How Mapping London Helped Stop A Cholera Outbreak

The following is an excerpt from Mapmatics: A Mathematician’s Guide to Navigating the World by Paulina Rowińska.

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Overcrowded, dirty and smelly, nineteenth-century London wasn’t a particularly nice place to be—at least not for humans. For germs, on the other hand, it was a paradise. In 1831, cholera arrived in England. Tens of thousands succumbed to this nasty disease, which causes vomiting, diarrhea, and, in turn, dehydration so severe that it leads to death, often within hours. As with other contagious diseases, cholera was attributed to bad air, which was commonly called “miasma.” Doctors thought that people caught the disease by inhaling the “cholera mist,” which seemed a logical proposition given that cholera often appeared in places that smelled terrible. Places like nineteenth-century London.

A young doctor by the name of John Snow first encountered cholera as a nineteen-year-old apprentice sent to treat the sick in a mining village close to Newcastle. There he meticulously documented his stay and started questioning the theory of miasma. Why, he asked, was it the coal miners who would mostly get sick, not people who worked or lived close to the smelly sewage dump? He also wondered how a disease that started in the intestines, not in the lungs or the throat, could be caused by inhaling bad air instead of ingesting poison. This line of reasoning wasn’t entirely correct, but he was on to something.

By the time of London’s third cholera outbreak in 1854, Snow had moved to the capital and had become an established physician. His reputation as an anesthetist was so solid that he had been asked to anesthetize Queen Victoria during her royal labors. In addition to developing modern anesthesia, Snow continued to study modes of transmission of cholera. In 1849, in his pamphlet On the Mode of Communication of Cholera, he argued that cholera is most likely spread through water contaminated with the bodily fluids of an infected person, although he admitted that his hypothesis needed more evidence. The examples he described in the book, however, were compelling.

In a brief period when London was cholera-free, Snow studied the areas that had suffered the most during the previous outbreaks. In one case, he looked at two rows of houses on opposite sides of the same alley. On one side, nobody had died of cholera; on the other side, the disease had taken dozens of victims. If bad air was the culprit, surely a narrow passage wouldn’t be a strong enough barrier to protect half of the inhabitants? A further investigation showed that on one side, the waste was flowing toward the well that provided the residents with drinking water, while on the other side, the waste was flowing away from the well. Snow realized it was the residents who drank contaminated water who got sick, and only they. Though he described it all in his pamphlet, it didn’t persuade the miasma believers— more evidence had to follow.

A Natural Experiment

Cholera didn’t discriminate: rich and poor, men and women, children and the elderly would suffer from the disease and quickly die. But why did some people contract it while others avoided it? Snow set out to find a pattern. After poring over municipal records, he noticed that the areas of London that got water from dif­ferent companies had vastly dif­ferent cholera death rates. Southwark & Vauxhall (S&V) and Lambeth water companies brought water from the same River Thames, so why would cholera kill 315 out of 10,000 residents of the areas supplied by the former, and only 37 by the latter?

The Thames was not only the source of running water for Londoners but also the endpoint for the London sewer system. While sewage still ends up in the river today, it’s thoroughly treated beforehand, which makes it safe for the environment. This wasn’t the case in the mid-nineteenth century: raw waste would flow straight into the river, carrying all the germs it had encountered along the way. S&V carried this water “in a most impure condition,” as Snow described it, straight back to its customers. Lambeth, on the other hand, had recently moved their facilities upstream from the sewage discharge. Lo and behold, areas served by Lambeth had a much lower cholera incidence than the ones with water provided by the competitor. While this strongly suggested to Snow that cholera was spread through contaminated water, it still wasn’t enough to convince the miasmatists. They pointed to other causes, arguing that residents of different districts were breathing dif­ferent air, and that their living conditions could vary in other ways too. For Snow, this argument didn’t, erm, hold water, and to prove it, he conducted possibly the first ever natural experiment.

To rigorously prove causation, it isn’t enough to show that dif­ferent outcomes (cholera death rates) coincide with dif­ferent factors (water suppliers), as there might be other factors in play. What if residents of S&V-supplied areas were poorer than the ones with water provided by the Lambeth company, and perhaps this could explain worse health outcomes? What if they were older on average, which would make them more prone to disease and less likely to survive illness? Snow’s observation proved only a correlation between water suppliers and cholera death rates; to prove causation, he needed more evidence.

He found a great opportunity in the area on the map where the two companies overlapped. In a part of South London, neighboring houses were supplied by dif­ferent companies, and this was the only relevant difference between such houses: “[e]ach Company supplies both rich and poor, both large houses and small; there is no difference either in the condition or occupation of the persons receiving the water of the dif­ferent Companies.” In other words, people similar in most aspects were assigned to one or other of the two water companies “without their choice, and, in most cases, without their knowledge.” If Snow managed to prove that his hypothesis held in this overlapping area, he’d have strong evidence that cholera spread through contaminated water. So, when cholera struck again in July 1854, he started knocking on some doors.

Armed with the addresses of cholera victims from the General Register Office, Snow went door to door, asking who supplied water in the house of each of the deceased—and he learned next to nothing. Often, the bills were paid by landlords who lived somewhere else, and even those who dealt with their bills themselves rarely remembered the name of the water company. (I, for one, wouldn’t be able to tell you the name of mine.) To save the mission, whenever the residents couldn’t provide him with the information, he’d ask for a water sample, in which he’d later measure the salt content. From this, he could identify the water supplier since he’d figured out that S&V water contained about four times more of this compound than Lambeth water.

The results were striking: by mid-August, thirty-eight out of the forty-four deaths in the area had occurred in houses supplied by S&V. With such promising data, Snow would have needed maybe just a few more weeks to finish up his grand experiment, as it’s called today—but then, disaster struck.

Detective Work

Snow had been pursuing his grand experiment for almost a year when the epidemic appeared in his neighborhood—Golden Square in central London’s Soho. Being a scientist, he must have been tempted to continue with his experiment—he was so close to proving his theory!—but the local outbreak was more pressing. He suspected that the culprit was the Broad Street pump, so his priority became to act fast to prevent more deaths. Although his examination didn’t find any impurities in the pump water, he couldn’t think of other reasons for the outbreak. So, he dropped the experiment and started knocking on doors again, but this time, in a place he knew inside out. After comparing the data from his on-ground investigation with the list of cholera deaths that occurred in the neighborhood in the week ending September 2 that year, a pattern emerged.

In his mind, Snow started seeing each death as a point on a map of the Broad Street area.† For almost all victims, the closest water source was the said street pump. Only ten deaths occurred in houses closer to other street pumps, but Snow was able to explain most of those cases too. Families of five of those victims told Snow that their loved ones would always bring home water from the Broad Street pump because, ultimately to their demise, they had preferred its taste. Another three victims were children who attended a school near the suspected pump and liked to take a sip of its water along the way.

What about the people who lived close to the Broad Street pump but didn’t contract cholera? For example, out of the 535 residents of the workhouse on nearby Poland Street, only five died of cholera.‡ Snow promptly visited the institution and learned that they owned a private pump. Then there was a brewery, where none of the seventy-plus employees had died of cholera. The owner explained that they mostly drank malt liquor and, in the unlikely case they would prefer water, they could use their private deep well. In forty-eight hours, Snow managed to explain almost all such outliers by running back and forth between the houses and comparing the information he gathered with the data from the Registrar General Office. By then, Snow was certain that the Broad Street pump was to blame.

Excerpted from MAPMATICS: A MATHEMATICIAN’S GUIDE TO NAVIGATING THE WORLD by Paulina Rowińska, published by The Belknap Press of Harvard University Press. Copyright © 2025 by Paulina Rowińska. Used by permission. All rights reserved.