This is a great question but also very broad! You could try sending a message to some of the flaired users with expertise in the history of science and perhaps some North Americanists will comment as well. In short, yes, there was lots of science going on in the New World! I’ll speak to science in the Spanish Empire around 1800, especially in the Río de la Plata region. Due to the prevalence of the Black Legend, many people believe that the Spanish Empire was backward and dogmatic, and while there are lots of examples of backwardness, the recent historiography has largely discredited (or at least significantly complicated) these narratives. For instance, many historians have shown that Spanish science was highly developed. Scholars like Jorge Carñizares-Esguerra, Neil Safier, Paula de Vos, David Goodman, Daniela Bleichmar, and Helen Cowie have demonstrated how vibrant Spanish scientific innovation was. It did differ somewhat from Enlightenment science in other empires; the Crown tended to believe that any science that was not royally sponsored was dangerous and antimonarchical. This attitude retarded somewhat individual scientific innovation, but under the supervision of the Crown, Spanish science in the New World thrived.

In Spain, the Crown established the Royal Pharmacy and Chemical Laboratory, the Royal Mathematics Academy, the Royal Natural History Museum, and the Royal Botanical Garden which housed thousands of plants from their colonial possessions and from around the world. Similar institutions sprang up in cities throughout the empire in which individuals debated advances in physics, chemistry, biology, geology, alchemy, and cosmology. Additionally, the monarchy sent dozens of scientific expeditions to their colonies, which relied on local expertise to inform European “discoveries.” Unfortunately, many of the men and women who helped were never credited for their work and were forgotten. Also, keep in mind that science as we know it today was very much in its infancy; physics and chemistry were only first developing (I know, this is a big generalization). During the Enlightenment, physics and chemistry were intimately tied to the natural world, and the people with the prerequisite education necessary to participate in advanced scientific study and research often became “jack of all trades” scientists. Individuals tended to have their hands in many scientific disciplines at once. Thus, it is difficult to talk about physics or chemistry research individually without also mentioning biological research. The New World represented all sorts of new learning opportunities. Scientists attempted to figure out just what this massive space contained and how it related to scientific learning that already existed. In the process, the New World became the testing ground for the scientific debates of the day.

The best “lab science” facilities in the Spanish Empire were in major metropolitan areas like Mexico City and Lima. Here, the most educated men, both criollos and europeos, participated in the scientific debates of the day. For example, Paula de Vos, in her article “Research, Development, and Empire: State Support of Science in the Later Spanish Empire” published in Colonial Latin America Review describes how scientists in Mexico City participated in the debate over “the use of chemicals and chemical techniques in the preparation of medicine” (62). Scientists in Mexico City tested the ingestion of mercury to treat syphilis and advocated for its use due to the results of their studies. Their work altered Europeans’ understanding of how the body reacted to chemicals and changed the leading theories of how medicine should be created. De Vos also points out in another article that major cities in the empire were also among the first places where scientists tried to carry out vaccination campaigns, representing significant advancement in the fields of chemistry and pharmacy.

Four of the most famous scientists that spring to mind from South America in the eighteenth and early nineteenth century were Alejandro Malaspina, Félix de Azara, Pedro Franco Dávila, and Charles Marie de la Condamine. Malaspina led a lengthy expedition that sailed around South America, along the Pacific coast as far north as Alaska, the Philippines, China, Australia, and back across the Pacific again, all while taking vast amounts of specimens, notes, and astronomical readings on the way. The men brought on this expedition some of the finest scientific equipment available in the entire Spanish Empire, which had no equal and was of great interest to local enthusiasts in every port they visited. They assembled mountains of data and collected unpublished scientific information in cities, libraries, and private collections throughout the colonies. Azara was sent to the Río de la Plata to set the border between the Spanish and the Portuguese empires. He taught himself natural science, documented hundreds of birds and animals for the first time, and included information about local plants and their suggested medical and scientific uses. While in the Río de la Plata, he received a copy of Buffon’s Historie Naturelle and used his observations to correct many of the inconsistencies he found between his observations from the field and observations made in Buffon’s lab. Azara helped demonstrate that science needed to be done both in the field and in the lab to show how scientific theories, chemical properties, or animal behavior changed in more complex systems. Dávila was a creole from Ecuador who eventually became director of the Royal Natural History Museum. He collected vast amounts of scientific work from the colonies and published several important books that added to Europeans’ understanding of chemistry, biology, and physics. More importantly, he helped develop the scientific network between Spanish officials in Europe and the colonies. Lastly, Charles Marie de la Condamine traveled to Ecuador to test Newton’s hypothesis that the Earth was not a perfect sphere. He took extensive astrological observations but also documented rubber and the antimalarial properties of the cinchona tree (among many other scientific observations).

When published (if a scientist was wealthy enough and had the connections to make that happen), their works were met with enthusiasm and skepticism by European audiences hungry for both scientific information in general and information about the New World itself. At the time, many believed that the New World was naturally inferior to the Old, so works that called this idea into question were heavily debated. For example, Azara’s publications were highly praised for their content but demeaned for their blunt corrections of Buffon’s work. Scientists ridiculed Azara for spending twenty years on the fringes of the Spanish empire, believing that his experiences in the “inferior” New World had rubbed off on him and his work. The Spanish Crown did not necessarily believe this scientific convention though. Products thought to have useful medicinal or chemical properties were sent to the scientific academies, tested, and if successful, marketed to the public. Publications that tested physics theories in physics or astronomy were met with a great deal of interest as well since data collection or testing often could not be done in Europe at the time. However, the vast majority of Spanish scientific research never reached European audiences. The Crown is infamous for remaining tight lipped about their colonies, so much of the research was collected in manuscripts by royal institutions but failed to reach larger scholarly audiences.

Getting equipment to scientists proved difficult in such a massive empire with very little infrastructure. Sending equipment to major metropolitan centers like Mexico City or Lima would have taken a few months, more time if the individual needed to request it and pay for it. Wealthy creoles in major cities amassed large libraries, specimen collections, and scientific equipment holdings as a result. However, shipping grew more infrequent as Spanish naval capabilities decreased. Getting scientific materials on the fringes of the empire was much more difficult and expensive. Azara waited years to receive the most popular scientific works of the day. He waited even longer to get scientific equipment that allowed him to take more accurate measurements of elevation for example. He even documents in his work Viajes por la américa meridional an episode in which he spends several weeks working and comparing notes with another scientist who built homemade lab equipment to test pressure and elevation theories because the individual neither had the contacts to find the equipment nor the funds to pay for it even if he found it.

So although they sometimes struggled to get the respect they deserved and the equipment they needed, science was very important in the Spanish Empire. Scientists were able to access the New World to test ideas, read new scientific research, publish their findings, participate in scientific debates, and get equipment. That being said, only an elite, educated, and wealthy few were able to participate in science because few average people had access to royal Spanish scientific networks and intraempire connections. The vast majority of americanos were poor and uneducated who, in the eyes of many Europeans, lived outside of the “pale of civilization” altogether. Ironically however, it was often these people who knew of the medicinal or chemical properties of local products, led scientists or expeditions to the best places to carry out their experiments, and played key roles behind the scenes that made scientific advances possible. Unfortunately, their influence remains in the shadows or has disappeared completely.