David W. Henderson was a mathematician whose career was marked by a rare transition from the heights of abstract, infinite-dimensional topology to a deeply humanistic and pedagogical approach to geometry. Throughout his five decades at Cornell University, Henderson challenged the notion that mathematics is a cold, purely formal discipline, instead advocating for it as a lived, experiential, and culturally diverse human endeavor.
Biography: Early Life, Education, and Career Trajectory
David Wilson Henderson was born on February 23, 1939, in Walla Walla, Washington. He grew up in a Quaker family, a background that informed his lifelong commitment to social justice and his egalitarian approach to education.
Henderson attended Swarthmore College, earning his B.A. in 1961. He then moved to the University of Wisconsin–Madison for his graduate studies, where he worked under the supervision of the legendary topologist R.H. Bing. He completed his Ph.D. in 1964 with a dissertation titled Extensions of Dehn's Lemma and the Loop Theorem.
After a brief stint as a member of the Institute for Advanced Study (IAS) in Princeton (1964–1966), Henderson joined the faculty at Cornell University in 1966. He remained at Cornell for the rest of his career, eventually becoming Professor Emeritus. His early career was defined by high-level research in topology, but by the mid-1970s, his interests shifted toward the philosophy of mathematics and the way geometry is taught, particularly to future secondary school teachers. Henderson passed away on December 20, 2018, following a pedestrian accident in Newark, Delaware.
Major Contributions: From Topology to Experiential Geometry
Henderson’s intellectual contributions can be divided into two distinct but related phases:
Infinite-Dimensional Topology
In the 1960s and early 70s, Henderson was a leading figure in infinite-dimensional topology. His most significant technical achievement was proving that every separable metric Hilbert manifold is homeomorphic to an open subset of the Hilbert space $l^2$. This work was foundational in classifying manifolds that do not have a finite dimension, bridging the gap between abstract functional analysis and geometric topology.
Experiential Geometry and "Living" Mathematics
Henderson’s later work revolutionized the pedagogy of geometry. He moved away from the "Definition-Theorem-Proof" model, which he felt alienated many students. Instead, he developed Experiential Geometry. He argued that students should explore geometric concepts—such as the meaning of a "straight line"—on various surfaces (spheres, planes, and hyperbolic planes) before formalizing them.
He was a pioneer in using physical models to understand non-Euclidean geometry. He famously utilized the "crochet models" developed by his wife and collaborator, Daina Taimina, to provide a tactile way to explore the properties of hyperbolic space, which had previously been considered nearly impossible to visualize.
Notable Publications
- "Infinite-dimensional manifolds are open subsets of Hilbert space" (1969): Published in Topology, this remains his most cited technical paper in pure mathematics.
- Experiencing Geometry: Euclidean and Non-Euclidean with History (1996; 3rd Ed. with Daina Taimina, 2005): This is his magnum opus. It is used worldwide to train math teachers and is celebrated for integrating the history of mathematics (including non-Western contributions) directly into the exploration of geometric proofs.
- Differential Geometry: A Geometric Introduction (1998): This textbook reinvented the teaching of differential geometry by focusing on intuitive geometric understanding rather than just tensor calculus.
- "Alive Mathematical Reasoning" (1996): A seminal essay exploring the internal, intuitive processes mathematicians use before they write down a formal proof.
Awards & Recognition
While Henderson was not a seeker of prizes, his work earned him significant respect within the mathematical community:
- Sloan Research Fellowship: Awarded early in his career for his work in topology.
- National Science Foundation (NSF) Grants: He received numerous grants for both his topological research and his innovative curriculum development projects.
- Invited Speaker: He was a frequent keynote speaker at conferences hosted by the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM), where he was viewed as a visionary in math education.
Impact & Legacy
Henderson’s legacy is felt most strongly in the way geometry is taught to the next generation of educators. He broke down the hierarchy between "pure" mathematicians and "educators," arguing that deep mathematical insight is required to teach simple concepts well.
His work on Hyperbolic Geometry had a surprising impact outside of mathematics, influencing the arts and sciences. By showing that hyperbolic planes could be modeled through crochet, he and Daina Taimina inspired a global movement of "mathematical fiber arts," including the Crochet Coral Reef project by the Institute For Figuring, which uses these geometric principles to raise awareness about climate change.
Collaborations
- R.H. Bing: His mentor at Wisconsin, who instilled in him a rigorous, visual approach to topology.
- Daina Taimina: A mathematician from Latvia who became his wife and closest professional collaborator. Together, they co-authored later editions of Experiencing Geometry and traveled the world giving workshops on the visualization of mathematics.
- The Cornell Mathematics Department: Henderson was a pillar of the Cornell "Math Explorer" culture, collaborating with colleagues to create a department that valued teaching as much as research.
Lesser-Known Facts
- Quaker Activism: Henderson’s pacifism was central to his life. During the Vietnam War, he was active in the protest movement and sought to apply the Quaker principle of "seeking the truth" to his mathematical inquiries.
- Ethnomathematics: He was an early proponent of ethnomathematics, often pointing out that ancient weavers and builders in non-Western cultures understood complex geometric principles long before they were formalized in Europe.
- The "Straight Line" Philosophy: Henderson would often start his classes by asking, "What is a straight line?" He would refuse to give a definition, forcing students to discover that a "straight" path depends entirely on the curvature of the space one inhabits—a profound realization that serves as the gateway to General Relativity.
David W. Henderson’s career serves as a bridge between the abstract rigors of 20th-century topology and a more inclusive, intuitive future for mathematics education. He proved that the most complex ideas in the universe could be understood if one was willing to pick up a needle and thread, or simply walk a straight line on a curved world.