The 15-minute city promises that every resident can reach essential services — including work — within 15 minutes. The concept is appealing. The mathematics is unforgiving.
Combining urban geometry with actual firm-size distributions reveals a fundamental lower bound on commuting times that holds regardless of planning choices or transport technology (arXiv:2603.12122). When employment is sufficiently concentrated geographically — a few large employers rather than many small ones — no rearrangement of workplaces can guarantee universally short commutes. The bound is not about infrastructure or policy. It is about the spatial mathematics of distributing workers to concentrated employment.
The critical threshold is employment concentration. Below it, the 15-minute city is achievable in principle. Above it, some workers must travel far no matter how cleverly the city is designed. The concentration threshold depends on the firm-size distribution, which follows heavy-tailed patterns in real economies — a few very large employers and many small ones. The large employers create obligate commuting distances for their workers.
Testing on Paris and surrounding areas confirms that universal 15-minute commutes would demand economic restructuring — fragmenting large employers into smaller, distributed units — or differentiated mobility strategies that accept longer commutes for some workers while minimizing them for others.
The right question is not “can we build a 15-minute city?” but “given our economy, what is the minimum achievable x for an x-minute city?” The answer is a property of the economic structure, not the urban plan.