Rubrica biografie

Minkowski Hermann - ing


Biografia estratta da:

Hermann Minkowski 's parents were Lewin Minkowski, a businessman, and Rachel Taubmann. Hermann was his parents' second son, the eldest being Oskar Minkowski who went on to become a famous pathologist. Lewin and Rachel Minkowski were Germans although their son Hermann was born while they were living in Russia. When Hermann was eight years old the family returned to Germany and settled in Königsberg where Lewin Minkowski conducted his business. Minkowski first showed his talent for mathematics while studying at the Gymnasium in Königsberg. Already at this stage in his education he was reading the work of Dedekind, Dirichlet and Gauss. The outstanding abilities he showed at this time were noted in a letter that Heinrich Weber, then at Königsberg University, wrote to Dedekind in 1881 (see [13]). He studied at the University of Königsberg, entering the university in April 1880. He spent three semesters at the University of Berlin, for example spending the winter semester of the academic year 1882-83 there. His became close friends with Hilbert while at Königsberg, for Hilbert was an undergraduate at the same time as Minkowski. In 1884, while he was a student at Königsberg, Hurwitz was appointed to the staff. The student Minkowski soon became close friends with the newly appointed academic Hurwitz. He received his doctorate in 1885 from Königsberg for a thesis entitled Untersuchungen über quadratische Formen, Bestimmung der Anzahl verschiedener Formen, welche ein gegebenes Genus enthält. Minkowski became interested in quadratic forms early in his university studies. In 1881 the Academy of Sciences (Paris) announced that the Grand Prix for mathematical science to be awarded in 1883 would be for a solution to the problem of the number of representations of an integer as the sum of five squares. Eisenstein had given a formula for the number of such representations in 1847, but he had not given a proof of the result. Now in fact the Academy of Sciences had set a problem for the Grand Prix which had already been solved, for Henry Smith had published an outline of a proof in 1867. However the Academy of Sciences were unaware of Smith's contributions when the prize topic was set. Eisenstein had been studying quadratic forms in n variables with integer coefficients at the time he published his unproved formula in 1847 but as he was already ill by this time details were never published. Minkowski, although only eighteen years old at the time, reconstructed Eisenstein's theory of quadratic forms and produced a beautiful solution to the Grand Prix problem. Smith reworked his earlier proof, adding detail and submitted that to the Academy. The decision was that the prize be shared between Minkowski and Smith but this was a stunning beginning to Minkowski's mathematical career. On 2 April 1883 the Academy granted the Grand Prize in Mathematics jointly to the the young Minkowski at the start of his career and the elderly Smith at the end of his. Minkowski's doctoral thesis, submitted in 1885, was a continuation of this prize winning work involving his natural definition of the genus of a form. After the award of his doctorate, he continued undertaking research at Königsberg. In 1887, a professorship became vacant at the University of Bonn, and Minkowski applied for that position; according to the regulations of German universities, he had to submit orally to the faculty an original paper, as an Habilitationsschrift. Minkowski presented Räumliche Anschauung und Minima positiv definiter quadratischer Formen (Spatial visualization and minima of positive definite quadratic forms) which was not published at the time but in 1991 the lecture was published in [11]. Minkowski taught at Bonn from 1887, being promoted to assistant professor in 1892. Two years later he moved back to Königsberg where he taught for two years before being appointed to the Eidgenössische Polytechnikum Zürich. There he became a colleague of his friend Hurwitz who had been appointed to fill Frobenius' chair after he left Zürich for Berlin in 1892. Einstein was a student in several of the courses he gave and the two would later become interested in similar problems in relativity theory. Minkowski married Auguste Adler in Strasburg in 1897; they had two daughters, Lily born in 1898 and Ruth born in 1902. The family left Zürich in the year that their second daughter was born for Minkowski accepted a chair at the University of Göttingen in 1902. It was Hilbert who arranged for the chair to be created specially for Minkowski and he held it for the rest of his life. At Göttingen he became interested in mathematical physics gaining enthusiasm from Hilbert and his associates. He participated in a seminar on electron theory in 1905 and he learnt the latest results and theories in electrodynamics. Minkowski developed a new view of space and time and laid the mathematical foundation of the theory of relativity. By 1907 Minkowski realised that the work of Lorentz and Einstein could be best understood in a non-euclidean space. He considered space and time, which were formerly thought to be independent, to be coupled together in a four-dimensional 'space-time continuum'. Minkowski worked out a four-dimensional treatment of electrodynamics. His major works in this area are Raum und Zeit (1907) and Zwei Abhand lungen über die Grundgleichungen der Elektrodynamik (1909). Kline, reviewing [9] This space-time continuum provided a framework for all later mathematical work in relativity. These ideas were used by Einstein in developing the general theory of relativity. In fact Minkowski had a major influence on Einstein as Corry points. In the early years of his scientific career, Albert Einstein considered mathematics to be a mere tool in the service of physical intuition. In later years, he came to consider mathematics as the very source of scientific creativity. A main motive behind this change was the influence of two prominent German mathematicians: David Hilbert and Hermann Minkowski. We have mentioned several times in this biography that Minkowski and Hilbert were close friends. Less well known is the fact that Minkowski actually suggested to Hilbert what he should take as the theme for his famous 1900 lecture in Paris. Minkowski, in a letter to Hilbert written on 5 January 1900, writes:- What would have the greatest impact would be an attempt to give a preview of the future, i.e. a sketch of the problems with which future mathematicians should occupy themselves. In this way you could perhaps make sure that people would talk about your lecture for decades in the future. Time has certainly proved Minkowski correct! Minkowski's original mathematical interests were in pure mathematics and he spent much of his time investigating quadratic forms and continued fractions. His most original achievement, however, was his 'geometry of numbers' which he initiated in 1890. Geometrie der Zahlen was first published in 1910 but the first 240 pages (of the 256) appeared as the first section in 1896. Geometrie der Zahlen was reprinted in 1953 by Chelsea, New York, and reprinted again in 1968. Minkowski published Diophantische Approximationen: Eine Einführung in die Zahlentheorie in 1907. It gave an elementary account of his work on the geometry of numbers and of its applications to the theories of Diophantine approximation and of algebraic numbers. Work on the geometry of numbers led on to work on convex bodies and to questions about packing problems, the ways in which figures of a given shape can be placed within another given figure. At the young age of 44, Minkowski died suddenly from a ruptured appendix.


© 2002 - 2020 ScienzaPerTutti - Grafica Francesca Cuicchio Ufficio Comunicazione INFN - powered by mspweb


NOTA! Questo sito utilizza i cookie e tecnologie simili.

Se non si modificano le impostazioni del browser, l'utente accetta. Per saperne di piu'


Informativa sulla Privacy e Cookie Policy

Ultima modifica: 28 maggio 2018


L’INFN si articola sul territorio italiano in 20 Sezioni, che hanno sede in dipartimenti universitari e realizzano il collegamento diretto tra l'Istituto e le Università, 4 Laboratori Nazionali, con sede a Catania, Frascati, Legnaro e Gran Sasso, che ospitano grandi apparecchiature e infrastrutture messe a disposizione della comunità scientifica nazionale e internazionale e 3 Centri Nazionali dedicati, rispettivamente, alla ricerca di tecnologie digitali innovative (CNAF), all’alta formazione internazionale (GSSI) ed agli studi nel campo della fisica teorica (GGI). Il personale dell'Infn conta circa 1800 dipendenti propri e quasi 2000 dipendenti universitari coinvolti nelle attività dell'Istituto e 1300 giovani tra laureandi, borsisti e dottorandi.

L’INFN con sede legale in Frascati, Roma, via E. Fermi n. 40, Roma, email:, PEC: in qualità di titolare tratterà i dati personali eventualmente conferiti da coloro che interagiscono con i servizi web INFN


Ai sensi degli artt. 37 e ss. del Regolamento UE 2016/679 relativo alla protezione delle persone fisiche con riguardo al trattamento dei dati, l’INFN con deliberazione del Consiglio Direttivo n. 14734 del 27 aprile 2018 ha designato il Responsabile per la Protezione dei Dati (RPD o DPO).

Il DPO è contattabile presso il seguente indirizzo e.mail:

Riferimenti del Garante per la protezione dei dati personali:


L'informativa è resa solo per i siti dell'INFN e non anche per altri siti web eventualmente raggiunti dall'utente tramite link.

Alcune pagine possono richiedere dati personali: si informa che il loro mancato conferimento può comportare l’impossibilità di raggiungere le finalità cui il trattamento è connesso

Ai sensi dell'art. 13 del Regolamento UE 2016/679, si informano coloro che interagiscono con i servizi web dell'Istituto Nazionale di Fisica Nucleare, accessibili per via telematica sul dominio, che il trattamento dei dati personali effettuato dall'INFN tramite web attiene esclusivamente ai dati personali acquisiti dall'Istituto in relazione al raggiungimento dei propri fini istituzionali o comunque connessi all’esercizio dei compiti di interesse pubblico e all’esercizio di pubblici poteri cui è chiamato, incluse le finalità ricerca scientifica ed analisi per scopi statistici.

In conformità a quanto stabilito nelle Norme per il trattamento dei dati personali dell’INFN e nel Disciplinare per l’uso delle risorse informatiche nell’INFN, i dati personali sono trattati in modo lecito, corretto, pertinente, limitato a quanto necessario al raggiungimento delle finalità del trattamento, per il solo tempo necessario a conseguire gli scopi per cui sono stati raccolti e comunque in conformità ai principi indicati nell’art. 5 del Regolamento UE 2016/679.

Specifiche misure di sicurezza sono osservate per prevenire la perdita dei dati, usi illeciti o non corretti ed accessi non autorizzati.

L’INFN tratta dati di navigazione perché i sistemi informatici e le procedure software preposte al funzionamento di questo sito web acquisiscono, nel corso del loro normale esercizio, alcuni dati la cui trasmissione è prevista dai protocolli di comunicazione impiegati. Questi dati - che per loro natura potrebbero consentire l'identificazione degli utenti - vengono utilizzati al solo fine di ricavare informazioni statistiche anonime sull'uso del sito e per controllarne il corretto funzionamento. Gli stessi potrebbero essere utilizzati per l'accertamento di responsabilità in caso di compimento di reati informatici o di atti di danneggiamento del sito; salva questa eventualità, non sono conservati oltre il tempo necessario all'esecuzione delle verifiche volte a garantire la sicurezza del sistema.


Questo sito utilizza esclusivamente cookie “tecnici” (o di sessione) e non utilizza nessun sistema per il tracciamento degli utenti.

L'uso di cookie di sessione è strettamente limitato alla trasmissione di identificativi di sessione (costituiti da numeri casuali generati dal server) necessari per consentire l'esplorazione sicura ed efficiente del sito. Il loro uso evita il ricorso ad altre tecniche potenzialmente pregiudizievoli per la riservatezza della navigazione e non prevede l'acquisizione di dati personali dell'utente.


Gli interessati hanno il diritto di chiedere al titolare del trattamento l'accesso ai dati personali e la rettifica o la cancellazione degli stessi o la limitazione del trattamento che li riguarda o di opporsi al trattamento secondo quanto previsto dagli art. 15 e ss. del Regolamento UE 2016/679. L'apposita istanza è presentata contattando il Responsabile della protezione dei dati presso l’indirizzo email:

Agli interessati, ricorrendone i presupposti, è riconosciuto altresì il diritto di proporre reclamo al Garante quale autorità di controllo.

Il presente documento, pubblicato all'indirizzo: costituisce la privacy policy di questo sito, che sarà soggetta ad aggiornamenti.