Charles Hermite
Contribution to mathematics: Minor improvement.
| ← Previous revision | Revision as of 03:59, 20 April 2026 | ||
| Line 49: | Line 49: | ||
In 1873, he published a lengthy paper demonstrating in two different ways that that [[e (mathematical constant)|''e'']], the base of the [[natural logarithm]], is [[Transcendental number|transcendental]],{{Cite book |last=Maor |first=Eli |title=e: The Story of a Number |publisher=[[Princeton University Press]] |year=1994 |isbn=0-691-05854-7 |location=Princeton, New Jersey|author-link=Eli Maor}}{{Reference page|pages=192-3}} based on prior work by Joseph Liouville.{{cite book|title=The Calculus Gallery|first=William|last=Dunham|isbn=978-0-691-13626-4|publisher=Princeton University Press|year=2005|page=|author-link=William Dunham (mathematician)}}{{Reference page|page=127}} However, Hermite did not address the transcendence of {{mvar|π}}, believing the question to be beyond his powers.{{Reference page|page=193}} But techniques similar to those he employed in this proof were later used by [[Ferdinand von Lindemann]] in 1882 to prove that result for {{mvar|[[Pi|π]]}}. (Also see the [[Lindemann–Weierstrass theorem]].) Hilbert subsequently simplified Hermite's original proof.{{Reference page|page=196}} |
In 1873, he published a lengthy paper demonstrating in two different ways that that [[e (mathematical constant)|''e'']], the base of the [[natural logarithm]], is [[Transcendental number|transcendental]],{{Cite book |last=Maor |first=Eli |title=e: The Story of a Number |publisher=[[Princeton University Press]] |year=1994 |isbn=0-691-05854-7 |location=Princeton, New Jersey|author-link=Eli Maor}}{{Reference page|pages=192-3}} based on prior work by Joseph Liouville.{{cite book|title=The Calculus Gallery|first=William|last=Dunham|isbn=978-0-691-13626-4|publisher=Princeton University Press|year=2005|page=|author-link=William Dunham (mathematician)}}{{Reference page|page=127}} However, Hermite did not address the transcendence of {{mvar|π}}, believing the question to be beyond his powers.{{Reference page|page=193}} But techniques similar to those he employed in this proof were later used by [[Ferdinand von Lindemann]] in 1882 to prove that result for {{mvar|[[Pi|π]]}}. (Also see the [[Lindemann–Weierstrass theorem]].) Hilbert subsequently simplified Hermite's original proof.{{Reference page|page=196}} |
||
==Publications== |
==Publications== |
||
