## Abstract

Richard J. Goldstein was a distinguished figure in both scientific and engineering research, who served in several important professional societies and was honored with fellowships and appointments to numerous domestic and international academies. His global impact is further felt through the distinguished students he mentored during his highly productive academic career and who have subsequently achieved success in academia, research, and industry. However, to many, Goldstein's most profound and personal impact was as an esteemed educator, thesis advisor, and mentor. The heartfelt gratitude expressed by these students and colleagues attests to his profound influence in their lives. This brief article endeavors to delve into Goldstein's academic genealogy, a history of groundbreaking contributors spanning over six centuries, which also bears witness to the evolution of the present-day fields of thermodynamics and heat and mass transfer. Richard J. Goldstein's academic lineage traces back through two primary branches: (i) an astronomy/physics branch and (ii) a mathematics/physics branch. The astronomy/physics branch commences its journey from the venerable Nicolaus Copernicus, whose revolutionary contributions laid the foundation for seminal research in the field of astronomy. The mathematics/physics branch is anchored by eminent figures such as the Bernoulli brothers, Leonhard Euler, Jean d'Alembert, and Pierre-Simon Laplace. Presented in this article predominantly in the form of a directed graph, this succinct academic lineage illustrates the historical roots of Goldstein's intellectual heritage, a journey incorporating key figures greatly revered by the contemporary thermodynamics and heat transfer research community.

## 1 Introduction

Any scientist's path is largely paved with the enduring legacy of his predecessors. Academic lineage (or, genealogy) traces this invisible thread of discovery, connecting generations of advisors, students, mentors, mentees, and collaborators. Interestingly, although academic genealogy is most often visualized as groups of branches at the top converging to a single root below, this genealogy is traced back from the root (or, the subject of interest) through individual branches and scholarly relationships that helped shape the academic ancestry of this individual. This article endeavors to chronicle the academic lineage of Richard J. Goldstein, who was himself a pioneer in the field of heat and mass transfer and is considered by many to be the father of film cooling [1].

Owing to the substantial history inherent in such genealogical trees, attributable to the common occurrence of multiple advisors (and multiple students), this article will focus only on pedagogical relationships in the context of doctoral, habilitation,^{1} or postdoctoral advisors. The discussion presents a concise overview of select branches within two main clusters in the general disciplines of astronomy/physics and mathematics/physics (refer to Fig. 1 for a brief summary of the scientists included in this article). Interested readers are encouraged to visit the educational genealogy webpage of Goldstein^{2} for a more thorough illustration of his remarkable academic pedegree. The data for the graphs illustrated in this article are a culmination of personal discussions with Goldstein and the use of online resources such as the Mathematics Genealogy Project [2] and the Physics Tree: The Academic Genealogy of Physics [3]. A more comprehensive genealogy tree for most of these mathematicians/physicists can also be found in Mathematics Genealogy Project^{3} [2] and the Physics Tree: The Academic Genealogy of Physics [3].

## 2 20th-Century Connections

The journey of uncovering Goldstein's scientific ancestry in the 20th century originates at the University of Minnesota Twin Cities and retraces its steps toward the Technical University of Munich.

### 2.1 University of Minnesota: Heat Transfer Laboratory.

Richard J. Goldstein's six decade long academic and research career, during which period he advised and mentored 82 master's and 74 doctoral students, unfolded chiefly in the Heat Transfer Laboratory at the University of Minnesota Twin Cities. Goldstein's seminal work on optical measurement systems for fluid velocity and temperature, development of cooling design strategies for high-performance gas turbines, and novel measurements in thermal and forced convection systems were realized within this laboratory. This laboratory (then called as the Thermodynamics and Heat Transfer Laboratory) was founded by his doctoral advisor, Ernst Eckert, the father of the modern engineering field of Heat and Mass Transfer who is also credited as the author of one of the first books on heat and mass transfer [5]. The widely recognized reputation of this laboratory as one of the premier research efforts in this field within the United States stems primarily from Eckert's, and later Goldstein's, groundbreaking contributions. Other prominent figures at the University of Minnesota having had a profound impact in this field include Ephraim Sparrow (heat transfer and fluid mechanics) and Warren Ibele (thermodynamics and mass transfer).

### 2.2 Technical University of Munich: Institute of Technical Physics.

As we move further back in time and examine Ernst Eckert's academic lineage, we connect to the German university system. Eckert completed his doctorate in engineering (Doctor of Ingenieurwissenschaften) from the German Institute of Technology, Prague. Later, after moving to Ernst Schmidt's laboratory at the Institute of Technology Danzig, he gained an interest in the area of thermal radiation and pursued a second doctorate (Dr. Habil.) with Schmidt. Schmidt was a highly regarded scientist whose contributions to the field include substantial advances in thermal diffusion and radiation, optical schlieren/shadowgraphy techniques, dropwise condensation, and mass transfer. Schmidt, in turn, was advised and mentored by Oscar Knoblauch, a physicist/mathematician known for his work on topics such as hydrodynamics, saturated and super-heated steam properties, heat conduction, and temperature measurements. Knoblauch advised and mentored a number of pioneering researchers in heat transfer.^{4} Figure 1 visualizes this connection to the institute (shown in red), featuring a few more eminent scientific/engineering researchers with this shared link.

Oscar Knoblauch was the first director of the Institute of Technical Physics at the Technical University of Munich [6,7], founded by scientist, engineer, and industrialist Carl von Linde, who discovered an early variant of the vapor compression refrigeration cycle and technologies for thermodynamic separation processes of air into industrial gases [6–8]. Notably, von Linde did not have an accepted dissertation and could not officially graduate due to a student protest at the University of Zürich in 1864 [2]. However, he was appointed as an associate professor (1868) and, later, full professor and chair of the Laboratory for Theoretical Machine Design. He oversaw the construction of this laboratory, a first-of-its-kind in Germany, tailored to his specifications [6]. Among his students during this period was Rudolf Diesel [6] (not shown in the genealogy tree), well-known for his invention of the diesel engine. As von Linde's innovative refrigeration technology gained traction, von Linde found himself increasingly consumed by its industrial applications. He later returned to the Technical University of Munich in 1902 as an extracurricular professor for applied thermodynamics. It was during this period that he established the Institute of Technical Physics at the Technical University of Munich to comprehensively understand outstanding issues in thermodynamics, fluid flow, and heat transfer, topics that were also of critical technical importance in von Linde's gas separation and liquefaction process [6,7]. Carl von Linde envisioned that this new institute should be led by a young physicist, someone capable of meeting its technological demands while simultaneously ensuring high-quality education of engineering students in physics and technology [7]. Knoblauch fulfilled von Linde's exacting criteria and led the institute as the first director, serving for the next 32 years until Walther Meißner took over in 1934 [7]. The Technical University of Munich bore witness to the inception of a number of other important laboratories and affiliated institutions, headed by many of the highly acclaimed scientists in the field of heat transfer, including but not limited to Wilhelm Nusselt, Ernst Schmidt, Max Jakob, Ulrich Grigull, and Franz Mayinger [6,7,9–11]. Among their notable contributions are the development of the theory of laminar film condensation and dimensional analysis (Nusselt), analogy of heat and mass transport (Schmidt), foundational contributions in multiphase flows and introduction of new optical techniques such as holographic interferometry and laser-induced fluorescence (Mayinger), and measurement of thermal conductivity, advances in the understanding high-purity steam behavior, convective heat transfer, and boiling and condensation (Jakob) [10,11].

## 3 19th–16th Century: Astronomy, Physics, Mathematics

Crossing over to the 19th century, our exploration now arrives at Oscar Knoblauch's advisor at University of Bonn, Rudolph Lipschitz, famed for his research on mathematical analysis, differential geometry, number theory, and classical mechanics [12]. Roughly before this time (in the last half of the 18th century and through the 19th century), the basic foundations of thermodynamics and the mechanisms and theory of heat transfer were being developed [5,13]. This is a noteworthy juncture in Goldstein's lineage, where his academic genealogy diverges into two branches of study, broadly speaking, the disciplines of astronomy/physics and mathematics/physics through Lipschitz and his student Knoblauch. It should be noted here that a clear distinction between the scientific disciplines of astronomy, physics, and mathematics is challenging before the 20th century. As an illustration, let us consider Abraham Kästner, just a few generations removed from Lipschitz, who has been represented in the Astronomy/Physics branch in Fig. 2. One of Kästner's doctoral students, Johann Pfaff (not represented in Fig. 2), was the advisor of Carl Gauss. Gauss is widely regarded as one of the greatest mathematicians of all time [8,12], with vast and influential contributions on topics including number theory, differential geometry, magnetism, astronomy, and optics. Another noteworthy example, Lipschitz's and Gauss' combined academic descendants lead to another famed German mathematician, David Hilbert, who is known for the calculus of variations, foundations of geometry, spectral theory, integral equations, and mathematical physics [2,8]. Therefore, while this partitioning of the graph into these two branches is not truly definitive, this distinction is useful as we proceed with this discussion. Once again, reader must bear in mind that only a few of the most influential figures within these two branches have been highlighted in this article.

### 3.1 Astronomy/Physics.

As we trace the astronomy/physics branch of Richard J. Goldstein's genealogy, we follow along two different branches of ancestors (as shown in Fig. 2). One branch journeys along Carl von Linde's advisor Ruldoph Clausius (this connection has not been expanded in Fig. 2). Rudolph Clausius, a German theoretical physicist and mathematician, is primarily known for his fundamental work in thermodynamics, in particular, his statements of the first and second law of thermodynamics replacing the caloric theory of heat and for the concept of entropy. He is also widely recognized as one of the most significant founders of the modern scientific discipline of thermodynamics [8,9,12]. The second branch progresses through Rudolph Lipschitz and Nicolaus Zapf, with both these branches culminating at Erasmus Schmidt. Erasmus Schmidt traces his ancestry back to Georg Rheticus, an Austrian mathematician/astronomer, perhaps best known for his trigonometric tables. Among Rheticus' descendants are Tycho Brahe, an eminent Danish observational astronomer, and Johannes Kepler, a German astronomer/mathematician acclaimed for his formulation of three important fundamental laws of planetary motion derived from Brahe's observational data [8,17]. It has also been stated that Kepler had “some inkling of the meaning of his laws—universal gravitation” [17]. Through Rheticus, who is the only known student of Nicolaus Copernicus and helped facilitate the publication of Copernicus' book, we arrive at the origin of the astronomy/physics branch of our genealogy tree: Nicolaus Copernicus. Copernicus was an esteemed Polish astronomer and mathematician well known for his formulation of a heliocentric model of the universe that was eventually widely accepted, displacing its predecessor, the geocentric model often associated with Aristotle and Ptolemy [8,17]. A major milestone in what is now commonly termed the Scientific Revolution was Copernicus publishing of the heliocentric model in his book titled *“On the Revolutions of the Celestial Spheres.”*

### 3.2 Mathematics/Physics.

Transitioning to the mathematics/physics branch of Richard J. Goldstein's ancestry, we retrace our steps to Oscar Knoblauch. Previously cited as the first director of the Institute of Technical Physics at the Technical University of Munich (Sec. 2.2), Knoblauch's doctoral research was completed at the University of Bonn in 1887 on the topic “mathematical development in the study in hydrodynamics about an ellipsoid.” Notably, in his thesis, he mentions an impressive list of mathematicians/physicists whom he had studied under during his academic preparation. These included Georg Cantor, Rudolf Clausius, Karl Weierstrass, and, of course, his mentor/advisor Rudolph Lipschitz. As we delve further into Lipschitz's history (see Fig. 3), we come across Gustav Dirichlet, his doctoral advisor at University of Berlin, and through Dirichlet transition into the mathematics/physics branch of Goldstein's academic ancestry. This branch includes some of the most distinguished group of scientists with profound contributions in many aspects of mathematics and physics. These include Jacob and Johann Bernoulli (contributions to calculus, calculus of variations, probability theory, fluid mechanics), Leonhard Euler (analytic number theory, complex analysis, fluid mechanics, astronomy), Joseph Lagrange (classical and celestial mechanics, number theory and analysis), Jean Fourier (harmonic analysis, differential equations, Fourier transform, theory of heat diffusion), Gustav Dirichlet (number theory, probability, potential theory, theory of heat and hydrodynamics), Jean d'Almbert (wave equation, dynamics/statics second law of motion, fluid mechanics), Pierre-Simon Laplace (Laplace transform, celestial mechanics, heat flow, and statistical inference), and Siméon Poisson (statistics, complex analysis, analytical mechanics, fluid mechanics). As clearly evident, many (if not all) of these mathematical physicists have had a direct and significant impact in mathematical analysis methods for fluid flow and heat transfer through their research.

## 4 Final Remarks

This brief discussion has only traced a few illustrative branches that connect Richard J. Goldstein with an astounding lineage of scientists who spearheaded the evolution of the fields of thermodynamics and heat and mass transfer engineering. It is fascinating to observe the confluence of astronomy, physics, and mathematics in the 16th–19th century and how it influenced the development of the Institute of Technical Physics at the Technical University of Munich, launching the academic journey of many pioneers in the field of heat and mass transfer, and culminating in the founding of the Heat Transfer Laboratory at the University of Minnesota Twin Cities and to Goldstein's own extensive influence in the field of heat and mass transfer research.

This exploration serves as a testament to the collaborative nature of scientific inquiry, with each succeeding generation building upon the knowledge of their predecessors. And as we celebrate the achievements and astounding academic genealogy of Richard J. Goldstein, we also recognize that Goldstein's legacy extends not only through his own scientific achievements, but also through the next generation of scientists and engineers whom he has advised/mentored and who continue to carry forward his legacy of scientific discovery.

## Acknowledgment

J.N.S. would like to gratefully acknowledge Professor Wolfgang Wall of Technical University Munich for his help in suggesting the web-based resource on the history of the University's Physics Department [7]. U.M. would like to thank Aruna S. Pisharody for her help in rendering the genealogy tree in LaTeX and editing the paper.

## Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

## Footnotes

A habilitation thesis is a comprehensive scholarly work required in many European countries after a doctoral degree, to demonstrate advanced research competence and teaching skills for eligibility to hold a professorship.

Posters of graphs can be requested directly from the MGP website, and also visualized with tools from [4].

Interestingly, Schmidt would return to the institute in 1952 as a director. “He was appointed to the chair of Theoretical Machine Design and, with A. Loschge and later R. Stroehlen, as director of the Laboratory for Heat Engines, Refrigeration, Heating, and Ventilation, as the laboratory was then called” [6].

## References

*JAKOB, MAX 1879-1955*

*NUSSELT, WILHELM (1882-1957)*

*SCHMIDT, ERNST (1892-1975)*