For eight decades, one of the most challenging geometric puzzles baffled mathematicians worldwide.
This conundrum originated from Paul Erdős, a renowned and unconventional Hungarian mathematician who authored over 1,500 papers and presented numerous problems to his peers globally. Known as the unit-distance problem, it questioned how many pairs of points could be evenly spaced on a flat plane.
Erdős surmised that a highly structured geometric arrangement would provide the solution. Despite this, generations of mathematicians were unable to prove his theory.
In May, OpenAI revealed that one of its models had solved the problem. Contrary to proving the hypothesis, it showed that Erdős’ conjecture was incorrect. The AI model, utilizing algebraic number theory, uncovered a superior asymmetric design, rejecting the geometric hypothesis.
This development was groundbreaking. The discovery revolutionized the field of mathematics, and its implications reach beyond geometry.
The lesson for medicine is clear: healthcare professionals will not address the longstanding issues of quality, accessibility, and affordability by adhering to outdated assumptions and beliefs.
Medicine’s Erdős Problem
The American healthcare system faces numerous enduring challenges despite significant efforts and expenditures.
Diagnostic errors result in the deaths or permanent disability of 800,000 Americans annually. Chronic diseases remain inadequately managed, leading to preventable heart attacks, kidney failures, and strokes each year, despite the availability of effective treatments and protocols. Millions of patients also face difficulties accessing timely care and affording prescribed treatments.
Despite an estimated $5.6 trillion spent annually on healthcare, the U.S. is not resolving these issues. Generative AI presents an opportunity for change, but its potential will not be realized if it is used merely to uphold the current system.
To advance, medicine must adopt the approach used by OpenAI’s model in mathematics: challenge historical assumptions and seek out innovative, previously overlooked opportunities.
While GenAI is not entirely absent from medicine, nearly two-thirds of clinicians report using some form of it today. However, these applications are mostly limited to administrative tasks like writing electronic health record notes, drafting billing appeals, and summarizing visits. While these uses may alleviate some daily pressures on doctors, they do not address the most significant challenges in medicine.
Few in the healthcare sector have focused on GenAI’s broader opportunities: empowering patients with medical knowledge, transitioning care from episodic to continuous, and preventing medical errors to save lives.
This is where medicine diverges from mathematics. In math, AI companies are likely to lead the field’s future, with academics taking a supportive role. In contrast, in medicine, doctors have the opportunity to lead if they are willing to challenge long-standing professional assumptions and discard persistent fallacies.
Fallacy 1: Outpatient Care Is Best Provided In Medical Offices
Doctors traditionally structure outpatient care around office visits, with patients scheduling appointments months in advance. Medication adjustments occur at fixed intervals, even when treatments have failed to control chronic diseases for extended periods.
This office-based model was suitable in the past when most medical issues were acute, such as broken bones or infections. Today, however, 75% of patients have at least one chronic condition.
Hypertension, diabetes, heart failure, and kidney disease are not episodic; they continuously harm vital organs when not properly managed.
Currently, medicine attempts to monitor and treat chronic diseases through in-person visits three or four times a year.
Consequently, hypertension, a leading cause of strokes, is well-controlled in fewer than half of patients. Diabetes, a significant contributor to heart attacks and kidney failure, is managed even less effectively.
An effective solution for hypertension control requires frequent home-based monitoring and evaluation. A GenAI tool connected to a blood pressure cuff, glucose monitor, wearable device, or bedside sensor could perform continuous data analysis as a physician would if they had the time.
Such a GenAI application could inform patients about their progress, suggest medication changes when necessary, and answer questions. This personalized approach allows clinicians to identify which patients are doing well and which require intervention, enabling poorly managed patients to receive frequent help without others needing to miss work for office visits.
Fallacy 2: Medical Expertise Must Flow Through Doctors
Historically, the belief that medical knowledge must pass through clinicians made sense. Doctors had access to resources and expertise that patients did not. However, this dynamic is changing.
Currently, one-third of U.S. adults use AI for health information, according to KFF. People turn to tools like ChatGPT for explanations of lab results, medications, diagnoses, and treatment options. As it becomes more challenging to schedule doctor visits for answers, these numbers are likely to grow. Already, 14 million adults report not needing a provider visit after using AI, according to recent Gallup polling.
As GenAI applications become more reliable and clinically advanced, the physician’s role as the primary source of medical information will lessen. Patients will increasingly start by entering symptoms, test results, and queries into a large language model, followed by questions on what actions to take.
To best support patients, doctors will need to provide care that technology alone cannot: confirming complex diagnoses, ordering studies, prescribing medications, performing procedures, and stepping in when GenAI detects issues that need human expertise. Ultimately, the synergy of dedicated doctors, empowered patients, and GenAI will yield far better outcomes than any could achieve independently.
Fallacy 3: Superior Clinical Outcomes Require Expanded Specialization
Medicine favors specialization. Over the past half-century, general practice has been replaced by numerous specialties, with many fields further divided into subspecialties. Cardiology now includes electrophysiology, interventional cardiology, heart failure, imaging, and preventive cardiology. Orthopedics branches into spine, hand, shoulder, hip, knee, and sports medicine, among others.
For surgical and procedural interventions, subspecialization has led to remarkable advances, improving outcomes as physicians refine their expertise through repetition.
However, specialization and subspecialization have also fragmented care. Patients with diabetes often have hypertension, kidney disease, depression, and atrial fibrillation, each typically managed by different specialists with separate appointments, medications, tests, and treatment plans. As a result, no single clinician sees the entire picture, leading to patient care gaps and increased risk of medical errors.
A key insight from the Erdős breakthrough is that GenAI’s strength lies in synthesis. The AI model applied algebraic number theory to solve a geometry problem, bridging two specialties that seldom collaborated. While physicians recognize the benefits of specialization, many overlook the problems it introduces.
A generative AI tool with access to the latest medical literature and treatment protocols could empower primary care doctors to act as “quarterbacks,” coordinating specialist teams for patient benefit. Alternatively, the large language model itself could help fulfill that role. Either solution requires physicians to abandon the belief that specialization alone ensures the best clinical outcomes.
