I was born in New York City in 1918 into a family that had a number of artistic people among its members. My father's brother and a sister's husband were probably the best known. The latter, Ivan Olinsky, taught for many years at the Art Students' League in New York City. I have been told that my paternal grandfather professionally made artistic decorations in peoples' homes.

The propensity for artistic endeavors extended to my generation and beyond. My mother was an excellent pianist and organist and it was one of her hopes that I would become a professional pianist. As a youth I was entered into "Music Week" competitions in New York City. I had some modest success, but found at an early age that I had no taste for public performance. On the other hand, I was strongly attracted to science as a lifelong career at an early age. I had the privilege of attending schools in the New York City public school system. Their standards of education, character building and discipline were very high and I, most certainly, benefited from them. They separated out the more advanced students and permitted them to progress at their own pace. In my case, this occasionally led to some curious circumstances. In my senior year in high school (Abraham Lincoln), the girls would join the boys to practice dancing.

I was 14 years old at the time and the girls were the usual 17 - 18 years old. The physical discrepancy between this 14 year old boy and 17-18 year old girls was considerable. Their first reaction was incredulity but after a while they got used to my presence and even danced with me. I took the chemistry and physics courses that were available, both taught by the same man. He recognized my interests and was very encouraging to me. I enjoyed a number of sports that I participated in at every opportunity, swimming in the ocean nearby, a game called single-wall handball, played with a little hard black ball and well-known mainly in some metropolitan areas, touch football whose rules eliminate the bruises from tackling and ice-skating that was facilitated by the flooding of a huge parking lot by the local fire department. I entered the City College of New York in 1933 and, at first, found it to be a bit of a struggle. Their academic standards were very high and they had a concentration of the best students in New York City. In addition, I spent three hours a day traveling on the subway system to and from home. This marked the end of piano practicing. City College had no tuition fee. The only financial requirement was one dollar per year for a library card. At the College, there were broad course requirements for all students that ranged through mathematics, the physical sciences, the social sciences and literature. There were even two years of compulsory public speaking courses.

I studied, in addition to the requirements, some additional mathematics, some physics, and much chemistry and biology. The year after graduation from City College was spent at Harvard University in the study of biology, for which I received a master's degree, M.A., in 1938. After a brief hiatus, I went to work with the New York State Health Department in Albany. While there, I had the opportunity to spend some time again at the piano. At the time I was in Albany, the fluoridation of drinking water was getting underway. I developed a procedure for determining the amount of fluorine in water supplies that became a standard method. This was my first modest contribution to science. It was my intention to save enough money while at the Health Department to return to graduate school. This I did, and I entered the Chemistry Department of the University of Michigan in 1940 where I met my wife, Isabella Lugoski, whom I married in 1942, at an adjoining laboratory desk the first day that I went to physical chemistry class. We were both attracted to physical chemistry and took our degrees with Professor Lawrence O. Brockway whose speciality was the investigation of gas-phase molecular structure by means of electron diffraction. Although my Ph.D. degree was awarded in 1944, I had completed all my work for it during the summer of 1943 and went off to work on the Manhattan Project at the University of Chicago.

Isabella joined me on this project a few months later. In 1944, we returned to the University of Michigan, I went to work on a project of the Naval Research Laboratory and Isabella as an instructor in the Chemistry Department. While at the University of Michigan, I performed some experiments on the structure of monolayers of long-chain hydrocarbon films involved in the boundary lubrication of metallic surfaces. I also derived a theory that explained the electron diffraction patterns obtained from the oriented monolayers. In 1946 we both went to work permanently in Washington for the Naval Research Laboratory. Our interest continued in developing the quantitative aspects of gas electron diffraction analysis. The solution of a key problem that arose in such analyses had evident implications for crystal structure analysis and, in fact, other areas of structure determination. At about the time that these matters were developing, Herbert Hauptman joined us at the Naval Research Laboratory and we decided to pursue the implications for crystal structures. This eventually led to the development of the direct methods for crystal structure analysis with the major part of the mathematical foundations and procedural insights established in the early 1950's. While all this was going on and with hardly missing a step from her research activities, Isabella mothered three children, Louise in 1946, Jean in 1950, and Madeleine in 1955. Louise is a theoretical chemist, Jean an organic chemist and Madeleine is a museum specialist trained in geology.

The initial applications of the procedure for structure determination for centrosymmetric crystals involving probability measures and formulas derived from the joint probability distribution were performed in the middle 1950's in collaboration with colleagues at the U.S. Geological Survey. Then, in the second half of the 1950's, through the efforts of Isabella Karle, an experimental X-ray diffraction facility was established in our own laboratory. During the 1960's, there was an intensive program in my laboratory to develop a procedure for crystal structure determination of broad applicability that would encompass noncentrosymmetric as well as centrosymmetric crystals. Largely through the efforts of Isabella Karle, such a procedure was developed and called the symbolic addition procedure.

This procedure had its origins in the theoretical work and the experience in practical application of the 1950's, but it also required some new procedural insights and some additional theoretical work to make it efficient and broadly applicable and avoid the pitfalls that easily arise when optimal pathways through a procedure must be chosen on the basis of probability measures. The first application of the symbolic addition procedure was published in 1963 and the first essentially equal atom noncentrosymmetric crystal structure to be solved by direct phase determination was published in 1964. This was followed by a number of exciting applications and toward the end of the 1960's many laboratories started to become interested in the potential of the direct method for structure determination. During the 1960's, I collaborated with Isabella in some of her investigations and derived with her a variance formula that was the basis for applying probability measures to procedures for analyzing noncentrosymmetric crystals. In addition, I also carried out a number of theoretical investigations. Perhaps, the most useful one concerned a procedure for developing a fragment of a structure into a complete one by use of the so-called tangent formula for phase determination. During the 1950's and 1960's, I maintained an interest in gas electron diffraction and made some experimental and theoretical studies of internal rotation and coherent diffraction associated with excitation processes.

The latter was especially interesting, but required extensive experimental development that the resources available to me did not permit. In the 1970's, I continued theoretical work in crystal structure analysis that included the derivation of a "tangent formula" for phase determination that was based on the more restrictive higher and higher order determinants from the determinantal inequalities. I showed how joint probability distributions relevant to crystallographic quantities could be put into an exponential form and thereby decrease considerably problems with asymptotic convergence. I also derived heuristic joint probability distributions based on the determinants involved in the determinantal inequalities and obtained from them formulas for evaluating triplet phase invariants and, later on, formulas for the expected values of phase invariants and embedded semi-invariants of any order, triplet, quartet, quintet, etc. The utility of phase invariants of high order in phase determination has so far been rather limited, except perhaps collectively in the high order determinants where they have been useful for refining the values of approximately determined phase values.

I participated with Wayne Hendrickson of my laboratory in some refinements of macromolecular structure with the use of the tangent formula and also had some early participation with John Konnert and Wayne Hendrickson in the constrained refinement technique for macromolecules. In collaboration with John Konnert and Peter D'Antonio, procedures were developed for determining atomic arrangements in amorphous materials based on criteria similar to those applied to molecular vapors.

Collaborations on structural problems also included Judith Flippen-Anderson, Clifford George, Richard Gilardi and Alfred Lowrey. At the end of the 1970's Wayne Hendrickson made some valuable advances in the application of anomalous dispersion to the determination of macromolecular structure that rekindled an interest that I formerly had in this subject. I developed an exact, linear algebraic theory that includes any number and type of anomalous scatterer and any number of wavelengths. It can also incorporate information from isomorphous replacement measurements. Exact data give exact values for the unknown quantities that include phase differences. I have also been investigating the evaluation of triplet phase invariants to see what their potential usefulness may be. This activity continues to the present and is greatly facilitated by Stephen Brenner who has performed my programming and computing for me since the early 1960's. In addition to participating in the development of new analytical methods and their applications, I have taught from time to time, mathematics and physics in the University College of the University of Maryland, I have taken an active role in the affairs of crystallography over the years as, for example, President of the International Union of Crystallography (1981-1984) and have enjoyed having a laboratory that investigates a broad variety of subjects ranging over gaseous molecules, amorphous solids, fibers, crystals and crystalline macromolecules.

During my entire married life I have had the strong support of my wife, both technical and spiritual. I also deeply appreciate the supportive atmosphere provided by the Naval Research Laboratory. This was especially helpful during the early 1950's when a large number of fellow-scientists did not believe a word we said.