This biography, written by J J O’Connor and E F Robertson, has been republished with permission from the School of Mathematics and Statistics at the University of St Andrews, Scotland.
Born: 6 December 1908, Austria
Died: 25 January 2000
Country most active: United States
Also known as: Herta Taussig
We have based the following biography of Herta Taussig Freitag mainly on references quoted below which were written after the authors had interviewed Herta, on the material supplied to us by George Phillips who was a friend of Herta’s collaborating with her on at least ten papers, and on EFRs personal knowledge of her through the Fibonacci conferences.
Herta Freitag, only known as Freitag after her marriage, was given the name Herta Taussig. She was the daughter of Josef Heinrich Israel Taussig (1876-1942) and Paula Caroline Sara Taussig (1880-1967). Josef had been born in Vienna on 26 July 1876 and Paula was born on 1 May 1880, also in Vienna. Herta had a younger brother, Walter Adolf Taussig (1908-2003), born in Vienna on 9 February 1908. We note that it is unusual for two siblings to have the same year of birth yet not be twins:-
[Herta] credits her wonderful home life for the success that both she and her brother ultimately enjoyed. Evenings were spent with the entire family together – mother, father, brother, and Herta – each doing what they most enjoyed. Her brother Walter would be composing, her mother would be doing needlework, her father would be reading ‘Die Neue Presse’ (he was managing editor of this Austrian newspaper), and Herta would be doing mathematics.
Before we continue with Herta’s biography, let us give some details of her brother Walter Taussig:-
[Walter Taussig] studied at Music Academy in Vienna, working on harmony, composition and piano with Franz Schmidt, the composer, and conducting with Robert Heger. He also studied the oboe. … After graduating in 1928, Mr Taussig worked as a conductor and coach in a number of theatres, from Finland through Germany and even to Istanbul, but Vienna remained home base. However, the climate in the German-speaking world was not healthy for a Jewish conductor, even one who had been baptized as a Lutheran as a safeguard, and Mr Taussig ultimately crossed the Atlantic, conducting the Havana Philharmonic (where he was succeeded by Erich Kleiber). He then worked at the Montreal Opera, the Chicago Opera and the San Francisco Opera. …
After 1949, when he became its assistant chorus master, the Metropolitan Opera was his main employer. He went on to the post of associate conductor … For 18 years, starting in 1964, he was also an assistant conductor at the Salzburg Festival, working with long-time friends and colleagues Herbert von Karajan and Karl Böhm. He was also a coach for the record company Deutsche Grammophon.
Let us return to details of Herta Taussig’s education. She began her education at a kindergarten in Vienna. In 1921, when she was twelve years old she wrote in her diary:-
I have finally found a subject where I do not need to memorise, but can think things out myself – mathematics.
A little later she wrote in her diary:-
I want to be a teacher of mathematics. I don’t know whether I will be good enough.
After kindergarten, she studied at a gymnasium in Vienna where mathematics was given pride of place. It was never taught as the first lesson since the pupils might by sleepy and never as the last lesson before lunch since the pupils might not concentrate enough if they were hungry. By the time she had completed her studies at the gymnasium she wrote in her diary:-
I don’t want just to be a teacher of mathematics. I want to be a good teacher of mathematics.
Herta entered the University of Vienna with the aim of training to become a teacher of mathematics at a gymnasium. She lived at home with her family and did a little mathematics tutoring to help with the family finances. She recalled how she and her fellow students felt at that time:-
We were exceedingly idealistic at that time. We loved mathematics and were preparing for teaching at gymnasium. We all knew that the chance of obtaining a position was practically nil as Vienna was overrun with professionals, and mathematics professors were anything but in short supply, but we really wanted to teach mathematics.
She received the degree Magister Rerum Naturalium, in Mathematics and Physics, from the University of Vienna in 1934. She impressed during teacher training and the certificate she was awarded stated:-
The candidate has an extraordinary command of her language to make even complicated mathematics topics easily accessible to her students.
Herta taught in Vienna from 1934 to 1938, first as a student teacher for one year, then as a “Gymnasium Professur”. Life changed for the Taussig family on 11 March 1938 for on that day Hitler sent an ultimatum to the Austrian Chancellor saying that if Austrian Nazis were not immediately put in control of the country, Germany would invade. In fact, without waiting for an answer Hitler ordered his army to invade and on the morning of 12 March they crossed the border. The Germans were greeted enthusiastically by many Austrians and, on 13 March, Austria and Germany were united. Josef Taussig, as editor of Die Neue Frei Presse, had written several editorials warning of the dangers of Nazism and knew immediately that he was in great danger. Herta recalled:-
Hitler took over on Friday March 13. I will never forget father’s toneless voice when he said to me, “There is no Austria anymore.” By the following Wednesday he was dismissed.
Herta’s brother was involved in a music tour of the United States at this time and was not in any danger. Herta and her parents, however, feared for their lives and decided to move immediately to a summer cottage they owned in the mountains around Vienna so they could plan their next moves. The best result for Herta, she decided, was to emigrate to the United States and continue her career as a teacher. This, however, was not easy to achieve. A sponsor in the United States was required and even when, though a friend of a friend, a surgeon in St Louis was asked and agreed to sponsor Herta, still there was a quota on numbers resulting in a long wait of an unknown length. Fearing for their safety, Herta decided to agree to travel to England where a visa could be obtained if she agreed to become a maid. This she did and shortly after this her parents were able to follow her.
On 1 September 1939 Germany invaded Poland and on 3 September the United Kingdom and France declared war on Germany. The Taussig family, of course, as Germans living in England were enemy aliens and, unless they could claim exemption from internment, they would be imprisoned. Josef and Paula’s application to a Tribunal was decided on 3 October 1939. Their nationality is given as “German by annexation,” their address as “‘Willow Mount’, Beacon Road, Crowborough, Sussex,” their present occupation as “None”, and both declared they did not desire to be repatriated. The decision of the Tribunal was “Exempted from all restrictions.” Herta’s application to the Tribunal was settled on 18 November 1939. Her nationality is given as “Austrian, German by annexation,” her address as “‘Letmans’, Jarvis Brook, Sussex,” her normal occupation “Teacher in Secondary School. Has title of ‘Professor’,” her present occupation as “Domestic servant employed by Miss Cicely H Washington, ‘Letmans’, Jarvis Brook, Sussex,” and she declared she did not desire to be repatriated. The decision of the Tribunal was “Exempted from all restrictions.”
Herta had various jobs in England over the following years, as a housemaid, governess, waitress and finally as a teacher. Her father, Josef Taussig, died in Cirencester on 28 November 1942:-
… content in the knowledge that his family had escaped Austria and would ultimately be reunited in the United States.
Herta and her mother eventually obtained visas for the United States and they embarked from Liverpool on the ship Delftdijk on 5 April 1944. The crossing to New York was hazardous since the United States and Britain were still at war with Germany and German submarines threatened any ships of these countries. The Delftdijk was part of a convoy of ninety-eight ships which included protecting navy vessels. To avoid German submarines, the convoy took a lengthy route and, as a consequence, took 21 days to make the crossing. They arrived in New York on 25 April, in thick fog so were not able to see the Statue of Liberty. Soon, however, they were able to disembark and were met by Herta’s brother Walter.
It was now Herta’s aim to find a teaching position and she signed up at an agency who found her a position at Greer School in Dutchess County, New York. This school, originally called Hope Farm School, had been founded in 1906 as a school for disadvantaged children. It had been renamed Greer School in 1940 for its founder David Hummell Greer. Herta said:-
My first teaching job in America was in Upstate New York at a school for poor children from broken homes. Naturally, I was apprehensive. Would the kids accept me? They accepted me once they discovered that I had been kicked around too.
Her mathematics career was thus rescued, although it had been effectively suspended for six years. These years, however, she didn’t consider as wasted. In the lecture A Last Lecture – How Kind of you to Want to Know Me she said of these times:-
All of this is a blessing – at least I see it this way. It has given me a greatly heightened sense of appreciation of life in my adopted land, a sharpened delight in small joys, and a deep love for all that is good in the world. And, for me, one of the best things in this world is mathematics.
She taught at Greer School from 1944 to 1948 and, in her second year there, she met the mathematics teacher Arthur Henry Freitag (1898-1978), whom she married in 1950. But Herta had ambitions to teach mathematics at a higher level and every summer she studied at Columbia University for her Master’s Degree; she graduated M.A. in 1948.
In 1948 she moved to Hollins College (now University), a private college for women in Roanoke, Virginia, where she was appointed as a mathematics instructor:-
Through great perseverance she established a mathematics department, where she was the sole member and taught seven courses in a language that was not her native tongue. At the same time she was working on a Ph.D. at Columbia.
She was particularly influenced at Columbia by Edward Kasner and Howard Eves (1911-2004):-
Throughout life, her early “love affair” with mathematics kept deepening. Number theory, especially recursive sequences, continued to tighten their grip on her fascination with numbers, and with problem posing and solving. She feels deeply moved when she is called a “problemist.” “I don’t call myself a mathematician,” she states, “but rather a student of mathematics, albeit quite an addicted one.” The happiest hours in her life have been spent “at the feet” of Edward Kasner and Howard Eves.
In 1953 she was awarded a Ph.D. from Columbia University for her thesis The Use of the History of Mathematics in its Teaching and Learning on the Secondary Level. Let us quote a few lines from the Abstract of the thesis:-
The fusion of the history of mathematics with its teaching and learning promises desirable outcomes for both student and teacher. Some of the possible contributions are in the nature of increasing results which may be obtained in the traditional way. Others lie in areas which cannot so readily be reached by the usual method. When mathematical ideas and the language of mathematics are studied in an evolutionary manner, better understanding may result. Meanings take on greater significance as their development shows the obstacles that had to be surmounted and as their values for human civilisation are recognised. Mathematical processes and methods are learned with more ease and greater retentivity. Awareness of mathematical situations becomes keener as understandings are deepened and interests are kindled. The interaction between mathematics and other forms of human accomplishments are seen. …
At Hollins College her career progressed from instructor to full Professor and departmental chairman, until 1971 when she took early retirement to care for husband who had become ill. Her husband, Arthur Freitag, taught mathematics at the Jefferson Senior High School, Roanoke, then at the William Fleming Senior High School, Roanoke. Herta and Arthur Freitag wrote a number of joint papers. As an example we mention Neopythagorean triangles (1956), and Using the history of mathematics in teaching on the secondary school level (1957) which begins as follows:-
More than two thousand years ago, Pythagoras lectured on the power of number, meaning only integers and fractions. He reiterated again and again, “Number rules the universe; the essence of all things is number.” Then one day he evaluated the diagonal of a unit-sided square. Alas, there was no number as he understood number which gave an answer.
Legend has it that one of his grief stricken students contrary to the rules of Pythagoras’ esoteric school divulged this number fiasco to an outsider. The student was drowned. Students are no longer drowned for breaking the rules of a school. But to know the difference between rational and irrational numbers is as important today as it was then.
Any educator interested in improving the teaching of mathematics must consider a more intelligent use of historical material. In ancient times, man was a local creature. During the Middle Ages he grew in social awareness and became provincial in his outlook. At the onset of modern history, nationality became his important social interest. Today not only do nearly all our problems affect the entire world, but many of them can be understood only in the light of their history. When discussing the uses of historical material in teaching secondary school mathematics, pertinent questions naturally arise. How does the knowledge and proper use of historical material aid both the teacher and learner of secondary school mathematics? Which historical approach will be most beneficial? Should the historical material be presented as part of an integrated course, or should specific units be given separately? Should it be chronological facts, as well as the biographies of the great mathematicians? And above all of these questions, do we have any valid criteria to offer as a basis of selection from these many possible approaches?
They also wrote the book The Number Story (1960) which has the following Introduction:-
During the sixth century B.C., the world’s earliest scientific society was holding meetings in Greece. Pythagoras, a pioneer in the teaching of mathematics, had founded a brotherhood of young men and women in which secrecy, magic, and religion were conglomerated with number inquiries. These inquiries laid a profound groundwork for the future development of mathematics.
Pythagoras discovered that the pitch of a note produced by a plucked string is closely related to its length; mathematics may, therefore, be used for describing musical intervals. With this insight he conjectured that mathematical language is qualified to help unravel nature’s, secrets, and thus mathematical physics was born.
The startling discovery that revealed an interdependence between number and physical phenomena intrigued the master. He thought he had found the nucleus of man’s most cherished dream – an understanding of the universe in which he lives. “Number is a universal measure of everything,” he reiterated, “number rules the universe,” “the essence of all things is number.”
What did he mean by “number”? How have more than two millennia in the evolution of mathematics affected his notions? Was Pythagoras right in his philosophy that number is the key for an understanding of our world?
For more than 2000 years generations of mathematicians have endeavoured to understand numbers fully. The concept of number has been extended and mathematical reasoning has become more rigorous and generalised. Has modern man, on the basis of these developments, lost Pythagoras’ viewpoint?
The book was reviewed by Frances Flournoy. The review begins:-
Through the ages, man has gradually developed number ideas, he has observed, noted relationships, and endeavoured to prove conclusively the general nature of ideas developed. In this monograph, the authors have presented some of the highlights in this story of the evolution of number from the first steps taken by prehistoric man to the mathematics of our present day. The historical development of the growth of number notions in regard to natural numbers, fractions, zero, and negative numbers, irrational numbers, and complex numbers is briefly presented. The authors also give a somewhat intuitive mathematical development of this structure.
During her years at Hollins College, and throughout her even longer period of retirement, she received many awards. For example, she received the first Virginia College Mathematics Teacher of the Year award in 1980. In May 1997 she was presented with the Humanitarian Award of the National Conference of Christians and Jews. The citation states:-
To have known her all these years, to have seen her joy of living expressed in so many ways, to have felt her gentle and guiding hand on the careers of so many, to have seen her look beyond hatred and see sharing, all these cannot be summarised better than to say wherever she has gone, whomever she has seen, she has left them richer and hoping to become more like her.
She was the first woman to become President of the Virginia, Maryland, and District of Columbia Section of the Mathematical Association of America.
Her lectures, always meticulously crafted and beautifully illustrated in her inimitably artistic calligraphy, are delivered so enthusiastically and yet so modestly, as if she fears that her personality might take any of the glory or attention away from Mathematics. One of her most inspired remarks concerns mathematicians’ fondness for generalising results:-
A mathematician is like a lover – give him a little finger and he wants the whole hand!
A colleague, with echoes of Gauss’s description of Mathematics as the Queen of the Sciences, and Number Theory as the Queen of Mathematics, named Herta Freitag as the Queen of the Fibonacci Association. For she has attended and given a paper at every International Conference of the Association since the first one in 1984. She has also contributed prodigiously to the Elementary Problems and Solutions Section of the Fibonacci Quarterly and published many papers in that journal. For example: On summations and expansions of Fibonacci numbers (1963), (with George M Phillips) A congruence relation for certain recursive sequences (1986), (with Piero Filipponi) Fibonacci autocorrelation sequences (1994), and (with Piero Filipponi) Division of Fibonacci numbers by k (1999).
Most appropriately, the Fibonacci Quarterly chose to honour her not on her 90th birthday, but on the threshold of her 89th year, since 89 is a number in the Fibonacci sequence. The dedication mentions one of Herta’s favourite stories:-
When two non-mathematicians meet on the street and one says, “I’ve got problems,” the other answers, “I’m so sorry for you.” When two mathematicians meet and one says, “I’ve got problems,” the other says, “Oh, goody!”
We noted that Herta took early retirement in 1971 to care for her husband. He died in October 1978 and the article, Herta Taussig to teach again, appeared in November. It ends as follows:-
She has a small apartment with a view of the Blue Ridge Mountains in a complex called Friendship Manor. “It is a place for old fogeys,” she said, “politely called a retirement home.” If Friendship Manor is for old fogeys, Herta Freitag is in the wrong place. She bought a tricycle and rides it 10 miles a day. She swims two hours a day. Her step has a lilt to match her eyes, especially when they suddenly brighten, as the other day. “I have good news,” she said, “I had a call from Hollins College. They asked me to come back next year to teach. Will I? Of course I will.”
Finally let us end by quoting Caren Diefenderfer’s memories of Herta Freitag:-
One of my favourite memories of Herta Taussig Freitag is the 48 hours that I spent with her and one of her college friends in Vienna during the summer of 1980. When we viewed the Danube, Professor Freitag declared with joy in her eyes, “It is only blue to those who are in love.” We travelled to Belvedere Palace to view the painting of her relative, Tina Blau, ate fine Viennese pastries and enjoyed an even finer friendship and joy. Sharing this time with Herta in Vienna was an amazing gift and a tribute to why Hollins is special to those who have taught and studied here. Herta’s portrait, a gift from the class of 1953 and the mathematics majors from 1949-1976, greets me every day when I come to my office. The portrait serves as a reminder of our shared passions: travel, music, swimming, and most important, the joy of solving mathematics problems.
Herta died in Roanoke at the age of 91. She donated her body to medical science.