Gerhard Ringel in collaboration with J.W.T. Youngs is accredited with the solution of the Heawood conjecture. They proved Heawood's assumption that you need only four colors to create a political map on any surface in such a way that each country is colored differently then its adjacent countries. An article called: "Solution of the Heawood map-coloring problem" published in 1968 represents the result of their research. The former Heawood conjecture could now be named Ringel-Youngs Theorem: H(p) = [ 1/2( 7 + √( 48p + 1)) ]. Ringel's proof marks a turning point in topology because it was developed before the digital revolution and relies on the capacity of the human brain itself. In 1976 the mathematicians Appel and Haken used a computer to prove the Four Color Theorem which is a case of the Heawood conjecture.

Along with Erdös, Harary and others Ringel was a trailblazer who revived and developed the discipline of graph theory in the early fifties of the 20th century. A number of his conjectures, among them the Ringel's conjecture, the Ringel-Kotzig conjecture, the Oberwolfach problem and the Earth Moon problem, are part of his legacy and inspire the next generation of graph theorists to continue his work.

Ringel published about eighty articles and three books: "Färbungsprobleme auf Flächen und Graphen"(Berlin 1963), "Map Color Theorem"(Berlin 1970 with a new edition in 2011) and a popular textbook "Pearls in Graph Theory" with co author Nora Hartsfield (London 1990 with a new edition in 2003). Besides numerous well illustrated exercises it contains a comprehensive introduction to graph theory of outstanding scholarly depth and clarity. "Map Color Theorem" was translated into Russian in 1974 and "Pearls in Graph Theory" was translated into Japanese in 2012.

Besides publishing Ringel transmitted the results of his research through his charismatic lectures. The sparkle in his blue eyes while he presented a particularily convincing solution became legendary. Unlike many other scientists he couldn’t care less about increasing the list of his publications. Teaching was his focus. He loved to share the joy of mathematical discovery with both experts and beginners. Professor Ringel did not have a desk in his house. He spent many hours filling an endless amount of writing pads with drawings and notes while comfortably curled up on his sofa. In his younger years he used to be so absorbed in his research that he did not see or hear anybody or anything around him.

Ringel has an Erdos number of 2 because of his collaboration with R. Guy from Calgary. Some of his mathematical findings were fundamental for economic theories and earned him in 1983 a honorary doctorate in political science from the Universität Karlsruhe. He received a second honorary doctorate in mathematics from the Freie Universität Berlin in 1994. On his 70th birthday he was honored by a collection of essays in the book: “Topics in Combinatorics and Graph Theory” edited by R. Bodendiek. L.W. Beineke and R. Wilson dedicated their 2009 book: “Topics in Topological Graphtheory” to his memory.

Gerhard Ringel was born 10/28/1919 in Kollnbrunn, Austria. He studied mathematics at the Charles University in Prague and after World War II at the Friedrich-Wilhelms- Universität in Bonn where he received his PhD in 1951. He became professor in 1958 and started teaching at the Freie Universität Berlin where he was chairman of the mathematical institute from 1967 until 1970. He started his career at UCSC in 1968 as visiting Professor and became a full professor in 1970. He was chairman of the math department for twelve years (1972 - 1984). His laissez faire style authority and calm friendly presence are fondly remembered by his students, colleagues and staff. He died June 24th 2008 in Santa Cruz.

## Tuesday, November 9, 2010

## Saturday, October 9, 2010

### A Long Life

Summer never used to end at Gerhard Ringel's house on the waterfront in Santa Cruz, California. The sundial he had installed on the southern wall showed daylight savings time all year around. To curious visitors he would point out that the hour was marked by the shadow of a rod parallel to the axis of the earth. He was a teacher at heart and loved to share whatever knowledge he was excited about. A young boy in school, he explained mathematical theories to his classmates guided by his teacher. Needless to say it was his job to do the math home work for those a grade above him. He became a famous mathematician, a pioneer in the field of graph theory who created a breakthrough to solve the four color map theorem. If you want to know more about his research check out the article about the Ringel-Youngs-Theorem in wikipedia.com. His popularity with his students in Germany and the United States was based on his excellent ability to explain the subject while telling stories and jokes during his lectures. Once a year he took his Santa Cruz students surfing, a sport that he taught himself when middle aged. He used to ride a unicycle and walk on his hands, at seventy his staff took a picture of him standing on his head. When his granddaughter told him that math and sports were her favorite subjects, he was pleased. Dr. Ringel was a survivor who endured nine years of serving in Hitler’s army and in Stalin’s POW camps. His way to avoid depression and illness was to focus on studying math while a soldier and learning Russian as a prisoner of war. When he returned from Russia, all he owned was the used Red Army uniform he wore. He had lost his home and possessions in Czechoslovakia, where the German minority had been forced to leave the country after World War II. He joined his wife, who was a refugee in West Germany, went back to school, got his PhD and started a family. For many years he taught at the universities of Bonn and Berlin before he was invited to continue his research at UCSC. Even though he was fluent in English and wrote his books and articles in this language he liked to joke that the best part about teaching math was that the students taught him English at the same time. Besides being a professor he was an excellent chess player and an avid butterfly collector. At one time he raised, to the dismay of his wife, seven generations of moths in the kitchen. He donated his world-class collection of butterflies to the Natural History Museum of UCSC. Gerhard’s love for life did not diminish when old and ill. Bedridden, without being able to talk he still enjoyed the warm sun, a bowl of strawberries or his favorite chocolates. Family and friends were blessed with his contagious smile of serenity and gratitude whenever they visited. He died peacefully in his home on June 24

^{th}in 2008. Gerhard Ringel outlived both of his wives and is survived by three children and four grandchildren.## Monday, October 4, 2010

### Born to Teach

Gerhard was an exceptional teacher who managed to turn mathematics into a fascinating subject for all his students including non majors. His natural gift for teaching was accompanied by a very early training. When he was ten years old his math teacher recognized his genius and habitually taught class by carrying on a conversation with the young boy. The teacher asked questions and Gerhard answered explaining the subject to his classmates. He knew how to capture his audience with clarity of mind and a subtle sense of humor. His nick name in school was "Spassl" (Fun).

## Thursday, September 30, 2010

### Professors are seldom good drivers

The book "Four colors suffice" by the British mathematician Robin Wilson contains the following anecdote about Gerhard Ringel that happened shortly after he and J.W.T.Youngs had published their proof of the Heawood Conjecture: "Ringel was driving up the California expressway when he was stopped by a traffic cop for speeding. The cop looked at his driving licence, and said 'Ringel, eh - are you the one who solved the Heawood conjecture?' Ringel, surprised, said 'yes'. It turned out that the traffic cop's son was in Professor Youngs' calculus class, and the result was that Ringel got let off with a warning - and if that doesn't show the uses of map colouring, I don't know what does!"

(quoted from the online transcript of his lecture at Gresham College on 21/10/2002)

(quoted from the online transcript of his lecture at Gresham College on 21/10/2002)

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