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==Life== |
==Life== |
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He was born in [[Paris]] on 24 July 1856 and educated there at the [[Lycée Henri-IV]]. He then studied mathematics at the [[École normale supérieure (Paris)|École Normale Supérieure]].<ref>{{cite book|title=Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002|date=July 2006|publisher=The Royal Society of Edinburgh|isbn=0-902-198-84-X| url=https://www.royalsoced.org.uk/cms/files/fellows/biographical_index/fells_indexp2.pdf |
He was born in [[Paris]] on 24 July 1856 and educated there at the [[Lycée Henri-IV]]. He then studied mathematics at the [[École normale supérieure (Paris)|École Normale Supérieure]].<ref>{{cite book|title=Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002|date=July 2006|publisher=The Royal Society of Edinburgh|isbn=0-902-198-84-X| url=https://www.royalsoced.org.uk/cms/files/fellows/biographical_index/fells_indexp2.pdf}}</ref> |
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Picard's mathematical papers, textbooks, and many popular writings exhibit an extraordinary range of interests, as well as an impressive mastery of the mathematics of his time. [[Picard's little theorem]] states that every nonconstant [[entire function]] takes every value in the [[complex plane]], with perhaps one exception. [[Picard's great theorem]] states that an [[analytic function]] with an [[essential singularity]] takes every value infinitely often, with perhaps one exception, in any neighborhood of the singularity. He made important contributions in the theory of [[differential equation]]s, including work on [[Picard–Vessiot theory]], [[Painlevé transcendents]] and his introduction of a kind of [[symmetry group]] for a [[linear differential equation]]. He also introduced the [[Picard group]] in the theory of [[algebraic surface]]s, which describes the classes of [[algebraic curve]]s on the surface modulo linear equivalence. In connection with his work on function theory, he was one of the first mathematicians to use the emerging ideas of [[algebraic topology]]. In addition to his theoretical work, Picard made contributions to [[applied mathematics]], including the theories of [[telegraphy]] and [[Elasticity (physics)|elasticity]]. His collected papers run to four volumes. |
Picard's mathematical papers, textbooks, and many popular writings exhibit an extraordinary range of interests, as well as an impressive mastery of the mathematics of his time. [[Picard's little theorem]] states that every nonconstant [[entire function]] takes every value in the [[complex plane]], with perhaps one exception. [[Picard's great theorem]] states that an [[analytic function]] with an [[essential singularity]] takes every value infinitely often, with perhaps one exception, in any neighborhood of the singularity. He made important contributions in the theory of [[differential equation]]s, including work on [[Picard–Vessiot theory]], [[Painlevé transcendents]] and his introduction of a kind of [[symmetry group]] for a [[linear differential equation]]. He also introduced the [[Picard group]] in the theory of [[algebraic surface]]s, which describes the classes of [[algebraic curve]]s on the surface modulo linear equivalence. In connection with his work on function theory, he was one of the first mathematicians to use the emerging ideas of [[algebraic topology]]. In addition to his theoretical work, Picard made contributions to [[applied mathematics]], including the theories of [[telegraphy]] and [[Elasticity (physics)|elasticity]]. His collected papers run to four volumes. |
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Latin: A a Á á À à  â Ä ä Ǎ ǎ Ă ă Ā ā à ã Å å Ą ą Æ æ Ǣ ǣ B b C c Ć ć Ċ ċ Ĉ ĉ Č č Ç ç D d Ď ď Đ đ Ḍ ḍ Ð ð E e É é È è Ė ė Ê ê Ë ë Ě ě Ĕ ĕ Ē ē Ẽ ẽ Ę ę Ẹ ẹ Ɛ ɛ Ǝ ǝ Ə ə F f G g Ġ ġ Ĝ ĝ Ğ ğ Ģ ģ H h Ĥ ĥ Ħ ħ Ḥ ḥ I i İ ı Í í Ì ì Î î Ï ï Ǐ ǐ Ĭ ĭ Ī ī Ĩ ĩ Į į Ị ị J j Ĵ ĵ K k Ķ ķ L l Ĺ ĺ Ŀ ŀ Ľ ľ Ļ ļ Ł ł Ḷ ḷ Ḹ ḹ M m Ṃ ṃ N n Ń ń Ň ň Ñ ñ Ņ ņ Ṇ ṇ Ŋ ŋ O o Ó ó Ò ò Ô ô Ö ö Ǒ ǒ Ŏ ŏ Ō ō Õ õ Ǫ ǫ Ọ ọ Ő ő Ø ø Œ œ Ɔ ɔ P p Q q R r Ŕ ŕ Ř ř Ŗ ŗ Ṛ ṛ Ṝ ṝ S s Ś ś Ŝ ŝ Š š Ş ş Ș ș Ṣ ṣ ß T t Ť ť Ţ ţ Ț ț Ṭ ṭ Þ þ U u Ú ú Ù ù Û û Ü ü Ǔ ǔ Ŭ ŭ Ū ū Ũ ũ Ů ů Ų ų Ụ ụ Ű ű Ǘ ǘ Ǜ ǜ Ǚ ǚ Ǖ ǖ V v W w Ŵ ŵ X x Y y Ý ý Ŷ ŷ Ÿ ÿ Ỹ ỹ Ȳ ȳ Z z Ź ź Ż ż Ž ž ß Ð ð Þ þ Ŋ ŋ Ə ə
Greek: Ά ά Έ έ Ή ή Ί ί Ό ό Ύ ύ Ώ ώ Α α Β β Γ γ Δ δ Ε ε Ζ ζ Η η Θ θ Ι ι Κ κ Λ λ Μ μ Ν ν Ξ ξ Ο ο Π π Ρ ρ Σ σ ς Τ τ Υ υ Φ φ Χ χ Ψ ψ Ω ω {{Polytonic|}}
Cyrillic: А а Б б В в Г г Ґ ґ Ѓ ѓ Д д Ђ ђ Е е Ё ё Є є Ж ж З з Ѕ ѕ И и І і Ї ї Й й Ј ј К к Ќ ќ Л л Љ љ М м Н н Њ њ О о П п Р р С с Т т Ћ ћ У у Ў ў Ф ф Х х Ц ц Ч ч Џ џ Ш ш Щ щ Ъ ъ Ы ы Ь ь Э э Ю ю Я я ́
IPA: t̪ d̪ ʈ ɖ ɟ ɡ ɢ ʡ ʔ ɸ β θ ð ʃ ʒ ɕ ʑ ʂ ʐ ç ʝ ɣ χ ʁ ħ ʕ ʜ ʢ ɦ ɱ ɳ ɲ ŋ ɴ ʋ ɹ ɻ ɰ ʙ ⱱ ʀ ɾ ɽ ɫ ɬ ɮ ɺ ɭ ʎ ʟ ɥ ʍ ɧ ʼ ɓ ɗ ʄ ɠ ʛ ʘ ǀ ǃ ǂ ǁ ɨ ʉ ɯ ɪ ʏ ʊ ø ɘ ɵ ɤ ə ɚ ɛ œ ɜ ɝ ɞ ʌ ɔ æ ɐ ɶ ɑ ɒ ʰ ʱ ʷ ʲ ˠ ˤ ⁿ ˡ ˈ ˌ ː ˑ ̪ {{IPA|}}
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