They’re partly right. The clustering of Democrats in cities does indeed give the Republicans an edge. But it’s a much smaller advantage than the turbo-boost the current map provides, as the Duke paper demonstrates. The main tool in the Duke paper is a method called the “Markov chain Monte Carlo” algorithm. Starting from the current Wisconsin district map, it makes a sequence of random changes, swapping wards from one district to an adjacent one, carrying out a “random walk” through the set of all possible maps. Completely unconstrained changes would create crazy-looking districts, so it weights its changes in favor of traditional districting criteria.

Few if any of these maps provide the Republicans the firewall against a Democratic electorate that the Wisconsin district map does. In other words, the map is an “outlier” — so far outside the ordinary run of things that it can’t be mistaken for a map without partisan purpose. It’s an outlier in another way, too: Research by the political scientist Jowei Chen suggests that the Wisconsin district map does much worse on traditional districting criteria than neutral maps do, despite the Wisconsin Constitution’s requirement that districts be “in as compact form as practicable.”

Outlier detection is a critical part of data analysis, and mathematicians have gotten really good at it by now. That’s the good news about advanced computation: You can use it to make electoral mischief, but you can also use it to detect and measure that mischief. It’s not math versus democracy; it’s math versus math, with democracy at stake.

If the Supreme Court sides with the three-judge panel that blocked the Wisconsin map, some liberals foresee an end to gerrymandering, while some conservatives imagine a districting process that is the purview of legislatures being completely usurped by the courts. Both sides of Gill v. Whitford agree: This is a momentous case with major implications for American democracy.

But what if it’s not? The panel’s standards for determining impermissible gerrymandering are hard to meet except in the most egregious cases. Judges empowered by an anti-gerrymandering precedent from the Supreme Court will blunt the worst cases, but won’t end gerrymandering. There will be many cases, maybe most of them, where it’s impossible, no matter how much math you do, to tell the difference between innocuous decision making and a scheme — like Wisconsin’s — designed to protect one party from voters who might prefer the other.