[2] For more than 30 years, he was employed in the Department of Physics and Astronomy of Arizona State University (ASU), where he retired with the rank of research professor and is now emeritus.

Beginning college as a pre-medical major at UCLA from 1950 to 1952, he graduated from Pacific Lutheran University in 1954 with degrees in philosophy and speech.

His mentor at UCLA was the physicist Robert Finkelstein,[3] who was working on unified field theories at that time.

[4] A serendipitous encounter with lecture notes by mathematician Marcel Riesz inspired Hestenes to study a geometric interpretation of Dirac matrices.

[4][5] Shortly thereafter he recognized that the Dirac algebras and Pauli matrices could be unified in matrix-free form by a device later called a spacetime split.

[8] In 1983 he joined with entrepreneur Robert Hecht-Nielsen and psychologist Peter Richard Killeen in conducting the first ever conference devoted exclusively to neural network modeling of the brain.

In 1987, he became the first visiting scholar in the Department of Cognitive and Neural Systems (Boston University) and worked on neuroscience research for a period.

Hestenes has worked in mathematical and theoretical physics, geometric algebra, neural networks, and cognitive research in science education.

[13][14] Spacetime algebra provided the starting point for two main lines of research: on its implications for quantum mechanics specifically and for mathematical physics generally.

The first line began with the fact that reformulation of the Dirac equation in terms of spacetime algebra reveals hidden geometric structure.

Its culmination is the book Clifford Algebra to Geometric Calculus[23] which follows an approach to differential geometry that uses the shape tensor (second fundamental form).

The AMTA has expanded to a nationwide community of teachers dedicated to addressing the nation's Science, Technology, Engineering, and Mathematics (STEM) education crisis.

[52] On August 30, 2023, Hestenes was named in a United States District Court case in Utah filed by several venture capitalists claiming he endorsed and participated in a Ponzi scheme related to a discredited anti-gravity propulsion technology that was being marketed by Science Invents, LLC in Salt Lake City, Utah, a company owned by Joe Firmage, the former founder of USWeb.