236
3 Sufficient Conditions of Extrema of Functionals
terms of mathematics are associated with his name. The works had Canon arithmeticus (1839), Vorlesungen über analytische Mechanik (1848, 1996) and Jacobi’s
lectures on dynamics (1866, 2009) etc.
Weierstrass (Karl Theodor Wilhelm, 1815.10.31–1897.2.19) German mathematician. Born in Ostenfelde, Province of Westphalia, died in Berlin. Graduated from the
School of Law, University of Bonn in 1838, later transferred to study mathematics.
Since 1841, taught in high school for 15 years. obtained an honorary doctorate
degree in 1854. Served as an associate professor at the University of Berlin in 1856,
became a professor in 1864, served as the president from 1873 to 1874. Was elected
a member of the Berlin Academy of Sciences in 1856, was elected as a member of
the French Academy of Sciences in 1868, became a member of the Royal Society
in 1881. The major contribution was in the mathematical analysis, analytic function
theory, calculus of variations, differential geometry and linear algebra, etc. Under
the joint efforts with Dedekind (Julius Wilhelm Richard, 1831.10.6–1916.2.12)
and Cantor (Moritz Benedikt, 1829.8.23–1920.4.9), founded the modern function
theory. Was in the 19th century’s most influential analyst, first-rate mathematician,
the father of modern analysis. Was a distinguished educator, had trained a large
number of successful mathematical talents, among them the famous mathematicians
had Kovalevcka (Cofff Bacillevna, 1850.1.15–1891.2.10), Schwarz, MittagLeffler, Bolza and Klein (Felix, 1849.4.25–1925.6.22) et al. The works had Zur
Theorie der Abelschen Funktionen (1854), Theorie der Abelschen Funktionen (1856)
and Mathematische Werke (1894–1927) etc.
Hilbert (David, 1862.1.23–1943.2.14) German mathematician. Born in königsberg,
died in Göttingen. Enrolled at the University of Königsberg in 1880, obtained a
Ph.D. degree in 1885. Served as a professor at the University of Königsberg in
1893. Served as a professor of the University of Göttingen in 1895, until his retirement in 1930. Was elected a communication academician of the Berlin Academy
of Sciences in 1913, became an honorary academician of the Berlin Academy of
Sciences in 1942. Was also an academician or honorary academician of academies
of sciences in many countries. In the invariant theory, algebraic number theory, geometry, calculus of variations, theory of differential equations, theory of integral equation, number theory, method of mathematical physics and mathematical logic, and
other fields had made brilliant achievements. In 1900, in Paris international Congress
of Mathematicians posed the 23 most important mathematical problems, later was
called the Hilbert problems, had a profound effect on the mathematical development of the 20th century. The main works had Grundlagen der Geometrie (1899),
Methoden der Mathematischen Physik I, II (1924, 1937), Grundzüge der Theoretischen Logik (1928), Anschauliche Geometrie (1932) and Grundlagen der Mathematik
(1934, 1939) etc. He was an outstanding researcher and excellent teacher, and had
outstanding leadership.
3 Sufficient Conditions of Extrema of Functionals
terms of mathematics are associated with his name. The works had Canon arithmeticus (1839), Vorlesungen über analytische Mechanik (1848, 1996) and Jacobi’s
lectures on dynamics (1866, 2009) etc.
Weierstrass (Karl Theodor Wilhelm, 1815.10.31–1897.2.19) German mathematician. Born in Ostenfelde, Province of Westphalia, died in Berlin. Graduated from the
School of Law, University of Bonn in 1838, later transferred to study mathematics.
Since 1841, taught in high school for 15 years. obtained an honorary doctorate
degree in 1854. Served as an associate professor at the University of Berlin in 1856,
became a professor in 1864, served as the president from 1873 to 1874. Was elected
a member of the Berlin Academy of Sciences in 1856, was elected as a member of
the French Academy of Sciences in 1868, became a member of the Royal Society
in 1881. The major contribution was in the mathematical analysis, analytic function
theory, calculus of variations, differential geometry and linear algebra, etc. Under
the joint efforts with Dedekind (Julius Wilhelm Richard, 1831.10.6–1916.2.12)
and Cantor (Moritz Benedikt, 1829.8.23–1920.4.9), founded the modern function
theory. Was in the 19th century’s most influential analyst, first-rate mathematician,
the father of modern analysis. Was a distinguished educator, had trained a large
number of successful mathematical talents, among them the famous mathematicians
had Kovalevcka (Cofff Bacillevna, 1850.1.15–1891.2.10), Schwarz, MittagLeffler, Bolza and Klein (Felix, 1849.4.25–1925.6.22) et al. The works had Zur
Theorie der Abelschen Funktionen (1854), Theorie der Abelschen Funktionen (1856)
and Mathematische Werke (1894–1927) etc.
Hilbert (David, 1862.1.23–1943.2.14) German mathematician. Born in königsberg,
died in Göttingen. Enrolled at the University of Königsberg in 1880, obtained a
Ph.D. degree in 1885. Served as a professor at the University of Königsberg in
1893. Served as a professor of the University of Göttingen in 1895, until his retirement in 1930. Was elected a communication academician of the Berlin Academy
of Sciences in 1913, became an honorary academician of the Berlin Academy of
Sciences in 1942. Was also an academician or honorary academician of academies
of sciences in many countries. In the invariant theory, algebraic number theory, geometry, calculus of variations, theory of differential equations, theory of integral equation, number theory, method of mathematical physics and mathematical logic, and
other fields had made brilliant achievements. In 1900, in Paris international Congress
of Mathematicians posed the 23 most important mathematical problems, later was
called the Hilbert problems, had a profound effect on the mathematical development of the 20th century. The main works had Grundlagen der Geometrie (1899),
Methoden der Mathematischen Physik I, II (1924, 1937), Grundzüge der Theoretischen Logik (1928), Anschauliche Geometrie (1932) and Grundlagen der Mathematik
(1934, 1939) etc. He was an outstanding researcher and excellent teacher, and had
outstanding leadership.