A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_URI::$config is deprecated
Filename: core/URI.php
Line Number: 101
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Router::$uri is deprecated
Filename: core/Router.php
Line Number: 127
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$benchmark is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$hooks is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$config is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$log is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$utf8 is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$uri is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$exceptions is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$router is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$output is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$security is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$input is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$lang is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$load is deprecated
Filename: core/Controller.php
Line Number: 78
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Cache::$apc is deprecated
Filename: libraries/Driver.php
Line Number: 188
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Cache::$file is deprecated
Filename: libraries/Driver.php
Line Number: 188
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$cache is deprecated
Filename: core/Loader.php
Line Number: 1279
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$cacher is deprecated
Filename: core/Loader.php
Line Number: 1279
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$jscript is deprecated
Filename: core/Loader.php
Line Number: 1279
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Return type of CI_Session_files_driver::open($save_path, $name) should either be compatible with SessionHandlerInterface::open(string $path, string $name): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice
Filename: drivers/Session_files_driver.php
Line Number: 132
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Return type of CI_Session_files_driver::close() should either be compatible with SessionHandlerInterface::close(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice
Filename: drivers/Session_files_driver.php
Line Number: 290
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Return type of CI_Session_files_driver::read($session_id) should either be compatible with SessionHandlerInterface::read(string $id): string|false, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice
Filename: drivers/Session_files_driver.php
Line Number: 164
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Return type of CI_Session_files_driver::write($session_id, $session_data) should either be compatible with SessionHandlerInterface::write(string $id, string $data): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice
Filename: drivers/Session_files_driver.php
Line Number: 233
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Return type of CI_Session_files_driver::destroy($session_id) should either be compatible with SessionHandlerInterface::destroy(string $id): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice
Filename: drivers/Session_files_driver.php
Line Number: 313
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Return type of CI_Session_files_driver::gc($maxlifetime) should either be compatible with SessionHandlerInterface::gc(int $max_lifetime): int|false, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice
Filename: drivers/Session_files_driver.php
Line Number: 354
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 284
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: session_set_cookie_params(): Session cookie parameters cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 291
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 306
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 316
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 317
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 318
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 319
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 377
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: drivers/Session_files_driver.php
Line Number: 108
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: session_set_save_handler(): Session save handler cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 110
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: session_start(): Session cannot be started after headers have already been sent
Filename: Session/Session.php
Line Number: 143
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$session is deprecated
Filename: core/Loader.php
Line Number: 1279
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$agent is deprecated
Filename: core/Loader.php
Line Number: 1279
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$contentsStatus is deprecated
Filename: libraries/Common.php
Line Number: 64
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$articleStatus is deprecated
Filename: libraries/Common.php
Line Number: 71
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$db is deprecated
Filename: core/Loader.php
Line Number: 390
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_DB_mysqli_driver::$failover is deprecated
Filename: database/DB_driver.php
Line Number: 371
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents_model::$best_cnt is deprecated
Filename: ver3/Contents_model.php
Line Number: 17
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents_model::$popular_cnt is deprecated
Filename: ver3/Contents_model.php
Line Number: 18
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$member_model is deprecated
Filename: core/Loader.php
Line Number: 353
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$contents_model is deprecated
Filename: core/Loader.php
Line Number: 353
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$menuList is deprecated
Filename: libraries/Common.php
Line Number: 561
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$common is deprecated
Filename: core/Loader.php
Line Number: 1279
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$dto is deprecated
Filename: core/Loader.php
Line Number: 1279
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$together_end_date is deprecated
Filename: ver3/Contents.php
Line Number: 17
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Cache::$dummy is deprecated
Filename: libraries/Driver.php
Line Number: 188
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$benchmark is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$hooks is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$config is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$log is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$utf8 is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$uri is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
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수학동아 - 폴리매스
단원 별 수행평가
실생활에서 수학이 어떻게 활용되는지 확인해 보세요!
[수학자] 수학자들의 선생님 히로나카 헤이스케
수학동아 2021.03.31 22:28
조회 1021
“선생님! 수첩 떨어트리셨어요!”
길을 가던 대학원생이 수첩을 떨어뜨리자 한 소녀가 수첩을 주워 건네며 말했습니다. 좋은 성과를 내지 못해 의기소침해 있던 그 대학원생은 소녀의 ‘선생님’이라는 한마디가 머릿속에서 떠나지 않았습니다. 선생님이라는 명칭에 걸맞는 사람이 되기 위해 반드시 자신만의 이론을 만들어야겠다고 결심했죠. 그리고 훗날 교수가 돼 학생은 물론 수학자들을 가르치는 수학계 최고의 선생님으로 그의 이름 ‘히로나카 헤이스케’를 널리 알립니다.
1931년 4월 9일 일본 야마구치현에서 태어난 히로나카는 일본 교토대학교에서 수학을 공부했습니다. 이 시기 연구에 슬럼프를 겪던 히로나카가 소녀를 만난 것입니다. 소녀를 만나고 마음을 다잡은 뒤, 히로나카는 미국 하버드대학교로 유학길에 올라 박사학위를 취득했습니다. 또 미국 브랜다이스대학교 수학과 조교수가 됐죠. 그리고 1964년 대수기하학의 난제인 ‘특이점 해소 정리’를 완벽하게 증명하고 그 내용을 세계 최고 권위의 수학 학술지인 ‘수학연보’에 발표했습니다. 1970년에는 그 공로를 인정받아 수학계의 노벨상이라 불리는 필즈상을 수상했죠.
대수기하학에서 특이점이란 좌표명면에 그린 함수의 그래프에서 선이 뾰족하거나 선끼리 겹칠 때 생기는 매끄럽지 않은 점을 말합니다. 하지만 특이점 해소 정리를 이용하면 공간의 차원을 한 단계 높여서 특이점을 없앨수 있죠.
대학자가 된 히로나카는 2008년 3월 서울대학교 수리과학부 석좌교수로 초빙돼 수학을 가르쳤습니다. 그때 강의를 들은 사람들 중 한 사람이 바로 허준이 미국 스탠퍼드대학교 수학과 교수입니다. 허 교수는 여러 수학 난제를 증명하며 한국인 최초로 필즈상을 받을 수 있을 거라 점쳐지는 수학자입니다. 그런 허 교수가 수학에 뜻을 품게 된 계기가 바로 히로나카의강의라고 합니다. 히로나카는 훌륭한 제자를 길러낸 위대한 선생님이기도 한 것이죠.
히로나카는 “나를 선생님이라 불렀던 소녀 덕분에 수학자가 될 수 있었다”고 1992년 발행한 자서전 ‘학문의 즐거움’에서 밝혔습니다. 히로나카에게는 그 소녀가 선생님이었던 셈이죠. 위대한 수학자를 향한 첫걸음이 우연한 만남에서 시작됐다니 무척 인상적입니다. 그는 “수학을 연구할 때는 시간이 얼마나 걸리든지 끝까지 해내는 것이 중요하다”고도 말했죠. 여러분은 어떤 마음으로 수학을 대하나요?
지금 바로
로그인 하면 내가 찜한 문제와 수행 평가를 한곳에서 볼 수 있어요!
