Carl Jacobi

The Extraordinary Life & Work of One of the Most Brilliant Mathematicians of the 19th Century.

There have been very few people who have earned a good name and fame for showing genius abilities in not only one, rather several different fields. And Carl Gustav Jacob Jacobi belongs to this category of rare intellectuals whose work has found extended applications in several different areas. So today, on Jacobi’s 216th birth anniversary, let’s learn a little bit about his celebrated life.

Carl Gustav Jacob Jacobi (Image: wikipedia)
Carl Jacobi

Background and Education:

Carl Jacobi was born to a Jewish banker’s well-off family in Postdam, Germany, on December 10, 1804. Carl was the second son of the family. His eldest brother Moritz Jacobi went on to become a famous physicist and engineer.

Carl was initially homeschooled by his maternal uncle Lehman. Lehman instructed him mainly in the classical languages and elements of mathematics. In 1816, Jacobi went to the Potsdam Gymnasium. Students were mainly taught classical languages, history, philology, mathematics, and sciences in the gymnasium. However,  Jacobi was already well trained in all these subjects, thanks to the quality education that he had received from his uncle. Eventually, looking at Jacobi’s remarkable abilities, he was moved to the senior year despite his young age in less than half a year after joining the gymnasium. 

However, as per the University’s protocols, students younger than 16 years old could not be accepted for higher studies, due to which Carl had to remain in the senior class until 1821. Contrary to what is expected from children of his age, Carl utilized this time quite productively. He used this time to advance his knowledge in Latin, Greek, philology, history, and mathematics and make his first attempts at research while trying to solve the fifth-order algebraic expressions.

In 1821 Carl Jacobi went to study at Berlin University from where he finally obtained his Ph.D. degree with a dissertation on the partial fraction decomposition of rational fractions in 1825.

Professional life of Carl Jacobi:

Although Carl Jacobi was born to a Jewish family, he gave up on his Jewish roots and converted to Christianity in 1825 to qualify for a university position. Following this, Carl was offered a teaching position by Berlin University for the 1825–26 academic year. In 1827, Carl got appointed as a mathematics professor at the Königsberg University. After serving there for two years, he got promoted as a tenured professor and served in this position until 1842. 

Scientific contributions:

While managing his teaching duties,  Carl didn’t fail to make some breakthrough contributions in the area of research. In his research career, he contributed extensively to mathematics and physics.

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Contributions to Mathematics: 

Carl Jacobi is mostly celebrated for his extraordinary work on elliptic functions and their relation to elliptic theta functions. He became the first mathematician ever to have formulated a theory of elliptic functions based on four theta functions. Jacobi discovered that just as elliptic functions can be obtained by inverting elliptic integrals, the same way we can also obtain hyperelliptic functions by inverting hyperelliptic integrals. This realization led to the formation of the theory of Abelian functions. Isaac Newton also worked on elliptical functions with partial success.

In 1835, Carl devised theta functions’ fundamental properties, including the functional equation and the famous Jacobi triple product formula. He became the first person to apply elliptic functions to number theory and was also one of the early founders of the theory of determinants. He invented the functional determinant, which is now named in his honor.

Contributions to Physics:

Although Carl was a mathematician, some of his works are of utmost importance in physics. For example, his theory of elliptic functions holds great significance in the field of mathematical physics. Moreover, he carried out important research in partial differential equations of the first order and then applied them to the differential equations of dynamics. Not to forget, the famous Hamilton-Jacobi equation now plays a significant role in providing the most direct link between classical and quantum mechanics. Carl is also known to have made some important contributions to planetary theory.

Legacy and later life:

It is said that in 1843, Carl Jacobi suffered from a mental breakdown. So, he took a break and moved to Italy to rejuvenate and to recover his health. In the year that followed, Carl Jacobi returned to Berlin and lived there as a royal pensioner until his death. Another interesting instance from Carl’s life states that in the 1848 Revolution, he became politically involved. During this time, he addressed an imprudent speech that cost him his royal pension after the revolution’s suppression. However, such was his fame and status that the pension got restored shortly. 

Carl Gustav Jacob Jacobi succumbed to smallpox on February 18, 1851. Being the great mathematician that he was, his grave has been preserved at a cemetery in the Kreuzberg section of Berlin in his honor. Moreover, several theorems, equations, symbols, functions, and even a crater on the moon bears his name. This shows how much people admire Jacobi for his intellectual prowess.

Happy Birthday Carl Jacobi!

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