Peter Gustav Lejeune Dirichlet
Peter Gustav Lejeune Dirichlet was a German mathematician known for his invaluable contributions to number theory. He is credited with the creation of the field of analytic number theory and was one of the earliest mathematicians to give the modern formal definition of a function. He also made noteworthy contributions to the fields of analysis and mechanics, but number theory remained his greatest interest. His research in number theory led to the development of several theorems and principles, many of which were later named after him. Dirichlet was born with an innate love for mathematics. In spite of hailing from a family of modest means, he received good education and convinced his parents to send him to the Jesuit Gymnasium in Cologne where he had the good fortune of being tutored by the physicist and mathematician, Georg Simon Ohm, who groomed the young man and encouraged his research. However, he faced some problems when he decided to further his education as there was little opportunity in his home country to study higher mathematics. He moved to France for his higher education and returned home in order to embark on a career. Over the course of his illustrious career, not only did he contribute greatly to the field of mathematics, but also mentored several brilliant students who went on to become famous mathematicians in their own rights
Childhood & Early Life
Peter Gustav Lejeune Dirichlet was born on 13 February 1805 in Düren—the town was part of the French Empire at that time—to Johann Arnold Lejeune Dirichlet and his wife Anna Elisabeth. His father was a postmaster, merchant, and city councilor.
Peter Gustav Lejeune Dirichlet hailed from a family of modest means and was the youngest of the seven children of his parents.
He displayed a keen interest in mathematics from an early age. He loved the subject so much that he bought books on the subject with his pocket money as a young boy.
Initially his parents had hoped that he would grow up to be a merchant, but the boy’s fascination with mathematics was so much that they finally gave in to his wishes and let him pursue higher studies in mathematics. They sent him to the Gymnasium in Bonn in 1817 when he was 12 years old.
After studying at Bonn for three years he moved to the Jesuit Gymnasium in Cologne in 1820 where he was taught by the mathematician Georg Ohm. This helped him widen his mathematical knowledge though he could not learn much because of his inability to speak fluent Latin.
He wanted to study further, but at that time there was little opportunity in Germany to study higher mathematics. Thus Gustav Lejeune Dirichlet decided to go to Paris, France, in May 1822.
In France he attended the Collège de France and at the Faculté des sciences de Paris. At the same time, he embarked on a private study of Gauss's ‘Disquisitiones Arithmeticae’. He also started working as a private tutor in order to earn his livelihood.
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Peter Gustav Lejeune Dirichlet began his research during his student days and his first original research comprised part of a proof of Fermat's last theorem. This work brought him immediate fame as a budding mathematician, and in 1825 he was appointed to lecture at the French Academy of Sciences. He was only 20 years old at that time and had no degree!
He decided to return to Germany in November 1825. However, in order to teach in a German university he needed an habilitation which he did not have. Also the fact that he could not speak Latin was another problem.
The University of Cologne awarded him an honorary doctorate in February 1827 and the Minister of education granted him a dispensation for the Latin disputation required for the Habilitation. Thus he earned his habilitation without much difficulty and lectured in 1827–28 at Breslau.
He found the academic standards at Breslau to be low and hence moved to Berlin in 1828. He worked at the Military College and was also appointed a professor at the University of Berlin the same year. He taught at the university till 1855, while continuing with his job at the Military College.
In 1832, Dirichlet became a member of the Prussian Academy of Sciences; he was the youngest member and was only 27 years old at the time.
In spite of his hectic schedule he always found time for research, and number theory was the field closest to his heart. He did extensive research in this field and developed several theorems and principles. Several concepts he worked on were later named after him including Dirichlet's approximation theorem, Dirichlet kernel, Latent Dirichlet allocation, and Dirichlet principle.
In 1855, Gauss died and Dirichlet was offered his position at the University of Göttingen. He accepted the offer and moved to Göttingen. This new position allowed him to devote more time to research which Dirichlet enjoyed.
Peter Gustav Lejeune Dirichlet is primarily remembered for his contribution to the field of number theory. He created the branch of analytic number theory, introduced the Dirichlet characters and L-functions, and proved the Dirichlet unit theorem, a fundamental result in algebraic number theory.
Awards & Achievements
Dirichlet was awarded the civil class medal of the Pour le Mérite order in 1855.
Personal Life & Legacy
He married Rebecka Mendelssohn, the daughter of a prominent Jewish banker, in 1832. The couple had two children.
He suffered a heart attack in the summer of 1858. Even though he survived the attack, his health deteriorated badly thereafter and he died on 5 May 1859.