Nabby Adams (daughter of John Adams) died in 1813 at the age of 48 from breast cancer. How were they able to diagnose her prior to 20th century technology?

Breast cancer is actually one of the few modern cancers that was basically as easily diagnosable, roughly speaking, in antiquity as it is now- by detecting a lump in the breast. Of course, modern technology is more easily able to find lumps through mammography and ultrasound and determine whether a lump is benign or malignant, and the advent of genetic testing assists a great deal with determining courses of treatment, but fundamentally, breast cancer is one of the oldest known, and diagnosed, cancers (with a possible first reference to it being in the Edwin Smith Medical Papyrus, from about 3000 BCE and possibly attributable to the Egyptian physician Imhotep, as “cool to touch, bulging and spread all over the breast”- and considered incurable) and is still initially perceived today in much the same way as it was thousands of years ago- by noting abnormalities of the breast.

It's worth noting that this wasn't just a matter of them diagnosing breast TUMORS or GROWTHS. It was clear quite early on that breast CANCER, as diagnosed through tumors, was some kind of a systemic disease that could spread, as Galen noted in the 3rd century CE- he agreed with Hippocrates, six centuries earlier, that the systemic issue was an imbalance of humors, and he stated specifically that the problem was an excess of black bile. While the medical papyrus above considered breast cancer to be incurable, and therefore not worth operating on, in the 1st century CE Leonidas of Alexandria was performing breast cancer surgeries that were quite similar to modern ones- only operating on early stage tumors and removing a wide margin around the tumor itself.

In medieval times, Greek and Roman medicine was more commonly used in Islamic lands than in Christian ones, and in Christian lands the use of surgery for breast cancer patients sharply declined, as surgery was seen as barbaric. In Islamic lands, however, where Greek and Roman texts were translated into Arabic, there was a revival of breast cancer surgery- and, apparently, they even used caustic pastes after surgery in a similar way to which adjuvant chemotherapy would be used today (to eradicate the cancer at the margins). In the late Middle Ages, Greek and Roman medical texts were reintroduced to Europe by being retranslated from Arabic to Latin and other European languages (to doff my Jewish history cap a bit, often these translators were Jewish and Hebrew was a middleman language for many of these documents....), and by the Renaissance, surgery had a new resurgence of popularity in Europe.

From the 16th century on, new work was being done in anatomy- such as Andreas Vesalius's mapping of the human body, which did a great deal to puncture the supremacy of Galenic humors in medical education at that time. In particular, Vesalius couldn't find Galen's mythical black bile which was the cause of cancers like breast cancer. With medicine being increasingly based on hands-on knowledge- or at the very least Vesalius's detailed illustrations- of the human body, surgery became extremely popular. Even as a cause for breast cancer, in the absence of black bile, could not be determined (and would not be for centuries), the treatment of breast cancer increasingly included surgery. These surgeries were generally done in insanitary conditions and with minimal or no anesthesia, and many women preferred to wait things out, even if it meant dying, to actually going through with surgery given the pain that was inevitably involved.

It's actually instructive to go through the case of Nabby Adams- it reveals a lot about the state of the field of both breast cancer and breast surgery. Her cancer was diagnosed by a doctor after she detected a small lump in her own breast at the age of 42, though there was no real way of knowing, at that time, whether or not it was malignant. It steadily grew over the next year, terrifying her- she wrote to her parents from her home in rural New York about the tumor, and they urged her to come home to Boston, which she did. The Adams family, naturally well-connected, consulted with many distinguished doctors, many in Boston alongside correspondence between John Adams and his friend Dr Benjamin Rush in Philadelphia. The Boston doctors by and large recommended hemlock as a way to "poison" the disease (presaging the use of chemotherapy as a "poison" for the cancer cells), but Dr Rush disagreed. In a letter to Adams he stated that

After the experience of more than 50 years in cases similar to hers, I must protest agst: all local applications, and internal medicines for her relief. They now and then cure, but in 19 Cases Out of 20 in tumors in the breast, they do harm, or suspend the disease Until it passes beyond that time in which the only radical remedy is ineffectual. This remedy is the knife. From her account of the Moving state of the tumor it is now in a proper Situation for the Operation. Should She wait ’till it suppurates, or even inflames much, it may be too late. The pain of the Operation is much less than her fears represent it to be. I write this from experience having about two Years ago had a tumor of perhaps a larger Size cut out by Dr Physick from my Neck. I was surprized when the Doctor’s assistant told me the operation was finished, and could not help saying After Cæsar when he had finished his conquests—“and is this All.”—I repeat again—let there be no delay in flying to the knife. Her time of life—calls for expedition in this business, for tumors such as hers tend much more rapidly to cancers after 45, than in more early life. I sincerely sympathize with her, and with you and your dear Mrs Adams in this family Affliction, but it will be but for a few minutes if She submits to have it extirpated, & if not, it will probably be a Source of distress and pain to you all for years to come. It shocks me to think of the Consequences of procrastination in her case.

This demonstrates that at this time, it was understood that breast cancer tumors came in stages (something which had been documented since Hippocrates in the 4th century BCE)- since Nabby's tumor was "movable," and not attached to the chest wall, it was seen as less likely to have metastasized, or spread to other body parts, meaning that surgery stood a decent chance of curing her cancer. If she waited until the tumor had grown, then that might change, and surgery would no longer be recommended.

So, after the family convinced Nabby's husband of the necessity (he was in denial), the surgery was undertaken by Dr Warren of Boston, and was by all accounts extremely painful- for the non-squeamish, about halfway down in this article is a very graphic description of her experience. It took more than twice as long to dress her wounds as for the surgery itself to take place. The surgery left her weak and with her left arm disabled, as her lymph nodes there had been removed. Seven months later she returned home to New York- but only a few weeks after that, she noticed headaches and pain in her spine and abdomen, which her doctor first attributed to rheumatism- but then he changed his mind. Her cancer had not been in an early enough stage for surgery after all, at least not without modern adjuvant chemotherapy- it had, as noted, spread to the lymph nodes, and similarly had spread elsewhere in her body long before surgery. Nabby Adams, her husband once again in denial and insisting she needed only to convalesce, returned to her parents' home to die in great agony, her mother too depressed by the sight of her pain to care for her and her father, therefore, constantly nursing her.