火星表面出现蓝色的，像是液态水的地形区域，或

百度 《资本论》的“希望空间”在《资本论》中，马克思通过“政治经济学批判”揭示出了劳动、资本和时间这些最基本的概念在资本主义社会化大生产条件下的“双重空间”本质：劳动是“价值增殖过程”与“协作生产”的空间，资本是“资本的文明面”与“个人受抽象统治”的空间，时间是“工作日的缩短”与“人类发展”的空间。

????? | ?????? | ??????? | ??? | ????? | ?????? | ???????? | ?????? | ????????? | ?????? | ??????????? | ??????

????  

???? ????????

??????

?????? (Mathematics) ??????????????? ??? ??????????????. ??? ????????, ?????????, ??????????? (space), ????? ????????? (structures), ??????? ??????????? ("change") ?????? ????? ?????. ????????? ?????? ????????, ??????????, ????????? , ?????-????????? ???? ???????? ?????? ????????????? ????????? ??? ???????? ???????????. ?????????? ??? ???????????? ?????????????? ???????, ????????, ?????????, ???????? ????? ??????????????, ?????????, ??????, ?????? ????? ???? ????, ????????, ??????? ????? ??????????? ?????, ?????????????? ?????????????? ??????? ???? ??????? ?????????? ?????? ????? ?????????? ??????????? ?????????????? ???????????? ???? ????????? ???????? ??????? ??????????????? ?????? ????????. ??????? ???????????? ?????????? ????????????, ??????????? ????????? ????????? ???????. ???????????????? ????????? ?????? ?????? ???????????? ?????????? (abstract) ??????????? ???? ?????????????? ?????????????? ??????? ??????? ???????. ??????? (topology) ??????? ??????????? ????? ?????? ??????? ???????????? ???????????? ?????????? ???????? ??????? ?????? ?? ??????? ????? ??????? ?????????? ??????? ???????????. ?????????? ??????????? ????????? ???????? ???????????? ??? ??????? ???????????. ??????? "?????????? ???????? ???? ????????????? ????????" ????? ????????. ??????? ?????? ???????? ‘?????????? ?????’ (Father of Numbers) ?? ?????????????????.

?????? ?????????????? ?????????????? ?????????? (arithmetic) ????????? ?????????????? ?????????????? ???????? ??????? ????????? ????? ?????????? ????. ??????? ????? ???????????? ?????? ????????????? ?????? ?????????? ?????????? ?????????? ???????? ?????????? ???? ?????????? ??????? ????? ??????. ??????? ????? ????????? ???? ??????? ???????? ???????? ???? ?????????? ?????? ????? ???????. ????? ?????? ??????????? ??????? ?????????? ?????.

?????? ????? ??????...

????  

????????? ???????

???????? ?????????? (elementary algebra) ?????? ?????????????? ??? ????????? ??????. ??? ?????????????? ?????????? ?????????????? ????????????. ????????? ??????? ?????????? ??????????????? ??????? ????????, ?????????????? ???????????? ???????????. ????????????? ?????? ??????? ???????? ?????? ???????????? ?????????? ????????? ???????, ????????, ?????????, ???????? ?????? ??????? ???????????? ???????????????????. ???????? ?????????????? x ??????? y ????? ?????????, ???????????? ????? a ??????? b ????? ??????????? ????????????????? ?????? ???????? ????????????????????.

??????? ?????????? ???????? (abstract) ?????????? ???????????? ???????????? ???????? ?????????? ???????????. ????????? ?????? ???????? ????? ?????? ?????? ???????? ??????????????? ??????? ?????????????????. ???????, ????????? ??????? ????????? ?????, ??????? ?????????????? ????? ?????? ?????????? ????????? ????????????????????. ?????????????? ??????????? ????????? ????? ???????????.

????  

???????????? ????????...

• ?????? ????????????? x ???? ???? ??????? ????????? ?????? ??????????? ??? ????????????? ??????????.
• ???? ?????? ?????? ???? ?????? ????????? ????? ?????? ?????????? (1, 2, 3, …), ???????? ??????????????? (?1, ?2, ?3, ...) ??????? ???? ????????????? ??????????????.
• ????? (1) ?????? ????????? (0) ???? ??? ??????????? ?????? ?????? ??????????? ?????????? ?????? ???? ??? ???? ???????, ????? ?????? ?????? ??? ???? ????????? ??????????.
• ??????? ????????????? ?????? ?????? ??? ????????? ??????? ??????? ??? ????????? ?????????????????.

?????? ???????

?????? ?????? ??????? ?????? ?????? ???????????????? ???? ??????????? ??????? ??????????? ??????? ?????????? ????????????? ???????? ???? ?????????? ???? ??????? ???? ????????? ???? ?????????? ???? ????????????? ?????? ?????????????? ?????? ????? ?????? ???????????? ?????? ????????????? ?????????? ?????? ????????? ???????? ?????????? ????????? ?????? ????????? ?????? ???????? ??????????????? ??????????????? ?????? ???????? ?????? ???????????? ???????? ???????? ????? ????????? ??????? ?????? ?????? ????????? ?????????? ?????? ?????????? ?????? ????????????? ?????? ?????????? ??????????? ??????????? ????????? ?????? ????????? ???? ??????????? ????????? ???? ????????? ??????????? ???????? ???? ?????? ????????? ?????????

????  

????????? ????

????????

????????? ?????? ?????????? ?????.

?????????? (Algebra)	????????	??????? ???????? ?????????	??????????? ??????
?????????? ???????? ?????????? ??????? ?????????? ????????????? ?????????????? ???????????? ???????????? ???????? ????????? ?????????? ??????? ?????????? ????? ?????? ????????????? ???????????????? Order theory ???????? ?????????? ???????	???????? ?????????????? ??????????????? ??????????????? ????????????????????? ???????? ???????????????????????? ???????? ????????????? ?????????? ?????????? ??????? ?????????? ??????????? ??????????? ??? ?????????? ???? ?????????? ???????????????? Harmonic analysis Measure theory ????? ????????? ????????????	????????? ??????? ???? ??????? ???????? ??????? ???? ??????? ???????? ???????? ?????????? ???????? Affine geometry Projective geometry Differential geometry Riemannian geometry Lie groups Algebraic geometry	??????????? ?????? Numerical analysis ????????? ??????????? Optimization (mathematics) Dynamical systems ??????????? ???????? ????????? ?????? ???????? ?????? Financial mathematics Cryptography
???????????	??? ????????	?????????? ??????	????
?????????? ??????????? ???? ???????? Naive set theory Axiomatic set theory Mathematical logic ??????? ???????? Model theory Category theory Topos theory	??? ???????? ???????? ??? ???????? ?????????? ???????? ????????? ?????? ??????????? ??? ?????? ??????????? ????????? ?????? ????????? ?????? ???????? ?????? ??????????? ????????????	?????????? ?????? ????????? ????????????? Game theory Discrete geometry Theoretical computer science Computability theory (computation) Computational complexity theory Information theory	??????????????? ?????????? ?????? ?????????? ????????? ?????? ?????????? ???? ?????????? ???? ?????? ????? ?????????? ????????

????  

?????????? ???????????

:?????????????	????????	?????????
?????????????	????????	?????????

???? ?????????? - ?????

• ??????? - ????? - ????? 10 ??? ???????????? ?????? ????? - ???????? ???, ????????
• ????? ???? ??????????????? ???? ????????? ??????
• Chennai Mathematical Institute