Blichfeldt's theorem remains a foundational result in the geometry of numbers, providing a method to translate bounded subsets of Euclidean space to cover integer points. Hans Frederick Blichfeldt spent his career advancing group theory, the representation theory of finite groups, and quadratic forms, ultimately shaping mid-twentieth-century mathematical inquiry from his long-held post at Stanford University.
Early Life and Education
Born in 1873 at Grønbæk Parish, Denmark, Hans Frederick Blichfeldt moved to Copenhagen in 1881. Despite achieving high marks on university entrance exams in 1888, his family lacked the resources to fund his higher education. Upon moving to the United States, he worked as a lumberman, railway worker, surveyor, and draftsman. In 1894, he enrolled at Stanford University as a special student due to his lack of a diploma, before graduating with a bachelor's degree in 1896 and a master's degree in 1897. Supported by professor Rufus L. Green, he completed his doctoral studies at Leipzig University in 1898 under the supervision of Sophus Lie.
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Blichfeldt returned to Stanford University to serve as an instructor in 1898, eventually advancing to a full professorship by 1913. He chaired the mathematics department from 1927 until his retirement in 1938. Throughout his tenure, he held visiting positions at the University of Chicago in 1911 and Columbia University during the 1924 and 1925 academic years. His professional service included acting as vice-president of the American Mathematical Society in 1912 and representing the United States at the International Congress of Mathematicians in 1932 and 1936.
Mathematical Contributions
His research output spanned group theory and lattice geometry. In 1916, he co-authored a comprehensive text on finite groups with George Abram Miller and Leonard Eugene Dickson, focusing on complex linear transformation groups. His 1914 discovery, now identified as Blichfeldt's theorem, established volume constraints for covering integer points within Euclidean space. Later in his career, he focused on quadratic forms and sphere packing, proving the optimality of the E8 lattice in eight dimensions in a 1935 study.
Awards and Recognition
The scientific community recognized his work through several memberships, including the National Academy of Sciences in 1920 and the National Research Council between 1924 and 1927. In 1939, he received the Knight of the Order of the Dannebrog. Blichfeldt remained a lifelong member of the American Mathematical Society. He died in Palo Alto in 1945 and was buried at Alta Mesa Memorial Park.
Fast facts
- Born: 1873, Grønbæk Parish
- Died: 1945, Palo Alto
- Citizenship: United States
- Education: Stanford University, Leipzig University
- Notable Work: Blichfeldt's theorem
- Academic Home: Stanford University
- Awards: Knight of the Order of the Dannebrog
- Burial: Alta Mesa Memorial Park
Questions readers ask
What is the primary significance of Blichfeldt's theorem?
It establishes that a bounded subset of n-dimensional Euclidean space with volume V can be translated to cover at least the ceiling of V integer points.
Did Blichfeldt hold any major academic roles?
He served as a mathematics professor at Stanford University from 1898 to 1938 and acted as the department chair starting in 1927.
Achievements
- Knight of the Order of the Dannebrog — 1939
- Notable work: Blichfeldt's theorem
- Held posts at Stanford University
