Homotopy type theory is a new branch of mathematics that combines aspects of several different fields in a surprising way. It is based on a recently discovered connection between homotopy theory and type theory. It touches on topics as seemingly distant as the homotopy groups of spheres, the algorithms for type checking, and the definition of weak ∞-groupoids. Homotopy type theory offers a new “univalent” foundation of mathematics, in which a central role is played by Voevodsky’s univalence axiom and higher inductive types. The present book is intended as a first systematic exposition of the basics of univalent foundations, and a collection of examples of this new style of reasoning — but without requiring the reader to know or learn any formal logic, or to use any computer proof assistant. We believe that univalent foundations will eventually become a viable alternative to set theory as the “implicit foundation” for the unformalized mathematics done by most mathematicians.
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讀後感
Will Computers Redefine the Roots of Math? A Story from Quanta Magazine
評分Will Computers Redefine the Roots of Math? A Story from Quanta Magazine
評分Will Computers Redefine the Roots of Math? A Story from Quanta Magazine
評分Will Computers Redefine the Roots of Math? A Story from Quanta Magazine
評分Will Computers Redefine the Roots of Math? A Story from Quanta Magazine
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翻到這個圖書，真心想做一B站視頻。背景音樂是基督教福音歌麯AmazingGrace，畫麵前端放一個瑞腦消金獸的那個香爐，旁邊是你這些年讀過的所有數學書，還有一個藍色紙闆做的B乎logo……然後你在畫麵中奮力地焚燒著，對要奮力地焚燒著，要做齣畫作呐喊那種錶情，要燃齣焚琴煮鶴的爽快，要燒齣南美大盜焚幣的豪情！最後畫麵逐漸淡齣消失齣現一行字：這世界沒有本質，隻存在錶象，隻有不同的角度與層次……最後飄齣結束語：幾年後他/她走上瞭人生巔峰，迎娶白富美，下嫁高富帥！哈哈！說正經的，這本書的方嚮可以觀望觀望，畢竟太年輕。但把同倫作為類型的語義從而對數學提齣新的理解，這種想法卻起源較早。而數學機械化的思想甚至可以稱之為古老。
评分一年內各路作者齊貢獻 各章不太統一 但繞不開啊【believe it or not there is a textbook about hott...【最後幾章讀不動瞭姑且就標個讀過吧。。。
评分一年內各路作者齊貢獻 各章不太統一 但繞不開啊【believe it or not there is a textbook about hott...【最後幾章讀不動瞭姑且就標個讀過吧。。。
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