He entered the Eidgenössische Polytechnikum Zürich in 1874 to study civil engineering but, after three semesters in the Engineering Department, he moved to the Mathematics and Physics Department, influenced by the inspirational teaching of Karl Geiser. It was only in the year before Rudio entered the Polytechnikum that Geiser had been appointed to a full professorship of higher mathematics and synthetic geometry, with special responsibility for teaching mathematics to engineering students and to mathematics students. Rudio also had Kurt Culmann (1821-1881), Wilhelm Fiedler and Hermann Schwarz as lecturers. From 1877 until 1880 Rudio studied at the University of Berlin where he attended the seminar of Eduard Kummer and Karl Weierstrass. Advised by these two famous mathematicians, he obtained a doctorate from the University of Berlin with a thesis on Kummer's problem of determining all surfaces of which the centres of curvature form second order cofocal surfaces. He reduced this problem to the problem of solving a differential equation. An abstract of his thesis, Zur Theorie der Flächen, deren Krümmungsmittelpunktsflächen confocale Flächen zweiten Grades sind Ⓣ (1880), was published in Crelle's Journal in 1883.
After the award of his doctorate in 1880, Rudio followed the advice of Karl Geiser and returned to Zürich to work on his habilitation thesis. In 1881 Rudio habilitated at the Eidgenössische Polytechnikum Zürich and became a privatdocent there. The year 1883 marked the centenary of Leonhard Euler's death and on the 6 December of that year a small seminar was held in Zürich to celebrate the occasion. Rudio gave a short biographical talk on Euler at the seminar, an event which in itself was pretty minor but would become much more significant 25 years later when Rudio published the text of his 1883 talk as part of the 1907 celebrations of the 200th anniversary of Euler's birth. In 1885, Rudio was promoted to extraordinary professor and, in 1889, he was appointed to a full professorship of mathematics. He was to hold this professorship until he retired in 1928. He married Maria Emma Müller, the daughter of Carl Wilhelm Nepomuk, in 1888. Maria was from Rheinfelden, near Basle on the Swiss-German border; Ferdinand and Maria Rudio had three daughters. Rudolf Wolf, the professor of astronomy at the Eidgenössische Polytechnikum Zürich and director of the Zürich Observatory, also held a role as director of the Eidgenössische Polytechnikum library. He died in December 1893 and, in 1894, Rudio was appointed to fill this position as head of the library. He played an important role in bringing the library up-to-date and continued in this role for 25 years. Over the first few of these years he managed the complete renovation of the library that was newly opened in 1900.
The first International Congress of Mathematicians was held at the Eidgenössische Polytechnikum Zürich from 9 to 11 August 1897. The chairman of the organising committee was Karl Geiser, who was elected president of the Congress, and Rudio was one of the two secretaries. Rudio made a report to the opening session of the Congress in which he said :-
It suffices to consult the program or to glance at this room to agree that the congresses already would be justified even if they did not have any other goal than of offering the mathematicians of all the countries of the world the occasion to talk sincerely and to share ideas. The personal relations and the progresses that directly or indirectly report to science are always one of the primary targets of any scientific meeting.This address by Rudio to the opening session of the first ever International Congress of Mathematicians, entitled On the object and organization of international congresses, contained much of importance, as Curbera explains in :-
Ferdinand Rudio, one of the Swiss organizers of the congress, listed the new directions opened by the congress, which needed international agreements. They included the issue of unifying mathematical terminology and units, as had been done recently by the physicists with the volt, the ampere, and the ohm. There was also the need for an international literary journal for mathematics; the 'Jahrbuch über die Fortschritte der Mathematik' Ⓣ had been in publication since 1868, and the 'Repertoire Bibliographique des Sciences Mathématiques' Ⓣ since 1885, but they were slow in delivering the information on the developments of a science producing many more results at a much faster speed. He also mentioned the need for a general classification of mathematics that would help the bibliographic effort. He pointed out that the list of participants of the congress should be seen as the starting point of an international directory of mathematicians, where one could find addresses and field of speciality of all mathematicians in the world (this idea had to wait until 1958 when the first World Directory of Mathematicians appeared). Rudio complemented this idea with the proposal of creating a biographical dictionary of current mathematicians, which would include portraits of the most important. Rudio summarized all projects in a lemma: " Viribus unitis! sei unsere Losung". ("United our forces! This is our watchword.").This address by Rudio is contained in the proceedings of the Congress which Rudio edited. It was published with the title Verhandlungen Des Ersten Internationalen Mathematiker-Kongresses in Zürich Vom 9. Bis 11. August 1897. James Pierpont reviews the volume in :-
The Zürich congress will always possess an especial interest as the first international congress. The present stately octavo volume is the official report of the same, prepared by Professor Rudio, one of the two general secretaries. The first eighty pages recount in an agreeable manner the events of the congress and are very interesting reading. The address of welcome by the president, Professor Geiser, and the paper by Professor Rudio "On the object and organization of international congresses" are given in full. ... The remaining 225 pages are devoted to the scientific addresses and papers read at the congress.Rudio worked on group theory, algebra and geometry. His best known publication in these areas is his classic textbook Die Elemente Der Analytischen Geometrie Ⓣ (1908). He is best remembered, however, for his work in the history of mathematics, in particular he wrote a major work on squaring the circle, Der Bericht des Simplicius über die Quadraturen des Antiphon und des Hippokrates Ⓣ (1902), and he also wrote biographies of mathematicians, for example he published important papers on Gotthold Eisenstein. One of his most important contributions to mathematics was editing the collected works of Euler. Rudio proposed the project in 1883 since this was the centenary of Euler's death. He continued to advocate the importance of this project and at the International Congress of Mathematicians at Zürich in 1897 he suggested it would be a suitable memorial for the year 1907 which was the bicentennial of Euler's birth. Andreas Kleinert and Martin Mattmüller write in :-
Mathematicians will be grateful to Professor Rudio for this very complete and attractive report. The book contains so much of general interest that it will be welcome to all.
Ferdinand Rudio had untiringly lobbied for an initiative that ultimately turned out to be successful. On every occasion, and most particularly at the First International Congress of Mathematicians, which was held at Zürich in 1897, Rudio had urged the worldwide community to honour its obligations toward the great scientist by undertaking the edition of Euler's complete works. When the city of Basel commemorated Euler's 200th birthday in 1907, Rudio delivered a thrilling speech in which he appealed to Swiss patriotism and to international solidarity in favour of an edition of Euler's works: "Switzerland will always be grateful to the academies of Berlin and St Petersburg for having given our Euler, to whom his native country was too narrow, the opportunity to perform his outstanding work". He addressed his speech in particular to the representatives of the Swiss Naturalist Society (Schweizerische Naturforschende Gesellschaft, SNG, now the Swiss Academy of Natural Science, SCNAT) and to the representatives of the academies of Berlin and St Petersburg who assisted at the ceremony.The project was not approved until 1909, twenty six years after Rudio first proposed it. Andreas Speiser writes in :-
The Swiss Society of Natural Sciences (Schweizerische Naturforschende Gesellschaft) at its annual meeting in Glarus on August 31, 1908, created the Euler Commission to edit the Collected Works of Leonhard Euler, in conjunction with the Central Committee. On September 6, 1909, the same Society decided on "the edition of the Collected Works of Leonhard Euler in the original languages, convinced of rendering the entire scientific world a service thereby."Rudio was appointed general editor for the project. He edited two volumes himself, namely Leonhard Euleri Opera Omnia: Series Prima: Commentationes Arithmeticae - 1st Part Ⓣ (1915) and Leonhard Euleri Opera Omnia: Series Prima: Commentationes Arithmeticae - 2nd Part Ⓣ (1917). He collaborated in the editing of three more. In fact he supervised the production of over 30 volumes in his role as general editor. The authors of  write:-
As managing editor he was also responsible for all the correspondence about the edition, as well as for the "contracts with the editorial staff." He had been able to acquire all of Euler's published writings and each editor received the "manuscript of his volumes from Rudio already put together, so that the editor's work was only a matter of looking through the whole and perhaps making remarks in the margins." The final responsibility lay with the managing editor.Note that the quotes within this quotation are from page 162 of .
In recognition to his outstanding contributions to mathematics, particularly to Swiss mathematics, he was awarded an honorary doctorate by the University of Zürich in 1919. He continued to teach at the Eidgenössische Technische Hochschule (as the Eidgenössische Polytechnikum Zürich was renamed in 1911) until 1928 and he also continued to manage the Euler project until this same date. He was forced to retire at this time due to poor health and indeed he died in the following year. In  his contributions are summarised as follows:-
As a professor of mathematics at the Eidgenössische Technische Hochschule (ETH) (Swiss Federal Institute of Technology) in Zürich, head of the library, a leading member of the GeP Society (an alma mater organisation of former "Polytechnicians,") and a member of the lectures' association of both the University and the Polytechnic (the representative body of the popular "Town Hall Lectures" in Zürich), as well as editor of the Zürcher Naturforschende Gesellschaft (Zürich Natural Sciences Society), Ferdinand Rudio greatly influenced the scientific culture of his chosen country of adoption. He achieved lasting fame, however, as an historian of mathematics, above all through his persistent efforts which led to the publication of Leonhard Euler's 'Opera omnia' (Complete Edition).We note that he was president of the Zürich Natural Sciences Society editing their quarterly journal from 1893 to 1912. He also wrote Geschichte der Naturforschenden Gesellschaft 1746-1896, an important article to celebrate the 150th anniversary of the founding of the Society.
Article by: J J O'Connor and E F Robertson