John Nash, a name synonymous with brilliance and resilience, marks the beginning of a legally recognized individual on June 13, 1928, in Bluefield, West Virginia. Born in the Bluefield Sanitarium, a hospital that has since vanished, Nash’s early life, like many, is shrouded in the mists of early childhood, memories becoming akin to “memories of memories,” folk tales passed down through time. Yet, despite the hazy nature of early recollections, concrete facts paint a vivid picture of the formative years of a mind that would revolutionize fields from mathematics to economics.
Early Years in Bluefield: Foundations of a Brilliant Mind
Nash’s father, also named John, was an electrical engineer, drawn to Bluefield by the Appalachian Electric Power Company. A World War I veteran, he served in France, though away from the front lines. His roots were in Texas, where he earned his B.S. in electrical engineering from Texas A. and M. Nash’s mother, Margaret Virginia Martin, known as Virginia, was a Bluefield native. Educated at West Virginia University, she was a schoolteacher, imparting knowledge of English and Latin before marriage. A significant chapter in her life was marked by partial hearing loss due to scarlet fever contracted during her university years.
Virginia’s parents, Dr. James Everett Martin, a physician trained at the University of Maryland in Baltimore, and her mother, arrived in Bluefield during its period of rapid growth. Dr. Martin initially established his medical practice but later transitioned into real estate investment. Although John Nash never met his grandfather, who passed away before his birth, he fondly remembered his grandmother and her piano playing in their centrally located Bluefield home. The family circle expanded with the arrival of Nash’s sister, Martha, born on November 16, 1930, adding another dimension to his early family life.
Nash’s education began in Bluefield’s standard schools, preceded by kindergarten. His intellectual curiosity was nurtured by Compton’s Pictured Encyclopedia, a treasure trove of knowledge he avidly explored. Supplementing this were various books from both his home and his grandparents’, enriching his learning environment.
Bluefield, nestled in the Appalachian Mountains, was not a hub of academia or cutting-edge technology. It thrived as a center for business and law, its prosperity tied to the railroad and the rich coalfields of West Virginia and Virginia. This environment, while not intellectually rarefied, presented a unique challenge: to seek knowledge from the wider world, beyond the immediate community. This self-driven approach to learning would become a hallmark of John Nash’s intellectual journey.
From Chemical Engineering to Mathematical Genius: Discovering a Passion
By high school, John Nash was immersed in “Men of Mathematics” by E.T. Bell, a book that likely fueled his burgeoning mathematical interests. He even tackled and proved Fermat’s Little Theorem, a significant achievement for a high school student. His scientific explorations extended beyond mathematics into electrical and chemistry experiments. Initially, envisioning a path similar to his father’s, Nash wrote an essay about a career in electrical engineering. This early inclination led him to enroll at Carnegie Tech (now Carnegie Mellon University) as a chemical engineering major.
However, the rigid structure of chemical engineering, with courses like mechanical drawing, proved unappealing after a semester. Nash shifted to chemistry, but quantitative analysis presented a different kind of challenge – one of lab technique rather than conceptual understanding. Simultaneously, the mathematics faculty recognized John Nash’s exceptional aptitude and encouraged him to switch to mathematics. They assured him that a fulfilling career as a mathematician in America was indeed possible. This pivotal advice led to another major change, and Nash officially became a mathematics student. His progress in mathematics was so rapid that upon graduation, Carnegie Tech awarded him both a B.S. and an M.S. in mathematics.
During his final year of high school, John Nash’s parents facilitated supplementary mathematics courses at Bluefield College, then a two-year Southern Baptist institution. While this didn’t grant him advanced standing at Carnegie, it provided him with a significant knowledge base, allowing him to excel in his university math courses.
Princeton and the Birth of Game Theory: A Groundbreaking Idea
Upon graduating from Carnegie Tech, John Nash received fellowship offers from both Harvard and Princeton. The Princeton offer was more financially attractive, particularly as he hadn’t won the Putnam competition. A personal touch came from Professor A.W. Tucker’s encouraging letter, and geographically, Princeton’s proximity to Bluefield was appealing to his family. Princeton became the chosen destination for his graduate studies.
However, an elective course in “International Economics” during his time at Carnegie sparked an idea that would profoundly impact the field of economics. This idea formed the basis of “The Bargaining Problem,” later published in Econometrica. This early work ignited his interest in game theory, a field being pioneered at Princeton, notably by the work of von Neumann and Morgenstern.
As a graduate student at Princeton, John Nash pursued mathematics broadly. Remarkably, he not only developed the groundbreaking concept of Non-Cooperative Games, but also made a significant discovery in manifolds and real algebraic varieties. This dual achievement provided a safety net; should his game theory work not be accepted as a mathematics Ph.D. thesis, his other results were substantial enough for doctoral recognition.
Ultimately, John Nash’s game theory ideas, while diverging from the established “von Neumann and Morgenstern line,” were accepted as his mathematics Ph.D. thesis. Later, during his time as an instructor at MIT, he further developed his work on Real Algebraic Manifolds for publication.
Career at MIT and Further Mathematical Explorations: Solving Classical Problems
John Nash joined MIT in the summer of 1951 as a C.L.E. Moore Instructor. Prior to this, he had spent a year as an instructor at Princeton after earning his Ph.D. The move to MIT was motivated more by personal and financial considerations than purely academic ones, as MIT offered a higher-paying instructorship. He remained on the mathematics faculty at MIT from 1951 until his resignation in the spring of 1959. During the academic year 1956-1957, supported by an Alfred P. Sloan grant, he spent a year at the Institute for Advanced Study (IAS) in Princeton.
This period at MIT was exceptionally productive. John Nash solved a long-standing problem in differential geometry concerning the isometric embeddability of abstract Riemannian manifolds in flat (Euclidean) spaces. While not as widely discussed as problems like the 4-color conjecture, it was a significant classical problem. Upon learning about its unsolved status at MIT, Nash began his focused study. His initial breakthrough revealed embeddability in surprisingly low-dimensional spaces, albeit with limited smoothness. Later, using “heavy analysis,” he achieved a solution with a more proper degree of smoothness.
During his Sloan sabbatical at IAS, John Nash tackled another challenging problem involving partial differential equations, one that remained unsolved beyond two dimensions. While he successfully solved this problem, he experienced an unfortunate coincidence. Unbeknownst to him, Ennio de Giorgi of Pisa, Italy, was working on the same problem in parallel. De Giorgi achieved the solution, particularly for the important case of “elliptic equations,” slightly ahead of Nash. It’s speculated that had either John Nash or de Giorgi faltered, the sole solver might have been recognized with the Fields Medal, mathematics’ most prestigious award for mathematicians under 40.
The Onset of Mental Illness and Personal Challenges: A Battle with Schizophrenia
This period of intense mathematical achievement was followed by a profound personal shift. John Nash transitioned from scientific rationality into the delusional thinking characteristic of schizophrenia or paranoid schizophrenia. Details of this period are intentionally omitted from his autobiography, a respectful veil drawn over a deeply personal and challenging time.
The mental disturbances began in early 1959, coinciding with his wife Alicia’s pregnancy. This led to his resignation from MIT and a period of 50 days of observation at McLean Hospital, followed by an attempt to seek refugee status in Europe. Subsequently, John Nash spent periods of five to eight months in hospitals in New Jersey, involuntarily committed and constantly seeking legal release.
However, hospitalization also brought periods of lucidity. After extended periods of treatment, John Nash would renounce his delusions, return to a more conventional understanding of reality, and resume mathematical research. These intervals of “enforced rationality” yielded significant mathematical contributions, including work on the Cauchy problem for general fluid equations, the “Nash blowing-up transformation,” “Arc Structure of Singularities,” and “Analyticity of Solutions of Implicit Function Problems with Analytic Data.”
Despite these periods of clarity, John Nash would relapse into delusionally influenced thinking in the later 1960s. However, his behavior became more moderate, allowing him to avoid frequent hospitalizations and psychiatric intervention.
Return to Rationality and Continued Contributions: An Unprecedented Recovery
Gradually, John Nash began to intellectually reject the delusional thought patterns that had dominated his orientation. This shift began with the rejection of politically-oriented thinking as a futile endeavor. Eventually, he returned to rational thinking, characteristic of scientists. He likened this return to rationality not as simple joy, but as a complex transition, like recovering from a physical disability. Rationality, he noted, imposes limitations on one’s cosmic perspective. He mused that from a non-believer’s perspective, Zarathustra could be seen as simply a madman, yet his “madness” led to lasting influence, contrasting with the anonymity of billions forgotten by history.
John Nash acknowledged the statistical improbability of a mathematician or scientist making significant new contributions at the age of 66. However, he held hope that his 25-year “vacation” from fully rational thinking might make his situation atypical. He expressed a continued commitment to research and a hope for future valuable discoveries.
John Nash’s autobiography concludes with a poignant reflection on his journey, written at the time of his Nobel Prize award. It stands as a testament to his extraordinary mind, his resilience in the face of debilitating illness, and his ultimate return to the world of mathematics he so profoundly impacted. John F. Nash Jr. passed away on May 23, 2015, leaving behind a legacy of groundbreaking work and inspiring personal story. His life, immortalized in books and film like “A Beautiful Mind,” continues to captivate and inspire, highlighting the extraordinary potential and fragility of the human mind.
