For 80 years, one of mathematics’ most stubborn puzzles, the unit-distance problem posed by the brilliant Hungarian mathematician Paul Erdős, went unsolved. In May, an OpenAI model shattered that legacy. Rather than proving Erdős’s hypothesis correct, the AI drew on algebraic number theory to find a superior design that was not symmetric, revealing the original assumption was wrong. The breakthrough stunned mathematicians, but its deeper significance may be felt most urgently in American medicine.
The United States spends an estimated $5.6 trillion on healthcare each year, yet diagnostic errors kill or permanently disable 800,000 Americans annually. Chronic diseases like hypertension and diabetes remain poorly controlled, leading to hundreds of thousands of preventable heart attacks, kidney failures and strokes. Generative AI is already used by nearly two-thirds of clinicians, but most restrict it to administrative tasks such as writing notes and drafting billing appeals. These uses ease daily burdens but do not touch medicine’s core failures. To solve those, the article argues, healthcare must follow the AI’s lead: question long-held assumptions and look for hidden opportunities.
The first assumption to challenge is the office visit model. In the past, when most medical problems were acute, scheduling appointments months in advance made sense. Today, 75% of patients have at least one chronic disease. Hypertension, diabetes and heart failure damage organs every day when poorly controlled, yet medicine monitors them through in-person visits three or four times a year. As a result, hypertension is adequately controlled in less than half of patients. A GenAI tool connected to a home blood pressure cuff or glucose monitor could analyze data continuously, recommend medication changes and inform patients of their progress. Clinicians would then know which patients needed help and which were doing well, personalizing care without requiring everyone to miss work for an appointment.
The second assumption is that medical expertise must flow solely through doctors. That world is ending. Already, a third of U.S. adults turn to AI for health information, according to KFF, and 14 million adults report they did not need a provider visit after using AI, based on recent Gallup polling. As GenAI becomes more reliable, patients will increasingly start by entering symptoms and test results into a large language model. The physician’s role will shift to providing the care technology cannot: confirming complex diagnoses, prescribing medications and intervening when the AI identifies a problem requiring human judgment. The third fallacy is that more specialization always yields better outcomes. Medicine has fragmented into dozens of subspecialties, but the article suggests that a combination of dedicated doctors, empowered patients and GenAI can achieve far better results than any could alone.
In mathematics, AI companies may now dominate the field, leaving academics in a supporting role. In medicine, doctors still have time to lead, but only if they are willing to discard persistent fallacies and embrace a new model. The Erdős breakthrough shows that the most powerful solutions often come from questioning what everyone assumed was true. For patients living with chronic disease, that shift cannot come soon enough.