o E P S P H e r u l i a e n n b e v a s d l m e s t i e c e c y a i h o A n n i l a u f o D f m n t a m i g r i f a r i y e o i v s l s v u e , i n e t , I s o n d g P o : s ? s r f t @ i i n y t i u o c a e u t s e t . r o e f c d n o h u , r a N A n J The Institute Letter d g v 0 e a 8 o n 5 f 4 c a e 0 d d d S r t e Summer u s d s y . IAS N U P P e r o . i S r n n m . - c P P i e o t r t s o o # t n f a 4 i , t g 9 N O e J r P g A . I D R D H P P N F a P S J P D N A J Y R E S F M E T N P D J A S R J V o e u o e e t t c v a i a n v l a a d h n o o n i i i a e a i a a e e a a a c n a o t t m c e a d t t d i b b w c c l t o g r n n I e e p t n r r t d h n n o - m t h n a i i W i u u b e i i e m r r t i i h A H e a i c i L a a l a c c t a e s r l m e B a W l l h T r M R u o e G S r l s k i r o i e u n l t l a A t t r a a g d o l n d a r a a o t y y F o s D i s t M o a t Z B e a r i J e d r u s n S r n H a d C n l W d k D T . C L l i a E o m S n e S e l r a s d V r L r G d a o a I a l p C m L h . r g B i i a s . m i c i o a d s o a e j b n y f c a k s A e t i a e e k a o A P k r o e e c n a t n i i b o h l e r i n v e a i a e n d s b n h r o g v e i l - r d n e n i r y s l m r c n e r H l l e i o n r r S e r K e g e e e y o A i e l i a r d c P O r a n a t a o r r t r i a s o i O s i r m g o s B f k o t a , t n T e y f D e T d s T O i s r H o e E r c H t o T h r e S I The Art of Bridging n In this issue, Danielle Allen writes about the art of bridging as an essential tool for linking people who s P P P G C B M P R C F G N C C M H A I J C R V S P J B E R M M N D N come from different social spaces and as especially powerful for the diffusion of knowledge (page 4). r t e o e e e p h i r i e h a r a h o h o . o o e a a i l e a v e c i o a a f h e t t t l e n i n i R r r b b g c i v f i a n n r a a i e e e r e t r r r i r l e l n r n n n o m o i o h e provides a real-world example in the establishment of a school for Arab and e l Catherine Rottenberg e b r i r o i r r r o s i t c c r t e m s i d A r l r o i o e g l r l r d t r a d e y y p b W t S i y n G P R e e d m C i J i t n i n . i e r c a F W e a D D L . s l a . a c S B . A C o o A t P o . a u L l J h e Jewish children in Israel (page 5). Depicted above is a mathematical torus (a donut-shaped object that . a n r H L n W r t a K . e r . S B n . B f . l D h t . M W . n . e d V v W a H a M l L v i e P F J L a s G . T F H H o r L t i h m i g i r i t o . n a e a t g e a j n B i . e w n e cannot be deformed into a sphere in a continuous way without tearing it) made of logical symbols. r s a r e a e a r t i a k a h s D n r l r r n d n v G c i t o r n u j i l i i z s c b r b e g e q g s e i o f k c n i b r e i g y n e M v s S f r e l l t r n r i u u i r h e i o s h e l l s c o t y r It represents homotopy type theory, a new branch of mathematics that connects homotopy theory (the e c t s a t k a o e a s r o e a m w i h h y o o i s k a l o n l r n d e s B F l l c u t s s f i d n a a d z e s t k Lett r y study of continuous deformations) and type theory (a branch of mathematical logic). n Steve Awodey t n z n , s n a n d J n u r k . and Thierry Coquand explain how an international team of thirty-two researchers in computer science, m l i n logic, and mathematics worked at the Institute during the past year to develop this theory and the re- lated univalent foundations of mathematics, which can be used to verify the correctness of e individual mathematical proofs and facilitate the large-scale formalization of mathematics by allowing r mathematicians to build shared, searchable libraries of formalized definitions, theorems, and proofs (page 1). Andrej Bauer describes the socio-technological aspects of writing the Homotopy Type Theory E I P w ( w f E w P H W J D M S J T B M S M R R V C J L M R H D H w o n 6 a a a r e h i a a i r r r i a h o w a a e a a S w w w r d 0 a a a i i n i s m m m c book, six hundred pages by two dozen mathematicians in less than six months, which can be freely t i r i u e d l A n n c l v v l a r m e t a c n 9 r r r h w t p s l e w w w l i o h i s u i i c a a i d r i t i t e e e n ) t b t e s n h a d d r . E a i n i i t e l e . u e n l y v s s s l n n y y s 7 S i f t d m e r downloaded and contributed to as an open-source project on GitHub (page 7). Hanno Rein writes d e m i t F a a o . l a a w a m t M K h E n d o 3 v J H D e G o e .