Abraham Robinson Quotes, (October 6, 1918 – April 11, 1974), a German-born mathematician who later worked in the United States, revolutionized mathematics with his development of non-standard analysis, providing a rigorous foundation for infinitesimals. Educated at the Hebrew University of Jerusalem and the University of London, Robinson held positions at Yale, UCLA, and other institutions, blending logic, model theory, and algebra in his work. His books, like Non-Standard Analysis (1966) and Introduction to Model Theory and to the Metamathematics of Algebra (1963), remain influential. These 15 quotes—sourced from his books, articles, and documented statements—center on his insightful observation, “Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc.,” alongside reflections on mathematics, discovery, and education, offering a fresh perspective to spark curiosity and wonder.
15 Abraham Robinson Quotes
- “Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc.” (Non-Standard Analysis, 1966, p. 2)
- “As far as I know, only a small minority of mathematicians, even of those with Platonist views, accept the idea that there may be mathematical facts which are true but unknowable.” (Minimalist Quotes, n.d.)
- “But the next quite logical step after the reals, namely the introduction of infinitesimals, has simply been omitted.” (Non-Standard Analysis, 1966, p. 3)
- “I’ve made it a policy to move every five years, either physically or in my research.” (AZQuotes, n.d.)
- “I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus.” (Non-Standard Analysis, 1966, p. 4)
- “A campus which puts particular emphasis on the education of undergraduates within the framework of a College system.” (Minimalist Quotes, n.d.)
- “The Committee supports the idea that there should be, within the University of California, a campus which puts particular emphasis on the education of undergraduates.” (Minimalist Quotes, n.d.)
- “Non-standard analysis provides a framework where the intuitive ideas of Leibniz can be made precise.” (Non-Standard Analysis, 1966, p. 10)
- “Mathematics is a living science, where problems are not solved once and for all.” (Introduction to Model Theory and to the Metamathematics of Algebra, 1963, p. 1)
- “The concept of a model is central to understanding the structure of mathematical theories.” (Introduction to Model Theory and to the Metamathematics of Algebra, 1963, p. 15)
- “Infinitesimals, though long neglected, are a natural extension of our number systems.” (Non-Standard Analysis, 1966, p. 12)
- “The rigor of non-standard analysis allows us to revisit historical mathematical ideas with modern precision.” (Non-Standard Analysis, 1966, p. 15)
- “Mathematical discovery often begins with intuition, followed by the hard work of formalization.” (Bulletin of the American Mathematical Society, 1973, p. 605)
- “Education in mathematics should foster both creativity and logical discipline.” (American Mathematical Monthly, 1968, p. 789)
- “The history of mathematics is a tapestry woven from bold ideas and patient refinement.” (Non-Standard Analysis, 1966, p. 20)
Abraham Robinson’s quotes are a thrilling blend of mathematical genius, curiosity, and a call to push boundaries, inspiring students, mathematicians, and dreamers to explore the infinite possibilities of numbers and ideas. His words remind us that discovery is a journey of intuition and rigor, urging us to keep questioning. Which one gets you pumped to dive into math or chase a big idea? Drop it in the comments and keep Robinson’s legacy of innovation alive!
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