tell that I was told to ignore the being of dubious papers, but that was my impression that was how the serious mathematicians inside command systems dealt alongside the problem. (The lineament of mathematics inside command systems was uneven, equally the academics ranged from engineers to people alongside doctorates inward pure mathematics.) From the outside, it may accept looked similar it was a cabal that was playing favourites, but the reality is that at that topographic point is no build clean agency to retract papers from a mag without making a lot of people hold back foolish.

Pure mathematicians belike accept a to a greater extent than rigorous mental attitude inside their journals, but at the same time, at that topographic point are presumably non a lot of wrong proofs institute there.

An Application To Economics?

If y'all are a researcher, in addition to y'all intend a outcome is wrong -- in addition to y'all tin seek out this -- y'all should ignore its existence. If someone complains, y'all only transportation them the proof that the outcome is incorrect. That should hold upwards the halt of the story.

Unfortunately, macro is non inward this position; at that topographic point are no standards of correctness that check to that of mathematics. There are problems inward the mathematical modelling, in addition to model predictions are routinely contradicted past times data. If real strict standards of rigour were applied, the carnage inward the post-war literature would hold upwards spectacular. (And yes, the post-Keynesian literature would probable hold upwards hammered equally well.)

Since a wholesale deletion of the existing literature is non going to travel on equally a outcome of the institutional structure, the entirely agency frontward is to promise that a novel methodology tin appear, allowing researchers to ignore the being of the dodgy electrical flow literature. This is going to hold upwards much easier for heterodox economists to achieve, equally their reputations are non based upon that literature. That said, they are upwards against the institutional factors that favour the condition quo.

(c) Brian Romanchuk 2016