Mathemagics is the second opening theme song of the Owarimonogatari anime series and the theme song of the Sodachi Riddle story arc. It was performed by Marina Inoue, who voiced Sodachi Oikura.
Background
The opening sequence used for the song involves images of Sodachi Oikura and Koyomi Araragi rendered through mirrored and kaleidoscopic views. The sequence also involves geometric shapes and optical illusions like tesseracts and toruses.
Lyrics
The original lyrics of the song is written in a cipher that substitutes most of the romanized Japanese lyrics into a two-digit number (from 01 for A to 26 for Z). The equal sign found in the song translates to "is" (は, wa) and "that is" (それは, sore wa), carrying the function of indicators in the mathematical and grammatical sense respectively. Meanwhile the "unpaired 1s" found in the song (underlined in the lyrics below) translates to the kanji for "one", creating the Japanese words "ichido" (一度) and "hitorikiri" (一人きり).
Numerical Cipher
2621202015 230111012020052001
111520150201 = 211915020111011809
11011420011414092301192118051821 06212001190809110104050109130109140113151415
1908091410092019211315140510090621190520051121
13010815211409140907051115140405
200109251521131511090520011401201921
11809110918090405 230120011908090701
13090308090209110904011908092001 1115200105
=
110913090401202001
1309201921110520011415
04011805251518091315 2001040119080909080126211415 11152001052315
1109200109190809200102211404011105
2301180911091805140111211401202005
0215112118011409 012005080113011821 11152119080911092315190107011908092005092001
110913090701 140505 2301180109110111051821040111050405 131521
21180519080911212005
200109251521131511090520011401201921
11809110918090405 230120011908090701
13090308090209110904011908092001 1115200105
=
110913090401202001
1309201921110520011415
04011805251518091315 2001040119080909080126211415 11152001052315
10090221140405 030801142015 130103080907012301140101092015
09201921130104050401202005 230111011801140111212005
2001202001 080920152019211415211915040525151101202001
1109130914152119151409 151908092001151901180520011101202001
130108152107012015110518211301051409
131521 1041504011105 23011801202005
200109251521131511090520011401201921
11809110918090405 230120011908090701
13090308090209110904011908092001 1115200105
=
110913090401202001
1309201921110520011415
1309201921110520012015
1513152020011415
04011805251518091315 2001040119080909080126211415 11152001052315
Romaji Lyrics
Zutto wakatteta
Kotoba wa usobakari
Kantan ni wasureru futashika de aimai na mono
Shinjitsu mo neji fuseteku
Mahou ni nigekonde
Taiyou mo kieta natsu
Hitorikiri de watashi ga
Michibiki dashita kotae
Sore wa
Kimi datta
Mitsuketa no
Dare yori mo tadashii hazu no kotae wo
Kitaishi tabun dake
Warikirenakunatte
Bokura ni ate wa maru koushiki wo sagashiteita
Kimi ga nee warai kakeru dakede mou
Ureshikute
Taiyou mo kieta natsu
Hitorikiri de watashi ga
Michibiki dashita kotae
Sore wa
Kimi datta
Mitsuketa no
Dare yori mo tadashii hazu no kotae wo
Jibun de chanto machigawa na ai to
Itsumade datte wakaranakute
Tatta hitotsu no uso de yokatta
Kimi no uso ni o shita osaretakatta
Mahou ga tokeru mae ni
Mou ichido dake waratte
Taiyou mo kieta natsu
Hitorikiri de watashi ga
Michibiki dashita kotae
Sore wa
Kimi datta
Mitsuketa no
Mitsuketa to
Omotta no
Dare yori mo tadashii hazu no kotae wo