Mathematical Calendar SUN MON TUE WED THU FRI SAT

rep- 29 30 31 1 2 2333 is 3 4 How many the smallest tiles On-line Paper twin primes prime having • Submission Open p and p +2? only three 3s. x lim ! 8

5 6 7 | 8 9 10 11 x 10999999999 is 1

pandigital 8 the smallest | On-line expression = prime having 11 +22 +33 + + 2 • 1 ··· sec (arctan 2) Registration Open 98532 14076 only nine 9s. 99 +1010 is prime. p37 + 41 + 43 ÷ 1 r1 = 12+14 Proclamation r = 1 12 • 13 2 32+14 14 15 16 17 18 Ceremony 1 r3 = 52+14 of the year 2014 . Notiﬁcation of csc 18 . • Every fullerene Cn 6 NANUM 2014 as the Korean 1 1 2 has exactly 12 . 2 2 2 22 Acceptance =goldenratio Mathematical Year ✓ ◆ 2 19 20 21 22 23 24 25 23 11111 ...11111 is 6 the third 24! 19 181716 ...321 3 smallest # of squares p152 +162 repunitz }| prime.{ Avogadro’s # Ramsey # R(4, 5) | ✓ ◆ ⇡ ⇡ 26 27 28 29 30 31 1

26: not palindromic e⇡ log 3 4 262:palindromic 1! + 2! + 4! Coxeter’s graph 5e(⇡ 1) 2 3 5 ⇡ log 2 5 ⇡ ⇥ ⇥ 2 3 4 2014.1. © SEOUL ICM 2014 Organizing Commitee All rights reserved. SUN MON TUE WED THU FRI SAT 26 27 28 29 30 31 1

i4 rep- 2 3 4 5 6 7 8 tiles ? 888888883 is 3 the smallest 4 - 2014 Period 3 The year 2014 is heptagon-shaped prime having implies chaos. not a leap year. 4 4+(4+4) 4 50 pence coin only eight 8s. ÷ 1 1 9 10 = 11 12 13 14 15 F11 89 cos 15 =0.01123595 p p ··· 4 = 6+ 2 1 F 4 2 1 k 2 2 3 13 + 1 odd # of faces, each face = k+1 10 1 ⇥ ⇥···⇥ 2 2 p3 has the same # of edges k=0 3 =59 509 1+⇡ + ⇡ X ⇥ ⇡ 16 17 18 19 20 21 22 19 The largest order of 1922222 ...2222219 icosian 2 3 8e 4 3 2 1 Etorsion(Q) p133 +143 4⇡ +2e is prime. game ⇡ e 1 +2 +3 +4 ⇡ ⇡ z }| {

23 24 25 Every 26 27 28 1 1! prime has one of Deadline for +2!+2! speciﬁc 26 primes • Abstract +3!+3!+3! 33 22 +11 30e 18⇡ as a substring. 27! + 1 is prime. Submission ⇡ 2 3 4 2014.2. © SEOUL ICM 2014 Organizing Commitee All rights reserved. SUN MON TUE WED THU FRI SAT 23 24 25 26 27 28 1

e⇡i 2 3 4 5 6 7 8 There are The smallest only 5 Platonic the smallet 3 prime number. ⇡ log 55 polyhedra. perfect number M3 =2 1 4+4+4 4 b c ⇡ 9 10 11 12 13 14 15 1 2 12 TWO + eleven 3 15 1! + 2! + 3! 10102 p121 = p1331 =TWelve+One ⇡ 3.14 2 +15isprime. ⇡ 16 17 18 19 20 21 22 17000000000000071 6+1 3+19 is the 6th is a 17-digit 2 =5+17 ⇡ ✓ ◆ p10 3.16 palindromic prime. 335 XIX e ⇡ triangular number. =11+11 ⇡ ⇡ 23 24 25 26 27 28 29 3 1023 23 is 26 the largest divides =17576 29 and 2929 are both 28 exotic 29 and 2929 are both 3 9 23 digit prime. n(n + 1)(n + 2)(n + 3) p72 +242 =(1+7+5+7+6) prime. 7-spheres prime. 30 31 1

5 2014.3. 339 2 1 © SEOUL ICM 2014 Organizing Commitee All rights reserved. SUN MON TUE WED THU FRI SAT 30 31 1 2 3 4 5 p2 36 24 51 10 2 2 1+ + + ? 9 cos ✓ +sin ✓ ⇡ 60 602 603 e<3 <⇡ S5 is not solvable. 1/7=0.142857 ... Nine lemma: 6 5/7=0.7142857 ... 7 888 8 0 0 0 9 10 11 12 4/7=0.57142857 ... 88 0 A B C 0 2 8 ⇡ 6/7=0.857142857 ... 0 A0 B0 C0 0 Notiﬁcation of 8 •

1 2/7=0.2857142857 ... +8 0 A00 B00 C00 0 Abstract 1 1000 eleven n=1 n2 3/7=0.42857142857 ... 0 0 0 Acceptance =eleven 12 pentominoes P 13 14 15 16 17 18 19 tan 15 =2 p3 13 13 2 1 #oftreeson minimal # of hints 13 1...13, 13...3 14-faced dice 2 p3 4labeledvertices for sudoku puzzle 3 (3 + 3) 4! 3! + 2! 1! | ⇥ z}|{ z}|{20 21 22 23 24 25 26 45 1 36 4/25 39 24 + 4 2 4 ⇥2 1+2+3+4+5+6 ⇡ p⇡ 1+2 3 4 =2 +4 2223 ⇥ ⇥

27 284 28 29 30 1 2 3 =614656 4 Fibonacci number x3 + px + q 6+1+4 = F29 =514229is ; = 4p3 27q2 +6 + 5 + 6 aprimeendingin29. 12 +22 +32 +42 ✓ ◆ 4 5 6 2014.4. © SEOUL ICM 2014 Organizing Commitee All rights reserved. SUN MON TUE WED THU FRI SAT 27 28 29 30 1 2 3

ex 1 lim x 0 x (Sn : An) Napoleon ! 4

4 5 5 6 7 8 9 10 =012 +021 Deadline for 2 0 • a+bi+cj+dk H +10 +12 Early Advanced 2 1 0 1 Quaternion +20 +21 p1+2+ +8 Fano plane ﬁgure 8 knot 32 Registration ··· 11 12 13 14 15 16 17

2 4 2 2 12 +112 +1112 dodecahedron How many s? @n : '(n)=14 11112 2 =4 F2 =2 +1 4 18 19 20 21 22 23 24 5 = 1 23 133 the✓ smallest◆ quadratic 21 2 ⇡ e2 7e (1 2+3) 4 2 21 is prime. 22 +22 +2 nonresidue modulo 23 4+4+4 4 ⇡ ⇥ ⇥ ⇥ 4 9 5 20 27 8 11 ⇡(100) = 93 93 93 26 21 25 26 27 5 28 29 13 3023 31 pandigital 10 pandigital 28 0 15 18 93 22 93 93 ⇡(25) = 9 expression x 24 expression =17210368 17 16 2 5 6 ú 14 12 1+7+2+1 93 29 65 948 170 93 93 856 = á 3 93 +0 + 3 + 6 + 8 25 19 1 ⇡(9) = 4 5⇡(e 1) ⇡ ⇡ + e 28 7 10 ⇥ 237 ⇡ ✓ ◆ 30 24 ⇥ 107 1 2 3 2014.5. © SEOUL ICM 2014 Organizing Commitee All rights reserved. SUN MON TUE WED THU FRI SAT

7.0000000857 rep- ··· 1 223 is 2 3 4 5 6 22 27 7 tiles 16 23 1 e the smallest ⇡ e 1 prime having 1+1+5 30 dx log5 2 3 1 x only two 2s. nontrivial knot ⇡ +5 +5 hexahedron Ed Pegg Jr.’s Z ✓ ◆ 4 8 9 10 11 12 13 14 pandigital 2+3+5+7+11 2n 12th Fibonacci expression +13+17+19+23 the same areas 1nano=10 9 s 11 100 ...001 number is 122. 103428 7956 12 +22 +32 | ÷ z }| { 15 16 pandigital 17 18 19 20 pandigital 21

expression 20 expression

⇥ 68 735 20 + 1111 1111 56 897

13 7 ··· 15 10 05 10 ⇥ 294 2 3+2! 3! magic hexagon is prime. 23 ⇥ 104 | ··· ⇥ ⇥ z }| { 2 6 7 22 23 24 25 11 26 27 28 28! + 1 5 10 is 2 3 8 magic 28 + 1 227 24! is 5 9 a28+1digits 12 1 sum p3 173 +183 ⇡ ⇡2 24 digits long. 1st Friedman # 4 33 prime. ⇡ 29 30 1 2 3 4 5

29 30 1 2 3 4 p:prime 5 det A3 #ofregular p2 p 2n 2n 2n 2 10 p5 1 2 + 3 tesselations =det 12 1 ) | p 1 2n ✓ ◆ ✓ ◆ 4 4+4 4 + 2n 1 of the plane " 0 12# ÷ ··· 6 7 8 9 10 11 12 9 Deadline for • 111111111 9 Advanced #of 4 5 ÷ 3 3 3 log(⇡ + ⇡ ) 1112 1Byte=8bits =12345679 Registration nets for a cube p9 +10 ⇡ z }| { ⇡ 13 14 15 16 17 18 19

19 19 1+2+3+ +12+13 15 There are 17 plane 2+3+13 ··· =12 +22 +32 + +62 p72 +82 +92 largest equilateral 16! = 14!5!2! symmetry groups. =2+5+11 19 1...19, 19...9 ··· ⇡ 4 | 20 21 22 23 24 25 z}|{ z}|{26 23

211111 ...111113 ⇤24 2 2 2 XX 12 112 1112 22/7 ⇡ is prime. Leech lattice 1+2 3 4 p14 +15 +16 ⇥ ⇥ ⇡ z }| { ⇥ ⇥ ⇡ 27 28 29 30 31 1 2

10000 days p3 2 cos 30 = 27 years (1 + 2 3) 4 329 229 is prime. 2 312 325 = 31 325 ⇡ ⇥ ⇥ ⇥ g 3 4 5 2014.7. © SEOUL ICM 2014 Organizing Commitee All rights reserved. SUN MON TUE WED THU FRI SAT 27 28 29 30 31 1 2

0! V E + F

3 44449 is 4 5 6 7 8 21 12 9 the smallest =32 23 prime having #oftetrominoes = ... (4 + 4 + 4) 4 only four 4s. pentagon in TETRIS ⇡1(8) = Z Z =98 89 ÷ ⇤ Opening Ceremony • Laudation for 10 11 12 • 13 14 15 16 Prize Winners Fields Medalist Nevanlina Prize • MENAO • Lecture 1 Fields Medalist Fields Medalist • Lecture • • Welcome Public Lecture Emmy Noether Lecture 2 Lecture 3 • • • IMU GA 1st day IMU GA 2nd day Reception (James Simons) Lecture Abel Lecture Conference Dinner • • • • 17 18 19 20 21 22 23 Math Education Special 2nd • • Day Math Invited Lecture Smith number • Fields Medalist Math History Day Popularization Day (Yitang Zhang) 22 = 2 11 • • ⇥ Excursion Day Lecture 4 Gauss Prize Lecture Chern Prize Lecture Closing Ceremony 2+2=2+(1+1) ⇡23 437 • • • • ⇡

24 25 26 27 28 29 20 30

pandigital ? 256 and 625 are both 26 2 expression = 50 60 1day=24hours squares. 65 5 7p2+6p3+3p5 129780 4635 p202 +212 ⇡ ÷

31 1 2

31 2 1 2 3 4 5 6 a (a b)(a c) b2 triangular 1 2+3 4+ + ·

(b a)(b c) p2 · 4

2 p2 · number: 1 ··· 5 = c p2 = nine + (c a)(c b) p2 1, 3, 6, 10, 15,... 4 4 4 4 4 4 2 +2 +3 +4 +4

THREE 7 8 9 10 THREE 11 12 13 The smallest TWO composite TWO doubly true Fibonacci 6weeks +ONEalphametic 1year 78910111213 ELEVEN p22 +32 +62 number Pappus conﬁguration =10!seconds =12months is prime. 14 15 16 17 18 19 20

16 1 19 1 God’s # = ⇡46 = 9tan1 1 +2+3+4+5 64 4 23 +32 p1! + 2! + +46! 95 5 for Rubik’s cube ⇡ ···

21 22 23 24 pandigital 25 26 pandigital 27 expression expression square p, q:primes> 3 68 975 cube 102546 3798 e 2 2 ÷ 1+(2+3) 4 ⇡ 23! is pandigital. = 24 p q 13 ⇥ 204 =175203 6489 ⇥ b c ) | ÷ 28 29 30 1 2 3 4

4 2k The second k perfect number k=0 3 X ✓ ◆ 3 +3 5 6 7 2014.9. © SEOUL ICM 2014 Organizing Commitee All rights reserved. SUN MON TUE WED THU FRI SAT 28 29 30 1 2 3 4 1 1 1 1 + + + 1 2 4 8 1 1 + + + 20 0.999999 16 32 ··· F0 =2 +1 tetrahedron ··· 5 6 7 8 9 10 11 #of 10000000019 is the smallest topologies 1 1+2+3 3 4 1+0+ +0+1+9 2 2 2 ··· K5 is not planar. =1 2 3 p3 +4 +5 Quaternion group Q8 on 1, 2, 3 2 ⇥ digits prime. ⇥ ⇥ ⇡ { } ✓ ◆ 12 13 14 15 16 17 18 sin 15 p6 p2 = pandigital 4 2 1 (13 1)! + 1 0 minimal triangulation expression 17-gon is 1818 2 ⌘ 1ft= 12in (mod 13 ) of a torus 2 p3 150768 9423 constructible. Ahalfof18is10. ÷ 18 19 20 21 22 22 23 24 25 two twos 1818 22 two twos 23 Every divisor 1 22 5 4 3 . =0 +1 +2 is prime . 2 1 0 n ‡’ Metonic cycle 37 cos 1 101012 . +3 +4 +5 except 1 & 2. 25 = 25 ⇡ ··· 26 27 28 29 30 311818 1 pandigital expression 1 n3 29 29 174690 5823 Ahalfof18is10. n 2 ÷ 2 3 n=1 338 446 29 2...29, 29...9 =174960 5832 2 +3 X | ÷ 2 3 4 z}|{ z}|{ 18

108 8 108+8 8 num 8 and 8 are 2+ 2+p2+ 1+2 1+3 1+4p coth log 2 sinh(log2) tangram both prime. ··· r ··· = ⇤+⇤+⇤+⇤ 3! q q p ⇣ ⌘ p 9 10 11 p 12 13 14 15 pandigital 1 2 4 Marion’s theorem: 7+8+9+ · is the 11 + 1.1 expression ··· 4+1 4 coth log cosh(log 2) 1 +18 + 19 ✓ ◆ 10 area =11 1.1 107352 8946 s 4th Catalan number. ⇣ ⌘ ⇥ ÷ p 16 17 18 19 20 21 22

2 1+2+3+ +19 Mayan base-20 19 ··· 4 4 ( 1+2+3) 4 p92⇡ 18 10 08 10 numeral system 1114 ⇡ ⇡ 3 ⇥ ⇡ | ··· 23 24 25 26 27 28 29

d c 30 1 2 a 3 4 5 6 b 0 ⇡ ⇡ 4 4 4 4 4 The identity sin xdx 3(a + b + c + d ) 95 2 2 2 2 2 =5 of multiplication 0 =(a + b + c + d ) 2+2=2 2 19 2 Z ⇥ ✓ ◆

77767777 is 7 8 9 10 11 12 13 the smallest 123456789 prime having 88 is (2, 4, 5, 7, 8) ⇡32 12th prime is 37. 78910111213 ⇥ coth log 2tanh(log2) only seven 7s. 8digitslong. are pandigital. ⇡ e23 21st prime is 73. is prime. ⇣ ⌘ 14 15 16 17 p 18 19 20 4 9 2 19 3 5 7 11111 ...11111 is

8 1 6 EIGHTEEN the second 6 20 1are =EIGHTEEN z }| { ⇥ ± 10p2 magic sum = 15 1lb= 16oz 34 43 repunit prime. both composite. ⌅ ⇧ circumference ⇡ 21 22 23 24 25 26 27 10 #of 22! is sporadic 2 highly composite Cubic surfaces 22 digits long. 10 log 10 number 1+3+5+7+9 simple groups contain 27 lines. ⇡ 28 29 30 31 1 2 3