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Sòo-ha̍k tiānn hông khuànn-tsò sī leh gián-kìu sòo-liōng, kiat-kòo, khong-kan kap piàn-tōng ê ha̍k-būn. Ū kuá sòo-ha̍k-ka kā sòo-ha̍k tòng-tsò sī kong-siat kap ting-gī thàu-kuè tshui-lūn tit--tio̍h ê tì-sik.

Ta̍k ê siā-huē leh tshik-liông thóo-tē, tshú-lí kuè-kè, ī-tshik thian-bûn sū-kiānn, ... ê sî tsha-put-to lóng ē-tit khuànn tio̍h ìng-iōng sòo-ha̍k ê iánn. Sòo-ha̍k thong-siông sī leh tshiau-tshuē bôo-sik, bô tiānn-tio̍h ài kap ìng-iōng ū tī-tāi. M̄-koh Eugene Wigner bat kóng kuè "sòo-ha̍k siunn kuè-thâu-á ū-hāu", siōng 'sûn' ê sòo-ha̍k tiānn tshuē tio̍h siōng si̍t-tsè ê ìng-iōng. Hiān-tshú-sî ê tsū-jiân kho-ha̍k, kang-tîng, king-tsè, i-ha̍k lóng tio̍h khuànn sòo-ha̍k ū sin huat-tián--bô.

Hi-lia̍p-gí ê μάθημα (máthema) piáu-sī "kho-ha̍k, tì-sik, ha̍k-si̍p", μαθηματικός (mathematikós) piáu-sī "kah-ì o̍h mi̍h-kiānn". Ing-gí kā sòo-ha̍k siá tsò mathematics, kán-siá tsò maths (Liân-pang Ing-gí), math (Bí-kok Ing-gí).

Sòo-ha̍k ê li̍k-sú[]

Sòo-ha̍k ê ián-piàn ē-tit khuànn tsò kóng thiu-siōng ê tsú-tê iah sī thîng-tōo ti̍t-ti̍t leh tsing-ka. Siōng tsá ê thiu-siōng huān-sè sī sòo-ba̍k. Liáu-kái kóng nn̄g lia̍p phōng-kó kap nn̄g lia̍p kam-á ká-ná ū sím-mih sio-kâng ê sóo-tsāi, sòo-ha̍k tō khai-sí huat-tián--a.

Sú-tsîng ê jîn-luī ē-hiáu sǹg kū-thé ê mi̍h-kiānn, mā tsai-iánn beh án-tsuánn sǹg thiu-siōng ê sòo-liōng, tshīunn kóng sî-kan (kang, kuì, , ...). Ē-hiáu sǹg, koh lâi tō sī sǹg-siàu (tshīunn ke, kiám, sîng, ).

M̄-koh beh sǹg tio̍h-ài ē-tàng siá kap 1 thò sòo-jī hē-thóng. Sú-tsîng ê jîn-luī huān-sè sī tī thôo-kha uē sûn iah sī tī tshâ-thâu khik sûn lâi piáu-sī sòo-liōng. Inca Tè-kok bô su-siá hē-thóng, in lī-iōng soh-á phah-kat ê hong-huat lâi sǹg-siàu, hō-tsò khipu.

Sòo-ha̍k ê huat-tián kap tshik-liông thóo-tē, tshú-lí kuè-kè, ī-tshik thian-bûn sū-kiānn ū tsin bi̍t-tshiat ê kuan-hē. In-uī ū su-iàu, sòo-ha̍k lāi-té tshú-lí khong-kan, kiat-kòo, piàn-tōng ê gián-kìu tō tuè leh huat-tián. Khah lōo-bué, beh kái-kuat sio kap kng ê bûn-tê, sòo-ha̍k bu̍t-lí-ha̍k mā khai-sí huat-tián.

Tû-khì íng-kuè tsiah-ê gián-kìu ê tsú-tê, sòo-ha̍k kàu tann mā îu-guân it-ti̍t leh tshòng-sin.

Sûn sòo-ha̍k kap ìng-iōng sòo-ha̍k[]

Ū oh kái-kuat ê būn-tê tō su-iàu sòo-ha̍k. Íng-kuè tshīunn siong-gia̍p, thóo-tē tshik-liông, thian-bûn-ha̍k; hiān-tshú-sî tuā-pōo-hūn uì tsū-jiân kho-ha̍k tit tio̍h lîng-kám, tsiânn tsē sòo-ha̍k-ka mā sī bu̍t-lí-ha̍k-ka. Tshīunn í-tsá Newton huat-tián bî-tsik-hun, Ritsard Feynman huat-tián Feynman kìng-tsik-hun, tsit-má thàu-kuè tshui-lí kap tuì bu̍t-lí ê tshim-ji̍p liáu-kái, tō huat-tián tshut hiân-lūn (string theory).

Ū būn-tê beh kái-kuat, gián-kìu siong-kuan ê sòo-ha̍k liáu-āu, tō ē-tit it-ti̍t ìng-iōng tsiah-ê sòo-ha̍k. Kā ū kiōng-tông ki-tshóo ê sòo-ha̍k khioh tsò-hué, tsi̍t-kuá kuan-liām ē-tit tha̍h tsò-hué. tsa̍p-káu sè-kí ê sî, tō án-ne kā sòo-ha̍k hun-tsò ìng-iōng sòo-ha̍k kap sûn sòo-ha̍k.

Sòo-ha̍k hōo lâng kám-kak iu-ngá, huān-sè i ê pún-tsit tō sī bí-ha̍k, huān-sè i pun-sin ū tsi̍t tsióng bí-kám, m̄-koh tse lóng tsin oh bîng-khak piáu-ta̍t. Kán-tan-sìng kap phóo-phiàn-sìng sī sòo-ha̍k nn̄g ê tsin tiong-iàu ê ti̍k-sik. Tsiah-ê khuànn--khí-lâi tàu bē tsò-hué ê sìng-tsit ū-tang-sî-á ē-tàng kiat-ha̍p, tshīunn kóng kā tsi̍t-kuá bô kāng hun-ki ê sòo-ha̍k it-thé-huà, iah sī huat-tián ē-sái kiōng-tông kè-sǹg ê ke-si. Sûn sòo-ha̍k tshoo-tshoo khuànn ká-ná kan-tann i ê bí-kám ū kuá kè-ta̍t, kan-tann sòo-ha̍k-ka ū tshù-bī. M̄-koh gián-kìu tsi̍t-ē tsìn-tián liáu-āu, sûn sòo-ha̍k tiānn ē pìnn-tsiânn ìng-iōng sòo-ha̍k.

Sòo-ha̍k hû-hō[]

Sòo-ha̍k ê bûn-tsiunn bô kài hó tha̍k. Stephen Hawking it kiú pa̍t pa̍t nî tshut ê Sî-kan kán-sú (A Brief History of Time) lāi-té kan-tann ū tsi̍t tiâu sòo-ha̍k kong-sik, in-uī tshut-pán-siong kóng muí tsi̍t tiâu kong-sik tō ē kā siau-lōo kàng tsi̍t-puànn.

Sòo-ha̍k-ka tsin giâm-keh iau-kîu ài kā siunn beh piáu-ta̍t--ê siá tshing-tshó, tsóng--sī sòo-ha̍k iáu-sī ká-ná huat-lu̍t tiâu-bûn hiah pháinn tha̍k. Sòo-ha̍k-ka khok-tshiong tsū-jiân gí-giân, īng tīng kah tsin bîng-khak ê sòo-ha̍k bîng-sû, sòo-ha̍k hû-hō kap bûn-huat (gí-huat) lâi ta̍t kàu giâm-keh ê bo̍k-phiau. Ū tsi̍t-kuá bîng-sû tsioh īng phóo-thong ê bîng-sû, m̄-koh ì-sù bô tī-tāi, tshīunn khuân (ring), kûn (group), luī (category); ū-ê bîng-sû sī sòo-ha̍k tsuan-iōng--ê, tshīunn homotopy, Hilbert khong-kan. Thiann kóng Henri Poincaré hông suán ji̍p-khì Huat-kok Gián-kìu-īnn (Académie Française) tō sī beh tshiánn i lâi tīng-gī automorphe.

Sòo-ha̍k kap kho-ha̍k[]

Carl Friedrits Gauss kóng sòo-ha̍k sī kho-ha̍k ê lú-ông. Sòo-ha̍k bu̍t-lí-ha̍k-ka Leon M. Lederman khau-sé kóng bu̍t-lí-ha̍k-ka kan-tann sūn-thàn sòo-ha̍k-ka, sòo-ha̍k-ka kan-tann sūn-thàn Siōng-tè, sui-bóng tsiah-nī kòo-khiam ê sòo-ha̍k-ka tsin oh tshuē.

Sòo-ha̍k gián-kìu ê huān-uî[]

Tsá-kî ê sòo-ha̍k uī tio̍h siong-gia̍p, tshik-liông, ī-tshik thian-bûn hiān-siōng, huat-tián kiat-kòo, khong-kan, piàn-tōng ê gián-kìu, tshīunn tāi-sòo (algebra), kí-hô-ha̍k (geometry), hun-sik (analysis). Āu--lâi, ta̍uh-ta̍uh koh huat-tián kàu lô-tsik, khah kán-tan ê ki-tshóo hē-thóng (foondations), kap khah si̍t-iōng ê ìng-iōng sòo-ha̍k (applied mathematics).

Sòo-ha̍k tsú-iàu ê gián-kìu[]

Tsia lia̍t--ê sī khah tsú-iàu ê gián-kìu tê-ba̍k. Khah uân-tsíng ê gián-kìu tsú-tê tshiánn tsham-khó sòo-ha̍k tsú-tê lia̍t-tuann.

Sòo-liōng (Quantity)[]

Leh tshú-lí sòo-ba̍k, tsi̍p-ha̍p, tuā-sè (size) tsit luī ê būn-tê, kap tsáu-tshuē tshú-lí ê hong-huat.

Tsū-jiân-sòo Tsíng-sòo pí-sòo Si̍t-sòo Ho̍k-tsa̍p-sòo )
Sòo-ba̍kTsū-jiân-sòoTsíng-sòopí-sòoSi̍t-sòoHo̍k-tsa̍p-sòoHypercomplex numbers – Quaternions – Octonions – Sedenions – Hyperreal numbers – Surreal numbers – Ordinal numbers – Cardinal numbers – p-adic numbersInteger sequences – Sòo-ha̍k tiānn-sòoNumber namesBû-hānki-té (Base)

Piàn-tōng (Tsange)[]

Leh tshú-lí sòo-ba̍k kap hâm-sòo ê piàn-huà.

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Sǹg-siàu (Arithmetic) Bî-tsik-hun Hiòng-liōng bî-tsik-hun Hun-sik (Analysis)
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Bî-hun hong-tîng (Differential equations) Tōng-thài hē-thóng (Dynamical systems) Hūn-tūn lí-lūn (Tsaos theory)
Sǹg-siàu (Arithmetic) – Bî-tsik-hunHiòng-liōng bî-tsik-hunHun-sik (Analysis) – Bî-hun hong-tîng (Differential equations) – Tōng-thài hē-thóng (Dynamical systems) – Hūn-tūn lí-lūn (Tsaos theory) – Hâm-sòo lia̍t-tuann

Kiat-kòo (Structure)[]

Leh tshú-lí tuā-sè (size), tuì-thīn (symmetry) kap tsi̍t-kuá sòo-ha̍k kiat-kòo (mathematical structure) ê būn-tê.

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Thiu-siōng tāi-sòo Sòo-lūn Kûn-lūn (Groop theory)
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Topology Category theory Order theory
Thiu-siōng tāi-sòoSòo-lūnTāi-sòo kí-hô-ha̍kKûn-lūn (Groop theory) – Monoids – Hun-sik (Analysis) – TopologySuànn-sìng tāi-sòo (Linear algebra) – Tôo-lūn (Graph theory) – Universal tāi-sòo (Universal algebra) – Category theoryOrder theoryMeasure theory

Khong-kan kuan-hē (Spatial relations)[]

Ē-tàng khuànn ê sòo-ha̍k.

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Topology Kí-hô-ha̍k Sann-kak-huat Bî-hun kí-hô-ha̍k Tshuì-hîng kí-hô-ha̍k (Fractal geometry)
TopologyKí-hô-ha̍kSann-kak-huatTāi-sòo kí-hô-ha̍kBî-hun kí-hô-ha̍kBî-hun topology (Differential topology) – Tāi-sòo topology (Algebraic topology) – Suànn-sìng tāi-sòoTshuì-hîng kí-hô-ha̍k (Fractal geometry)

Discrete sòo-ha̍k (Discrete mathematics)[]

Leh tshút-lí kan-tann ē-tàng tsi̍t ê tsi̍t ê sǹg ê mi̍h-á.



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Combinatorics Native tsi̍p-ha̍p-lūn (Naive set theory) Kè-sǹg lí-lūn (Theory of computation) Bi̍t-bé-ha̍k (Cryptography) Tôo-lūn (Graph theory)
CombinatoricsNative chi̍p-ha̍p-lūn (Naive set theory) – Kè-sǹg lí-lūn (Theory of computation) – Bi̍t-bé-ha̍k (Cryptography) – Tôo-lūn (Graph theory)

Ìng-iōng sòo-ha̍k (Applied mathematics)[]

Leh kái-kuat hiān-si̍t būn-tê ê sòo-ha̍k.

Sòo-ha̍k bu̍t-lí-ha̍k (Mathematical physics) – MetsanicsFluid metsanicsNumerical analysisOptimizationKi-lu̍tThóng-kè-ha̍kFinancial mathematicsGame theoryMathematical biologyBi̍t-bé-ha̍k (Cryptography) – Tsu-sìn lí-lūn (Information theory)

Tīng-lí (Theorems)[]

Tse lia̍t tsi̍t-kuá m̄-sī sòo-ha̍k-ka mā ē kám-kak sim-sik ê tīng-lí. Uân-tsíng ê tsu-liāu tshiánn tsham-khó Tīng-lí lia̍t-tuann.

Ti̍t-kak tīng-lí (Pythagorean theorem) – Fermat tsuè-āu tīng-lí (Fermat's last theorem) – Gödel's incompleteness theorems – Cantor's diagonal argument4 sik tīng-lí (Foor color theorem) – Zorn's lemmaEuler's identityTsurts-Turing thesisRiemann hypothesisContinuum hypothesisCentral limit theoremSǹg-siàu ki-pún tīng-lí (Fundamental theorem of arithmetic) – Tāi-sòo ki-pún tīng-lí (Fundamental theorem of algebra) – Bî-tsik-hun ki-pún tīng-lí (Fundamental theorem of calculus) – Fundamental theorem of projective geometryGauss-Bonnet theorem.

Tshai-tshik (Conjectures)[]

Tse lia̍t tsi̍t-kuá tng-leh gián-kìu ê būn-tê. Uân-tsíng ê tsu-liāu tshiánn tsham-khó Tshai-tshik lia̍t-tuann.

Goldbats Tshai-tshikTwin prime conjectureCollatz conjecturePoincare2 conjectureclassification theorems of surfacesP=nnP

Līng-guā, ū-ê sòo-ha̍k-ka jīn-uî continuum hypothesis kap ZFC bô tī-tāi, bián tshap i; ū-ê khah tsik-ki̍k leh gián-kìu.

Ki-tsân kap hong-huat (Foondations and methods)[]

Leh su-khó sòo-ha̍k ê pún-tsit kap sòo-ha̍k beh án-tsuánn gián-kìu.

Philosophy of mathematicsMathematical intuitionismMathematical constructivismSòo-ha̍k ê ki-tsân (Foondations of mathematics) – Tsi̍p-ha̍p-lūnHû-hō lô-tsik (Symbolic logic) – Bôo-hîng-lūn (Model theory) – Category theoryLô-tsikReverse MathematicsSòo-ha̍k hû-hō-pió (Table of mathematical symbols)

Sòo-ha̍k-sú kap sòo-ha̍k-ka[]

Tshiánn tsham-khó sòo-ha̍k-sú lia̍t-tuann

Sòo-ha̍k-súSòo-ha̍k nî-pióSòo-ha̍k-kaFields TsióngAbel PrizeMillennium Prize Problems (Clay Math Prize)International Mathematical UnionMathematics competitionsLateral thinkingMathematical abilities and gender issues

Sòo-ha̍k ê hûn-iánn[]

Sòo-ha̍k kap kiàn-tio̍kSòo-ha̍k kap kàu-io̍kSòo-ha̍k kap im-ga̍k

Tuì sòo-ha̍k ê gōo-kái[]

Sòo-ha̍k m̄ sī tsi̍t ê sím-mih būn-tê lóng kái-kuat tiāu ê hē-thóng, i lāi-té iáu tsin tsē ài gián-kìu ê būn-tê.

Ké-sòo-ha̍k khuànn--khí-lâi tshin-tshīunn sòo-ha̍k, i bô tī ha̍k-su̍t-kài tsiap-sīu kàm-tok, ū-sî-á koh si sòo-ha̍k-ka pìnn--ê. I thong-siông sī leh thó-lūn khah ū-miâ ê būn-tê, m̄-koh i koh m̄ sī īng lâng tsìng-bîng kuè ê lí-lūn tsò ki-tsân lâi tsìng-bîng. Ké-sòo-ha̍k kap sòo-ha̍k tō ká-ná ké-kho-ha̍k kap kho-ha̍k tshan-tshīunn. Tsit khuán tāi-tsì ē lâi huat-sing ê guân-in ū:

  • bô hù-ha̍p giâm-keh ê iau-kîu;
  • in-uī bóo tsi̍t-kuá in-sòo, bô tsun-tsiàu sòo-ha̍k lūn-bûn ài sing king-kuè tông-liâu sím-tsa, tī ha̍k-su̍t kî-khan huat-piáu, ... tsiah-ê tîng-sū;
  • tuì bûn-hiàn bô kài liáu-kái.


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