**Ruth Michler**was the daughter of Gerhard O Michler, a mathematician who has made major contributions to the theory of groups and representation theory. There were two children in the family, Ruth having a sister. Gerhard Michler was born in Braunschweig, Germany, on 5 May 1938. He was awarded a doctorate from the Johann Wolfgang Goethe-Universität Frankfurt am Main in 1965 for his thesis

*Radikale und Sockel*Ⓣ. His thesis advisor was Reinhold Baer. He undertook postdoctoral studies at Cornell University in Ithaca, New York, USA, and it was while he was there that his daughter Ruth, the subject of this biography, was born. The family returned to Germany in April 1968 and Gerhard habilitated at the Eberhard-Karls-Universität Tübingen.

Ruth Michler spent the first six years of her life in Tübingen but, before she began her schooling, her family moved to Giessen when Gerhard Michler was appointed as a full professor at the Justus-Liebig-Universität Giessen. The family moved to Giessen in March 1973 and Ruth began her elementary schooling there, then progressed to begin her studies at a Gymnasium in the same city. In 1978 the family moved again, this time to Essen when Gerhard Michler was appointed as professor at the Universität Duisburg-Essen. Ruth then entered a Gymnasium in Essen and completed her studies there, graduating in 1985. During her years at school, Ruth greatly enjoyed learning foreign languages and had a particular passion for mathematics, sciences, fine arts and music.

It was at the University of Oxford in England that Ruth Michler undertook her undergraduate studies. Matriculating in 1985, she was a student at Balliol College where her tutors were Keith Hannabuss and Frances Kirwan. Keith Hannabuss had obtained a doctorate from the University of Oxford in 1969 for his thesis *Quantum Dynamics in De Sitter Space*. At the time Michler studied at Oxford, he was a fellow and mathematics tutor at Balliol College. Frances Kirwan had obtained a doctorate from the University of Oxford in 1984 for her thesis *The Cohomology of Quotients in Symplectic and Algebraic Geometry*, supervised by Michael Atiyah, and after having obtained a fellowship at Magdalen College, she was appointed as a fellow and tutor at Balliol College in 1986. In 1987 Michler won a won a Jenkyns essay prize for her paper "Black Holes," under the direction of Roger Penrose, the Rouse Ball Professor of Mathematics at the University of Oxford.

After the award of a B.A. from the University of Oxford in 1988, Michler went to the United States to undertake research for her doctorate. She enrolled at the University of California, Berkeley, where her Ph.D. advisor was Mariusz Wodzicki and Arthur Ogus acted as a second advisor. Mariusz Wodzicki, whose research interests were non-commutative and algebraic geometry, analysis, and K-theory, had studied for his doctorate at the Steklov Institute of Mathematics in Moscow advised by Yuri Manin. Wodzicki had been awarded his doctorate in 1984 for his thesis *Spectral Asymmetry and Zeta-Functions*. Arthur Ogus, also an expert in algebraic geometry, had studied for his doctorate at Harvard University, receiving a Ph.D. in 1972 for his thesis *Local Cohomological Dimension of Algebraic Varieties*. Michler was awarded a Ph.D. in 1993 for her 80-page thesis* Hodge-components of Cyclic Homology of Singular Affine Hypersurfaces.* She had presented a paper based on her thesis to the *K-theory* conference held in Strasbourg 29 June 29 - 3 July 1992. The paper had the same title as her thesis and it was published in the *Proceedings* of the conference. Jerry Lodder, reviewing the paper, writes:-

Michler received an invitation from Leslie G Roberts to spend the academic year 1993-94 at Queen's University in Kingston, Canada, as a postdoctoral fellow. A lovely sketch of Leslie Roberts was written by Asia Matthews when he retired from Queen's University:-In this paper the author proves that the Hodge-components of Hochschild homology of a reduced affine hypersurface are given by torsion modules of Kähler differentials. Using results of T Goodwillie, J-L Loday and U Vetter, the author also proves a vanishing result for the Hodge-components(also called the l-decomposition)of cyclic homology of affine hypersurfaces. The non-zero summands in this decomposition are computed in terms of the de Rham cohomology of the underlying algebra. Furthermore, in the case of a hypersurface defined by a quasihomogeneous polynomial, an explicit computation of the Hodge-components of cyclic homology is given. The reduced cyclic homology groups provide a topological invariant of algebras formed by the quotient of such polynomials.

Michler spent a year at Queen's University and wrote papers such asIn well-worn construction boots, Leslie Roberts taught mathematics in a way that was concise and unembellished. Though he glowered at you if you asked a question, you soon came to realize it was the face he made while patiently thinking up an insightful and precise explanation. Leslie's many published works reflect this habit of precision and insight. He made a significant contribution to the Department through his years as Associate Head, particularly managing the demanding process of hiring new faculty. He arrived at work by bicycle in all weather and anyone who needed a spot of alcohol to thaw a frozen brake cable need only seek Leslie out.

*Torsion of differentials of hypersurfaces with isolated singularities*(1995) and

*Torsion of differentials of affine quasi-homogeneous hypersurfaces*(1996). In both of these she thanks Leslie Roberts, writing in the 1995 paper:-

After spending the year in Canada, Michler decided that she would try to spend her career in the United States rather than return to Germany, the country in which she was brought up. At this time academic jobs were not easy to get in either Germany or the United States, but the United States was the more promising. Michler, with an outstanding record, was offered a tenure-track position at the University of North Texas in Denton in 1994. She was pleased to accept. At the University of North Texas she taught a variety of different courses including a graduate course on financial mathematics which she designed herself. Caroline Melles writes in her tribute about meeting Michler for the first time at the Fields Institute in Toronto, Canada [4]:-I would like to thank Prof A Ogus and Prof L G Roberts for helpful discussions. Moreover, I would like to thank Queen's University for their hospitability and support from the NSERC grant of Prof L G Roberts, while preparing this paper for publication.

This quote illustrates the energy that Michler had and this led her to attend conferences in many different countries around the world giving talks at these meetings. She gave lectures at American Mathematical Society meetings in Belgium and in South Africa. The Belgium conference was the first Joint International Meeting between the American Mathematical Society and the mathematical societies of Belgium, The Netherlands, and Luxemburg. It was held in Antwerp 22-24 May 1996. The South African conference was the first Joint Meeting of the American Mathematical Society, the South African Mathematical Society and the Southern Africa Mathematical Sciences Association. It was held at the University of Pretoria, 26-28 June 1997.Ruth and I met in the spring of1997, at the Fields Institute, when we shared an office for a few days and became instant friends. Ruth had driven from Texas to Toronto in a day, hardly stopping for food or rest. She paused briefly in Toronto, then was off to Kingston, to visit friends at Queen's University. We talked about everything - mathematics, friends, teaching, houses, running, and especially being a woman in mathematics. When I talked to her it was like talking to a best friend I had known all my life. We would start in the middle of a conversation, and jump from topic to topic. North Texas was a big change for Ruth after graduate school in Berkeley. She talked of life in Denton, and her students, and taking up running. She would mention running100miles as if it was nothing but scenery with an occasional stretch of boredom.

Michler gave the lecture* Torsion of differentials of hypersurfaces with isolated singularities* in the Special Session on *Commutative Noetherian Rings and Modules* at the Joint Mathematics Meeting of the American Mathematical Society and the Mathematical Association of America conference in San Francisco, California on 4-7 January 1995. She delivered the lecture *Cyclic homology and de-Rham cohomology of affine hypersurfaces* at the Special Session on *Combinatorics and Graph Theory* at the Joint Mathematics Meeting of the American Mathematical Society and the Mathematical Association of America conference in Orlando, Florida held 10-13 January 1996. At the Joint Mathematics Meeting in San Diego, California, 8-11 January 1997 she gave two lectures; *Algorithms for computing the generators of the torsion module of differentials* in the Special Session on *Computational Algebraic Geometry*, and *On the number of generators of the torsion module of differentials* in the Special Session on *Commutative Algebra*.

She attended the Joint Mathematics Meeting of the American Mathematical Society/Mathematical Association of America in San Antonio, Texas on 13-14 January 1999. She was a co-organiser of the special session *Singularities in algebraic and analytic geometr*y at this joint meeting and gave the lecture* Isolated hypersurface singularities with "large" torsion module of differentials*, publishing the paper *Isolated singularities with large Hochschild homology *in the Proceedings. She attended the *International Conference on Valuation Theory* held at the University of Saskatchewan in July-August 1999 and gave the talk *Invariants of singular plane curves*.

In [2] her research contributions are mentioned:-

We have mentioned some conferences that Micher attended but her involvement with conferences took on another level when, as we have already mentioned, she began to play a major role as a conference organiser. We noted above that she was a co-organiser of the special sessionAs a mathematician, Ruth worked primarily in the area of cyclic homology and singularity theory and since her graduation from Berkeley she had made solid contributions to this field. She had seven articles printed or in press, with several more in preparation or submitted. In her papers on reduced isolated hypersurface singularities she showed that cyclic homology is a direct sum of Hochschild homology and de Rham cohomology. Furthermore, she gave some algorithms to compute these invariants. Ruth brought an intensity to everything she did, and her mathematical work reflected this intensity. In her research, Ruth used techniques from several different areas of mathematics and combined very abstract theory with concrete calculations of examples, using computer programs such as Macaulay and Maple. She was persistent, returning to problems again and again, approaching them from different viewpoints, and discussing variations and improvements with colleagues in related areas.

*Singularities in algebraic and analytic geometry*in San Antonio, Texas, in 1999. She was also a co-organiser of the special session

*Singularities in algebraic and analytic geometry*at the joint American Mathematical Society/Mathematical Association of America conference on 19-22 January 2000 in Washington D.C. when she gave the lecture

*Deformations of isolated hypersurface singularities*. Again she was a co-organiser of the special session on

*Singularities and Algebraic Geometry*at the 2000 Fall Western Section Meeting of the American Mathematical Society in San Francisco, California, 21-22 October 2000. At this meeting she gave the lecture

*New and old results on singular plane curves*. In addition to organising these national events, she organized a joint seminar for the University of North Texas, the University of Texas at Arlington, and Texas Christian University, called AGANT (Algebraic Geometry, Algebra, and Number Theory).

For all the three Special Sessions that Michler co-organised at the Joint Mathematics Meetings, her fellow organiser was Caroline Melles. In [4] Melles writes about these sessions:-

Michler was awarded a National Science Foundation Professional Opportunities for Women in Research and Education Fellowship to visit the Mathematics Department of Northeastern University for the academic year 2000-2001 to work with Tony Iarrobino and Marc Levine. She died in a tragic accident:-One day she wrote to me to see if I would be interested in helping her to organize a special session at an American Mathematical Society meeting. That was the first of three sessions which we organized, one of which resulted in a book of proceedings. These are projects which I would never have attempted without Ruth's initiative and energy. Ruth was fearless and full of ideas. She travelled everywhere and talked to everyone. She did not hesitate to take on any project, or ask any mathematician to contribute to our sessions. She thought a meeting should be more than just a sequence of short presentations. She organized social events and problem sessions and lengthened the talks so that people could discuss their work in more depth. We invited the mathematicians we would most like to hear talk, and to my amazement, many of them accepted! Our sessions succeeded far beyond my expectations - not in numbers, but in the level of mathematical discussion and the sense of mathematical community. It was as if by the sheer force of her personality, she could take any idea and make it happen.

The webpage for the 'Gathering To Commemorate Dr Ruth Ingrid Michler 1967-2000, Noon, 8 November 2000, Northeastern University's Sacred Space, 201 Ell Building, 360 Huntingtion Avenue' states [6]:-Dr Ruth Michler died1November2000in an pedestrian-construction truck accident a block from the Mathematics Department. She was returning to the Department on her bike, to get printout, to apply for a Radcliffe Bunting Fellowship for2001-2002. She had just given talks at Boston University's Algebra Seminar on Monday30October, and to Northeastern University's Geometry-Algebra-Singularities-Combinatorics Seminar on Monday16October.

Ruth Michler the runner has been mentioned several times in our biography above. Let us end with giving a few more details following Diane Meuser [5]:-In October2000, she gave a talk entitled "Isolated Hypersurface Singularities and their Differentials" at the Northeastern University Geometry-Algebra-Singularities-Combinatorics Seminar, and also at Boston University's Algebra Seminar. She had spoken with many of us in the Department, and was developing new results; on the blackboard of her office is a short proof of a new theorem, written31October2000. We were enjoying her visit, and believe she was enjoying us. On1November2000, Ruth died tragically after an accident with a construction vehicle, on a corner near the Department. Ruth enjoyed music, including the symphony, and opera: she was a regular visitor to the Dallas Opera. She also was an avid long distance runner, who ran seven miles a day; she ran in most of the Boston Marathons, for the last five years. She was known for her energy, and the level of her commitment to all that she undertook.

At the time of her death Michler was organising two conferences: "Résolution des singularités et géométrie non commutative" Ⓣ to be held at the Centre International de Rencontres Mathématiques at Luminy, France, from 20-22 July 2001; and Algebraic Geometry to be held in Annapolis, Maryland, USA, 25-28 October 2001. Following Michler's death, both conferences were held in her memory and a book was produced of the proceeding of both conferences entitled 'Topics in algebraic and noncommutative geometry' published by the American Mathematical Society in 2003.Ruth was a visiting mathematician at Northeastern University. She had completed the Chancellor Challenge100K Road Race on8October and the Cape Cod Marathon on22October of this year(2000). Her previous ultra-running accomplishments included the East Texas Ultra-runners50K trail run, first place woman in the Cross Timbers50Mile Trail Run in February1998, and successful completion of the Leadville Trail100Mile Run in August1999in29:26:03. I met Ruth at a mathematics talk she gave at Boston University two days before her death. I was eagerly looking forward to hearing a talk by a woman mathematician(fairly rare), in a subject area I was interested in(rarer still), and was most astounded to learn that she was also quite an accomplished runner, having completed30marathons and the above ultra races all while still at the relatively young33years of age. I will certainly miss having the opportunity to run with her and I'm sure the ultrarunning community will miss her as well.

The Association for Women in Mathematics awards the Ruth I Michler Memorial Prize in her honour. Here is where the funds for this prize came from:-

First awarded so that the prize could be taken up in the academic year 2007-2008, it is awarded annually to a woman recently promoted to Associate Professor or an equivalent position in the mathematical sciences. The prize provides a fellowship for the awardee to spend a semester in the Mathematics Department of Cornell University without teaching obligations.After the district attorney decided not to prosecute those responsible[for the accident], Michler's family chose to invest her estate in legal proceedings that might offer a measure of justice for her death, which they believe resulted from negligence. Her father, Gerhard Michler, an emeritus professor of mathematics at the University of Essen in Germany, filed a civil action suit. More than five years later the Michler family won a sizeable settlement. Now, to pay lasting tribute to Michler's memory and to advance the careers of accomplished young women mathematicians, the Michler family has made a $1million gift to establish the Ruth I. Michler Memorial Prize of the Association for Women in Mathematics at Cornell.

You can see winners of the Ruth I Michler Memorial Prize at THIS LINK.

**Article by:** *J J O'Connor* and *E F Robertson*