Isaak Gröbli (1822-1917) was a jacquard weaver who invented the "Schifflistickmaschine", a shuttle embroidery machine, in 1863. Soon the machine worked 10 times faster than a hand embroidery machine and became widely used, but it brought Isaak Gröbli only modest wealth. At the age of 64 he moved to Gossau (canton St. Gallen) to set up his own small embroidery business, supported by his son Hermann. The oldest son Arnold emigrated to the United States in 1876, where he refined his father's invention. Letters preserved in Gröbli's scientific estate  show that Arnold took an interest in his younger brother's career.
Walter, however, was not interested in weaving, but in mathematics. He completed his school education at the Kantonsschule in St. Gallen. Encouraged and supported by his father, he studied mathematics at the Polytechnic from 1871-1875, at the Department for Mathematics and Physics Teachers. His lecturers included Heinrich Weber and Schwarz, 'both of whom had great influence on his further scientific career' . Weber in particular got Gröbli, whom he referred to as the 'best student he had ever had' , interested in vortex theory and hydrodynamics. Probably encouraged by Weber and Schwarz, Gröbli went to Berlin to hear Kirchhoff, Helmholtz, Kummer and Weierstrass in 1875. In Berlin he caused a stir by solving the prize problem on vortex motion posed by Kirchhoff.
In 1876 Gröbli obtained his doctorate from the University of Göttingen for his thesis Spezielle Probleme über die Bewegung gradliniger, paralleler Wirbelflächen Ⓣ. His supervisor was Schwarz (or possibly Heinrich Weber); his oral examiners were Schwarz for mathematics and Johann Benedict Listing for physics. Upon his return to Zürich in 1877 he habilitated as Privatdozent at the Polytechnic. Along with the request he had to submit at least two papers and three references; his referees were Wilhelm Fiedler, Frobenius, and Geiser. The whole process, from application to appointment, took a remarkable two weeks . Gröbli also became Frobenius's assistant for the following six years. He held his teaching post until 1894; he mainly lectured on hydrodynamics.
In 1883 he was appointed professor of mathematics at the Gymnasium in Zürich. By all accounts he was a very demanding (school) teacher, but impressed his pupils with 'his phenomenal proficiency in mental arithmetic, which is not widely spread among higher mathematicians and of which astounding stories were told' . Despite his mathematical talent and encouragement from his former professors and his colleagues, Gröbli did not pursue a career as a research mathematician; he was content with being a schoolteacher.
Gröbli married Emma Bodmer in 1899, but there are no verified records of whether the couple had any children. In one note , Thomann writes that they had a son, Walter (1900-1975), in another , that they did not and that the couple got divorced before Gröbli's death.
Even after he had stepped down from his post at the Polytechnic, Gröbli continued to take great interest in the latest mathematical research. He was also very interested in languages, reading English and German literature, and learning Italian in his forties.
His main passion (besides mathematics) though was mountaineering. He climbed most of the more major peaks in the Alps; in many cases he was the first person to do so. Examples are climbing Piz Ela (3339m) in 1880 and traversing the north route of the Tödi (3614m). In addition, he was a keen hiker. Gröbli was a very active member of the Swiss Alpine Club: he led many mountaineering trips and served on the executive committee of the Club's local branch for many years. He also wrote several reports on his excursions for the Club's journal. A letter from the Federal Topographic Bureau  suggests that Gröbli combined his two passions in measuring the heights of mountains and mountain passes.
On 26 June 1903, he led a group of 16 of his pupils on a hike on Piz Blas (3019m, canton Grisons). Due to bad weather conditions, the group had to choose a different route, but they were still caught in an avalanche. Walter Gröbli and two pupils, Ernst Hofmann and Adolf Odermatt, perished on the mountain; another pupil, Richard Liebmann, died of his injuries later on.
It is hard to say whether Gröbli would have written any mathematical papers had he not died so early. But as it stands his only publication was his doctoral thesis. The basic model that he investigated had been discovered by his former professor Helmholtz (Crelle's Journal, 1858), but :
The subject matter [of Gröbli's thesis] was the motion of three vortices, the motion of four vortices assuming the existence of an axis of symmetry, and the motion of 2n vortices assuming the existence of n symmetry axes.He had already worked on a similar topic for his dissertation at the Polytechnic. The thesis was cited a number of times in the late 19th century, by G R Kirchhoff, D N Goryachev and H Lamb for example. People then forgot about it until 1949, when J L Synge published a paper on the converse of the problem that Gröbli investigated. The thesis is still cited today, in fact, 'few will write a thesis that will be the subject of attention a century later' .
At the time of the first International Congress of Mathematicians Gröbli had already given up his teaching post at the Polytechnic. He joined the enlarged organising committee in December 1896. At the meeting on 08 December he was elected president of the finance committee (one of the four sub-committees). As such he was responsible for creating the committee's budget and asking individuals (merchants, manufacturers etc.) for donations.
Article by: Stefanie Eminger, University of St Andrews
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