Medicine’s Erdős Problem

American healthcare has no shortage of problems that have persisted for decades, despite enormous effort and spending.

Diagnostic errors kill or permanently disable 800,000 Americans each year. Chronic diseases remain poorly controlled, resulting in hundreds of thousands of preventable heart attacks, kidney failures and strokes each year, despite the availability of effective medications and evidence-based protocols. Meanwhile, millions of patients struggle to get timely access to care, and millions more cannot afford the treatments their physicians prescribe.

And yet, despite spending an estimated $5.6 trillion on healthcare annually, the United States is not solving these problems. Generative AI offers a chance to change that. But the technology will not achieve its full potential if clinicians use it only to reinforce the current system.

To make progress, medicine will need to follow the same approach OpenAI’s model used in mathematics: question the assumptions of the past and look for innovative opportunities that had previously been hidden.

It is not that GenAI is completely absent from medicine. Nearly two-thirds of clinicians report using some form of it today. But most restrict these applications to administrative roles: writing electronic health record notes, drafting billing appeals and summarizing visits. These uses may reduce the daily burden and time pressures doctors face to some degree, but they will not solve medicine’s biggest problems.

In fact, very few in healthcare have focused on GenAI’s larger opportunities: empowering patients with medical expertise, making care continuous rather than episodic, and saving lives by preventing medical errors.

Importantly, this is where medicine differs from mathematics. In math, AI companies will likely dominate the future of the field, leaving academics to play a supporting role. In medicine, however, doctors still have time to lead if they are willing to challenge the profession’s longstanding assumptions and discard its persistent fallacies.

Fallacy 1: Outpatient Care Is Best Provided In Medical Offices

Doctors structure outpatient medicine around the office visit. Patients are told to schedule appointments months in advance. Medication adjustments are made at fixed points in time, even when the prescribed treatment has failed to control a patient’s chronic disease for months.

That office-based model made sense in the previous century, when most medical problems were acute: a broken bone, an infection, appendicitis or chest pain. Today, however, 75% of patients have at least one chronic disease.

Hypertension, diabetes, heart failure and kidney disease are not episodic problems. They damage blood vessels and vital organs (heart, brain, kidney) every day when they remain poorly controlled.

Yet medicine tries to monitor and treat chronic disease through in-person appointments three or four times a year.

As a result, hypertension, the nation’s leading cause of strokes, is adequately controlled in less than half of patients. Diabetes, a major contributor to heart attacks and kidney failure, is effectively controlled even less often.

To create and implement an Erdős-like solution powerful enough to achieve effective hypertension control, the solution will require frequent monitoring and blood pressure evaluation in the patient’s home. A GenAI tool connected to a blood pressure cuff, glucose monitor, wearable device or bedside sensor could accomplish this by continually analyzing the clinical data as physicians would do if they had the time.

Through this type of solution, a GenAI application would inform patients of their progress, recommend a medication change when control remains inadequate and answer patient questions. Instead of flooding doctors with raw data, clinicians would know which patients were doing well and which ones required assistance. By personalizing medical care in this way, patients doing poorly could obtain the assistance they needed frequently, while those doing well wouldn’t have to miss work to come to the physician’s office.

Fallacy 2: Medical Expertise Must Flow Through Doctors

For most of modern history, the assumption that medical knowledge must flow through clinicians made sense. Physicians had access to training, textbooks, journals, diagnostic tools and clinical experience that patients did not. There was no way patients could make diagnoses and begin treatment without clinician expertise. That world is ending.

Right now, a third of U.S. adults are turning to AI for health information and advice, according to KFF. They ask ChatGPT and other tools to explain lab results, medications, diagnoses and treatment options. As the demands on physicians grow and it becomes harder for patients to schedule office visits to get their medical questions answered, these numbers will continue to rise. Already, 14 million adults report that they didn’t require a provider visit after using AI, based on recent Gallup polling.

As GenAI applications become more reliable and clinically sophisticated, the physician’s role as the sole source of medical information will diminish. Patients will increasingly begin by entering symptoms, test results and questions into a large language model, then asking follow-up questions to understand what steps they should take.

To optimally support patients, doctors will need to provide the care technology alone cannot: confirming complex diagnoses, ordering studies, prescribing medications, performing procedures and intervening when GenAI identifies a problem that requires human expertise. Ultimately, the combination of dedicated doctors, empowered patients and GenAI will achieve outcomes far better than any could achieve alone.

Fallacy 3: Superior Clinical Outcomes Require Expanded Specialization

Medicine rewards specialization. Over the past 50 years, general practice has been replaced by dozens of specialties, and many of those fields have fragmented further into subspecialties. Cardiology now includes electrophysiology, interventional cardiology, heart failure, imaging and preventive cardiology. Orthopedics divides into spine, hand, shoulder, hip, knee and sports medicine, and so on.

For surgical and procedural interventions, subspecialization has produced extraordinary advances, improving outcomes because physicians gain expertise by performing the same intervention repeatedly.

But specialization and subspecialization have also fragmented care. Patients with diabetes often have hypertension, kidney disease, depression and atrial fibrillation, as well. Each condition is usually managed by a different specialist, with separate appointments, medications, test results and treatment plans. As a result, no single clinician sees the whole picture, and patients fall through the cracks, increasing the risk of medical errors.

A key lesson of the Erdős breakthrough is that GenAI’s power lies in synthesis. The AI model applied algebraic number theory to a geometry problem, connecting two specialties that rarely collaborated. Physicians understand the advantages of specialization, but most fail to recognize the problems it creates.

A generative AI tool with access to the latest medical literature and treatment protocols could equip primary care doctors with the expertise needed to serve as “quarterback,” coordinating teams of specialists on behalf of patients. Or the large language model itself could help fulfill that role. But either solution will require physicians to abandon the belief that medical specialization, alone, leads to the best clinical outcomes.

The Erdős Threat

If physicians wait too long to act, the future of medicine will be designed around them, not with them. Doctors still have time and opportunity to lead, but only if they abandon the assumptions that stand in the way of progress.

Should clinicians fail to lead, technology companies, entrepreneurial firms and insurers will build tools that help people evaluate new medical problems from home, monitor chronic conditions continuously and coordinate care on behalf of patients and their families. Those models will rely on far fewer clinicians than today’s system.

The Erdős breakthrough in mathematics shows how quickly new solutions can be found once outdated assumptions are cast aside. This moment serves as both a warning and a way forward. GenAI’s greatest power is not simply doing old work faster or with fewer people. It is helping experts see problems differently and challenging past assumptions. Clinicians can resist that process or lead it. But they will not be able to stop it.