Justin Jesse Price (1930–2011): The Master of Mathematical Exposition
Justin Jesse Price was a mathematician who understood that the beauty of mathematics lies not just in its discovery, but in its communication. A specialist in harmonic analysis and orthogonal functions, Price is perhaps best remembered by the broader academic community as one of the 20th century’s premier mathematical expositors—a scholar capable of distilling the most formidable abstractions into elegant, lucid prose.
1. Biography: From Philadelphia to West Lafayette
Justin Jesse Price was born in 1930. He pursued his higher education at the University of Pennsylvania, where he demonstrated an early aptitude for the rigorous demands of mathematical analysis. He earned his Ph.D. in 1956 under the supervision of Nathan Fine, a mathematician known for his work in number theory and analysis. Price’s doctoral dissertation, titled "Some Duality Theorems," laid the groundwork for his lifelong interest in the structural symmetries of mathematical systems.
Following his doctorate, Price held an instructorship and assistant professorship at Cornell University (1958–1963). In 1963, he joined the faculty at Purdue University, where he would spend the remainder of his career. At Purdue, he rose to the rank of Professor of Mathematics and eventually became Professor Emeritus upon his retirement. Price was a fixture of the Purdue mathematics department for nearly four decades, known as a rigorous researcher and a formidable teacher.
2. Major Contributions: Orthogonal Functions and Walsh Series
Price’s research focused primarily on Harmonic Analysis, specifically the study of orthogonal functions. While many mathematicians focus on the trigonometric functions (sine and cosine) used in Fourier analysis, Price specialized in Walsh functions—a family of square-wave functions that form an orthogonal basis.
His technical contributions include:
- Lacunary Series: Price conducted significant research into the convergence properties of lacunary (or "gap") series within orthogonal systems.
- Completeness of Systems: He explored the conditions under which a set of functions can represent any other function within a given space (completeness), providing deeper insights into the behavior of Walsh-Paley systems.
- The "Price’s Theorem" (Harmonic Analysis): In the context of Walsh functions, he developed results concerning the transformation of coefficients, which helped bridge the gap between classical Fourier analysis and the more "digital" world of Walsh-Hadamard transforms.
3. Notable Publications: Pedagogy and Research
Price’s bibliography is divided between high-level research papers and highly influential textbooks that shaped a generation of students.
- "Topics in Orthogonal Functions" (1975): Published in the American Mathematical Monthly, this paper is considered a masterpiece of mathematical writing. It provided a clear, unified overview of a complex field and remains a recommended text for students entering analysis.
- Calculus (with Harley Flanders and Robert Korfhage, 1970): This textbook was a mainstay in American universities during the 1970s and 80s. It was praised for its rigorous yet intuitive approach to the subject.
- Algebra and Trigonometry (with Harley Flanders): A series of foundational texts that emphasized logical structure over rote memorization.
- "Walsh Series and G-sets" (1977): A technical paper in the Proceedings of the American Mathematical Society that explored the relationship between set theory and harmonic analysis.
4. Awards & Recognition: The Chauvenet Prize
The pinnacle of Price’s professional recognition came in 1976, when he was awarded the Chauvenet Prize by the Mathematical Association of America (MAA).
The Chauvenet Prize is the highest award for mathematical expository writing. It is given to the author of an outstanding paper that clarifies a complex mathematical topic for a general mathematical audience. Price won the award for his paper "Topics in Orthogonal Functions."
"The citation noted his ability to make difficult concepts seem natural and almost inevitable."
Additionally, Price was a frequent recipient of teaching awards at Purdue, reflecting his commitment to the classroom as much as the research lab.
5. Impact & Legacy: Modernizing Mathematics Education
Justin Jesse Price’s legacy is twofold:
In Research
His work on Walsh functions proved to be prescient. While Walsh functions were once seen as a niche area of pure mathematics, they became fundamental to digital signal processing and telecommunications (specifically in CDMA technology used in cellular phones). Price's theoretical explorations of these functions provided the mathematical scaffolding for these later technological leaps.
In Education
Price was a vocal advocate for "mathematical literacy." He believed that mathematics should be taught as a language of logic rather than a collection of "tricks." His textbooks moved away from the "New Math" trends of the 1960s, which he found overly formal, and instead focused on a "middle way" that combined rigorous proof with practical application.
6. Collaborations: The Flanders-Price Partnership
The most significant collaboration of Price’s career was with Harley Flanders. Together, they formed one of the most successful textbook-writing duos in 20th-century mathematics. Their styles complemented each other perfectly: Flanders provided a broad, creative vision of the mathematical landscape, while Price brought a meticulous, crystalline clarity to the exposition.
At Purdue, Price was also a respected mentor. He supervised several Ph.D. students, including William C. Bauldry, who went on to become a notable mathematician and author in his own right, continuing Price’s tradition of high-quality mathematical communication.
7. Lesser-Known Facts: The Wit of a Scholar
- A Sharp Critic: Price was known for his dry wit and his intolerance for "sloppy" thinking. He once famously critiqued the state of mathematics education by noting that many students were being taught "how to get the answer without understanding the question."
- The "Price Method": In his classrooms at Purdue, he was known for a Socratic style of teaching. He rarely gave "standard" lectures; instead, he would challenge students to derive theorems on the chalkboard, guiding them with subtle hints—a method that was intimidating to some but transformative for those who pursued research careers.
- A Devotion to the Monthly: Price held a deep affection for the American Mathematical Monthly. He believed that short, elegant papers published there were often more valuable to the mathematical community than 100-page monographs that no one could read.
Justin Jesse Price passed away in 2011, leaving behind a body of work that serves as a reminder that the highest calling of a scholar is not just to know, but to teach.