Carl Gustav Jacob Jacobi facts for kids
Quick facts for kids
Carl Gustav Jacob Jacobi
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| Born | 10 December 1804 |
| Died | 18 February 1851 (aged 46) Berlin, Kingdom of Prussia
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| Nationality | German |
| Alma mater | University of Berlin (Ph.D., 1825) |
| Known for | Jacobi's elliptic functions Jacobian Jacobi symbol Jacobi ellipsoid Jacobi polynomials Jacobi transform Jacobi identity Jacobi operator Hamilton–Jacobi equation Jacobi method Jacobi eigenvalue algorithm Popularizing the character ∂ |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Königsberg University |
| Thesis | Disquisitiones Analyticae de Fractionibus Simplicibus (1825) |
| Doctoral advisor | Enno Dirksen |
| Doctoral students | Paul Gordan Otto Hesse Friedrich Julius Richelot |
Carl Gustav Jacob Jacobi (born December 10, 1804 – died February 18, 1851) was an important German mathematician. He made big discoveries in many areas of math, like elliptic functions, how things move (called dynamics), differential equations, determinants, and number theory. Sometimes his name is written in Latin as Carolus Gustavus Iacobus Iacobi.
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About Carl Jacobi
Carl Jacobi was born in Potsdam, Germany, on December 10, 1804. He was one of four children. His father, Simon Jacobi, was a banker. Carl's older brother, Moritz von Jacobi, also became famous as an engineer and physicist.
Early Life and Education
Carl was first taught at home by his uncle, Lehman. His uncle taught him old languages like Latin and Greek, and also the basics of mathematics.
In 1816, when Carl was 12, he went to a school called the Potsdam Gymnasium. Students there learned many subjects, including languages, history, and math. Carl was very smart and had learned a lot from his uncle. Because of this, he moved to the highest class in less than six months!
However, the university would not accept students younger than 16. So, Carl had to stay in the senior class until 1821. He used this extra time to learn even more. He was interested in everything, from Latin and Greek to history and advanced mathematics. During this time, he even tried to solve a very difficult math problem called the quintic equation.
University and Career
In 1821, Jacobi started studying at Berlin University. He loved both philology (the study of language) and mathematics. He was so good at philology that his professor noticed his talent.
Carl found the math classes at Berlin University too easy. So, he studied advanced math books by himself. He read works by famous mathematicians like Euler, Lagrange, and Laplace. By 1823, he decided to focus only on mathematics.
In 1825, he earned his Ph.D. (Doctor of Philosophy) degree. His paper was about breaking down complex fractions into simpler ones. After that, he became qualified to teach at a university. At just 21 years old, Jacobi started teaching math classes at the University of Berlin.
In 1827, Jacobi became a professor at Königsberg University. By 1829, he became a full professor and stayed there until 1842.
Later Life
In 1843, Jacobi became very sick from working too much. He went to Italy for a few months to get better. When he returned, he moved to Berlin. He lived there with financial support from the king until he died.
During a time of political change in 1848, Jacobi became involved in politics for a short time. This caused his royal support to be stopped for a while. But because he was so famous and respected, the support was soon given back to him. This happened thanks to the help of Alexander von Humboldt, another famous scholar.
Carl Jacobi died in 1851 from smallpox, a serious disease. He is buried in a cemetery in Berlin. A crater on the Moon is named Jacobi in his honor.
What Carl Jacobi Discovered
Carl Jacobi made many important discoveries in mathematics. He was especially good at solving problems using algebra.
Elliptic Functions
One of Jacobi's biggest achievements was his work on elliptic functions. These are special types of mathematical functions. He wrote a very important book about them in 1829 called Fundamenta nova theoriae functionum ellipticarum.
Elliptic functions are very useful in mathematical physics. For example, they help describe how a pendulum swings, or how planets move around the sun (called the Kepler problem).
Differential Equations and Mechanics
Jacobi also made big contributions to the study of differential equations. These are equations that involve rates of change. He also helped develop classical mechanics, which is about how objects move and the forces that affect them. His work led to something called the Hamilton–Jacobi equation.
"Invert, Always Invert"
Jacobi often told his students a famous piece of advice: "Invert, always invert." This meant that when you're looking for new ideas in math, you should try to reverse what you already know. For example, instead of just solving problems, try to understand the functions that make those problems solvable. This idea helped him discover new areas of math.
Other Contributions
- Number Theory: Jacobi was one of the first to use elliptic functions to solve problems in number theory. He helped prove famous theorems about how numbers can be written as sums of squares. He also continued the work of Carl Friedrich Gauss on quadratic reciprocity and introduced the Jacobi symbol.
- Determinants: He was one of the first to develop the theory of determinants. He invented the Jacobian determinant. This is a special tool used in math to help change variables in complex equations. In 1841, he also helped make the partial derivative symbol (∂) common in math.
- Algebra: He studied special types of polynomials called Schur polynomials. He also discovered a formula for determinants called the Desnanot–Jacobi formula.
- Jacobi Identity: In areas of math like Lie algebra and Hamiltonian mechanics, you might come across the Jacobi identity. This is a rule that works like the associative property for certain mathematical operations.
- Planetary Motion: Jacobi also studied how planets move. He introduced the Jacobi integral in 1836, which is useful for understanding motion in space.
Jacobi left behind many writings. Some of them were published after his death. His collected works were published by the Prussian Academy of Sciences.
See also
In Spanish: Carl Gustav Jakob Jacobi para niños
- Niels Henrik Abel
- Augustin-Louis Cauchy
- Friedrich Wilhelm Bessel
- Jacobi logarithm
- Last geometric statement of Jacobi
- List of things named after Carl Gustav Jacob Jacobi
