Infectious Outbreak and the Foundation of Epidemiology There was an infectious outbreak that was responsible for the foundation of epidemiology, it was the cholera outbreak that affected London between 1846 and 1860, which, in order to be resolved, demanded that a method of accurate causality be developed ""from day to day night"". This outbreak killed a lot of people and would kill a lot more if it weren't for John Snow, the father of epidemiology. At that time, there was still no method that could establish a causal link between a microorganism and a disease, Koch's postulates, for example, would only be published about 40 years after the creation of the method that Snow applied to discover the cause and the form of transmission of cholera.
Today, we know that cholera is transmitted by the bacterium Vibrio cholerae and that it thrives in contaminated water, for example, by sewage. But at the time, it was not even known that bacteria could cause pathophysiological conditions (although they had already been discovered).
The medical community then started shooting everywhere and the theory that gained the most traction at the time was the miasmatic one. The miasmatic theory pointed out that cholera was airborne. Snow, however, due to multiple observations, suspected that the transmission was through water and built a map that allowed us to see this better. And then the Voronoi diagram comes into play. Basically, all the water wells that the population used were marked on the map, and then the areas where any points were closest to a single well were established. See image below:
This is a map of a portion of the city. Red dots indicate cases of cholera and blue dots water wells: 

In this green area, all the points that make it up are closer to the water well within this same area than to any other. Do this for all water wells and you get something like this:

With this, it was possible to prove that the transmission of cholera took place through water, and not through the air, as proposed by the miasmatic theory, and that the source water well of the whole outbreak was the one on Broad Street. And then it was banned and the outbreak really got under control.
(The contaminated people outside the yellow area, despite having wells closer to them than the one in Broad Street, for some reason ended up consuming water from the contaminated well, and therefore contracted the disease)

Sources: Uncovering the cause of cholera | plus.maths.org
https://plus.maths.org/content/uncovering-cause-cholera
John Snow - a historical giant in epidemiology
http://www.ph.ucla.edu/epi/snow.html
https://www.rcseng.ac.uk/library-and-publications/library/blog/mapping-disease-john-snow-and-cholera/
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7150208/
Question: This story about Snow and the cholera outbreak resolution to see if you would frame his method as a method that found a mere correlation or as a method that actually established causality (which was the name I used)? I refer to the point before the well was closed. After all, after the Broad Street water well was closed, the cholera outbreak did indeed end. But even before the well was closed, did Snow's thematic map really prove causality? Or just correlation?

Yes, John Snow's research has shown just a mere correlation. In fact, a lot of research we do, including medicine, focuses on correlational evidence. Studying causal effects is hard, especially with observational data (see also causality), and at the time of Show, the methodology didn't mature yet (otherwise, how could the medical community believe in miasma?). We have a nice thread discussing Under what conditions does correlation imply causation? that you may find interesting. Snow didn't prove the water transmission theory, but he gave strong evidence that was consistent with the theory.
