Abraham Robinson
Early Life and Education
Abraham Robinson was born on October 6, 1918, in Waldenburg, Silesia, which was then part of Germany and is now known as Wałbrzych, Poland. His family was Jewish, and they moved to Palestine in 1933 to escape the rise of the Nazi regime. Robinson attended the Hebrew University of Jerusalem, where he studied mathematics and physics. He completed his undergraduate studies in 1939 and continued to pursue advanced studies in mathematics, earning a master's degree in 1942.
Career and Contributions
World War II and Early Career
During World War II, Robinson served in the British Army, where he worked as an instructor in the Royal Air Force. His expertise in mathematics was applied to the development of military technology, particularly in aerodynamics and the design of aircraft. After the war, Robinson returned to academia and began his doctoral studies at the University of London, where he earned his Ph.D. in 1949 under the supervision of renowned mathematician Paul Dirac.
Academic Positions
Robinson held several academic positions throughout his career. He started as a lecturer at the University of Toronto in Canada, where he taught from 1949 to 1951. He then moved to the Massachusetts Institute of Technology (MIT) in the United States, where he worked as a research associate. In 1957, he joined the faculty at the University of California, Los Angeles (UCLA), where he remained until 1962. Robinson later accepted a position at Yale University, where he became a Sterling Professor of Mathematics, one of the highest academic honors at the institution.
Non-standard Analysis
Robinson is best known for his development of non-standard analysis, a mathematical framework that rigorously formalizes the concept of infinitesimals. This work provided a new foundation for calculus, offering an alternative to the traditional epsilon-delta approach. Non-standard analysis uses model theory, a branch of mathematical logic, to extend the real number system to include infinitesimal and infinite numbers. Robinson's work in this area has had a profound impact on mathematics, providing new tools and perspectives for mathematicians and scientists.
Model Theory and Logic
In addition to non-standard analysis, Robinson made significant contributions to model theory, a branch of mathematical logic that studies the relationships between formal languages and their interpretations, or models. His work in this area laid the groundwork for further developments in logic and the philosophy of mathematics. Robinson's insights into the structure and properties of mathematical models have influenced a wide range of fields, from algebra to computer science.
Other Mathematical Contributions
Robinson's contributions to mathematics extend beyond non-standard analysis and model theory. He worked on a variety of topics, including algebra, topology, and differential equations. His research often focused on the application of logical methods to solve problems in these areas, demonstrating the power and versatility of mathematical logic.
Legacy and Influence
Abraham Robinson's work has left a lasting legacy in the field of mathematics. His development of non-standard analysis has been particularly influential, providing a new perspective on calculus and inspiring further research in mathematical logic and analysis. Robinson's contributions to model theory have also had a significant impact, shaping the way mathematicians approach the study of formal systems and their interpretations.
Robinson's influence extends beyond mathematics, as his work has found applications in fields such as physics, economics, and computer science. His innovative use of logical methods to address complex problems has inspired generations of mathematicians and scientists, and his legacy continues to be felt in the ongoing development of mathematical theory and practice.
Personal Life
Abraham Robinson was known for his intellectual curiosity and passion for mathematics. He was a dedicated teacher and mentor, inspiring many students to pursue careers in mathematics and related fields. Robinson was also an accomplished linguist, fluent in several languages, including Hebrew, German, and English. He passed away on April 11, 1974, in New Haven, Connecticut, leaving behind a rich legacy of mathematical innovation and discovery.