Lenore Blum’s long career has spanned the breadth of mathematics and computer science. She’s done influential work in logic and cryptography, and she formulated an entirely new model of computation. And though she didn’t set out to do so, she’s also devoted a significant chunk of her time to building institutions to help women follow in her footsteps.
“I had never wanted to think of myself as a woman mathematician,” she said. “But I started realizing I had a role to play.”
Her personal life, too, has led her to unexpected places. Born in New York City in 1942, Blum moved to Caracas, Venezuela, at the age of 9 when her father went into business with a relative. There she met Manuel Blum, who would become her husband of 62 years and a pioneering computer scientist himself. In Caracas, Blum also discovered the other great love of her life, mathematics.
After overcoming many obstacles, she made her way to graduate school at the Massachusetts Institute of Technology. There, she specialized in a branch of logic called model theory, which analyzes the common features of different mathematical theories derived from the same underlying assumptions. Blum received her doctorate at age 25 for developing a new way to apply this high-level perspective to mathematical structures called algebraic field theories.
Upon graduating, Blum received a prestigious postdoctoral fellowship, but she soon found the path to a traditional academic career closed off to female mathematicians. That’s when she first got involved in advocacy. She played a leading role in founding the Association for Women in Mathematics and went on to establish many influential programs for supporting women students.
But she never lost sight of mathematics and the nascent field of computer science. In the 1980s, Blum began to work with the mathematicians Stephen Smale and Michael Shub to develop a formal theory of computation using continuous real numbers instead of zeros and ones.
Continuous mathematics like calculus is an essential part of many algorithms in fields ranging from computational physics to machine learning. Implementing such algorithms on digital computers invariably involves approximation, but theoretical analysis of their limitations is plagued by subtleties stemming from those approximations. Blum’s work gave researchers a rigorous new way to study the mathematical foundations of calculus-based algorithms. It also enabled a new approach to computational complexity theory, the study of the fundamental difficulty of different computational problems.
And though Blum retired four years ago from Carnegie Mellon University, where she had been on the faculty since 1999, that hasn’t stopped her from finding new questions to explore. In recent years, she and her husband have worked together to formulate a mathematical model of consciousness inspired by theoretical computer science. And she’s putting her many years of leadership experience to use as the president of the newly formed Association for Mathematical Consciousness Science.
Quanta spoke with Blum about her path into mathematics, how to help women succeed in the field, and what computer science can tell us about consciousness. The interview has been condensed and edited for clarity.