Mathematics Atlas
Things this atlas does not know. Each entry is a question that specialists
have posed and not settled, recorded with what would actually resolve it and which
expertise the answer needs.
These are kept deliberately, rather than quietly omitted. An atlas that shows
only what it is sure of implies a confidence it has not earned, and the gaps are often where
the interesting work is. Several sit exactly where two fields fail to meet: identifying the
hyssop of the Hebrew Bible needs a botanist and a philologist of Biblical Hebrew, and neither
one settles it alone.
Grouped by the part of the atlas the question sits in. Start here if you know the territory better than the technique.
Not Yet Classified 4
Zimbabwe Hyperinflation
What was Zimbabwe's exact peak month-on-month hyperinflation rate?
Open Zimbabwe Hyperinflation
Why It Is Open Zimbabwe stopped publishing official inflation statistics in mid-2008, at the worst of the crisis, so every subsequent figure is a reconstruction. Independent estimates for the November 2008 peak range from tens of millions of percent to the often-cited 79.6 billion percent month-on-month (89.7 sextillion percent year-on-year) figure derived by Hanke and Kwok from private price data, itself contested on methodological grounds by other economists who reconstructed the series differently.
What Would Settle It A recovered, complete run of contemporaneous retail price data for the peak months, independently reconstructed by more than one research team using the same methodology, would let economic historians agree on a single figure rather than a range spanning several orders of magnitude.
Expertise Needed Monetary economics, economic history
Question posed in
Hyper Inflation in Zimbabwe, article text.
Minimum Wage
Does a Higher Minimum Wage Reduce Low-Wage Employment?
Open Minimum Wage
Why It Is Open David Card and Alan Krueger's 1994 study of New Jersey and Pennsylvania fast-food employment found no negative employment effect from a minimum-wage increase, contradicting the standard supply-and-demand prediction that a binding wage floor prices low-skilled workers out of work. Neither side has been able to close the dispute: later meta-analyses and replications split along methodological lines, with studies using different comparison groups, time windows and industries reaching different conclusions, so the disagreement persists among credentialed labor economists rather than resting on a factual gap either side denies.
What Would Settle It A body of quasi-experimental evidence, across enough minimum-wage changes, industries and regions, and using a comparison-group design both sides of the methodological debate accept, converging on a consistent sign and magnitude for the employment effect.
Expertise Needed Labor Economics
Question posed in
Wikipedia, Minimum wage, Debate over consequences.
Laffer Curve
Does cutting tax rates below their observed real-world range actually raise government revenue, as the Laffer Curve implies is possible?
Open Laffer Curve
Why It Is Open The Laffer Curve's logic (zero revenue at 0% and 100% tax rates, so some intermediate rate maximizes revenue) is not itself disputed, but whether actual, real-world tax rates sit on the curve's revenue-losing side, so that a cut would pay for itself, is a live empirical dispute between supply-side economists and the mainstream consensus. A 2012 University of Chicago IGM Forum survey of leading economists found essentially no support among them for the claim that cutting federal income tax rates would raise revenue within five years.
What Would Settle It A settled empirical estimate of where actual tax rates sit relative to the revenue-maximizing point, which depends on contested behavioral-response (elasticity) estimates that differ sharply between supply-side and mainstream public finance economists.
Expertise Needed Public finance and empirical tax policy economics
Question posed in
Wikipedia, Arthur Laffer, Criticism and Controversy.
Georgism
Can the unimproved value of land be assessed separately from the buildings and improvements upon it accurately enough, in practice, for a land value tax to work as Georgism's theory intends?
Open Georgism
Why It Is Open Georgism's theoretical case for taxing land value alone rather than improvements is not itself disputed among economists who accept it (see the Friedman and Stiglitz endorsements recorded on the mint), but assessors in practice must separate a parcel's bare land value from the value its buildings add, a split that is straightforward for vacant land and genuinely difficult for a developed urban parcel where land and structure value are entangled in the observed sale price. Jurisdictions that have tried split-rate or pure land value taxation, Pennsylvania cities among the most studied cases, report persistent assessment disputes and administrative cost as practical obstacles distinct from the underlying economic theory.
What Would Settle It A mass-appraisal methodology proven to separate land value from improvement value at the accuracy and low cost a nationwide or citywide land value tax would require, tested against jurisdictions that have actually implemented split-rate taxation over a long enough run to compare outcomes.
Expertise Needed Public finance and real estate / land valuation economics
Question posed in
Wikipedia, Georgism, Practical objections.