Warning: Undefined array key "preload-paths:/list-by-author/Rachel Thomas " in Drupal\Core\Cache\DatabaseBackend->getMultiple() (line 155 of core/lib/Drupal/Core/Cache/DatabaseBackend.php).

Drupal\Core\Cache\DatabaseBackend->getMultiple(Array, ) (Line: 126)
Drupal\Core\Cache\DatabaseBackend->get('preload-paths:/list-by-author/Rachel Thomas') (Line: 224)
Drupal\path_alias\AliasManager->getAliasByPath('/node/5589', 'und') (Line: 47)
Drupal\path_alias\PathProcessor\AliasPathProcessor->processOutbound('/node/5589', Array, Object, Object) (Line: 108)
Drupal\Core\PathProcessor\PathProcessorManager->processOutbound('/node/5589', Array, Object, Object) (Line: 403)
Drupal\Core\Routing\UrlGenerator->processPath('/node/5589', Array, Object) (Line: 305)
Drupal\Core\Routing\UrlGenerator->generateFromRoute('entity.node.canonical', Array, Array, 1) (Line: 108)
Drupal\Core\Render\MetadataBubblingUrlGenerator->generateFromRoute('entity.node.canonical', Array, Array, 1) (Line: 765)
Drupal\Core\Url->toString(1) (Line: 183)
Drupal\Core\Utility\LinkGenerator->generate(Object, Object) (Line: 102)
Drupal\Core\Render\Element\Link::preRenderLink(Array)
call_user_func_array(Array, Array) (Line: 113)
Drupal\Core\Render\Renderer->doTrustedCallback(Array, Array, 'Render #pre_render callbacks must be methods of a class that implements \Drupal\Core\Security\TrustedCallbackInterface or be an anonymous function. The callback was %s. See https://www.drupal.org/node/2966725', 'exception', 'Drupal\Core\Render\Element\RenderCallbackInterface') (Line: 870)
Drupal\Core\Render\Renderer->doCallback('#pre_render', Array, Array) (Line: 432)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 248)
Drupal\Core\Render\Renderer->render(Array) (Line: 974)
Drupal\views\Plugin\views\field\EntityField->render_item(0, Array) (Line: 1214)
Drupal\views\Plugin\views\field\FieldPluginBase->advancedRender(Object) (Line: 238)
template_preprocess_views_view_field(Array, 'views_view_field', Array)
call_user_func_array('template_preprocess_views_view_field', Array) (Line: 261)
Drupal\Core\Theme\ThemeManager->render('views_view_field', Array) (Line: 491)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 248)
Drupal\Core\Render\Renderer->render(Array) (Line: 1796)
Drupal\views\Plugin\views\field\FieldPluginBase->theme(Object) (Line: 767)
Drupal\views\Plugin\views\style\StylePluginBase->elementPreRenderRow(Array)
call_user_func_array(Array, Array) (Line: 113)
Drupal\Core\Render\Renderer->doTrustedCallback(Array, Array, 'Render #pre_render callbacks must be methods of a class that implements \Drupal\Core\Security\TrustedCallbackInterface or be an anonymous function. The callback was %s. See https://www.drupal.org/node/2966725', 'exception', 'Drupal\Core\Render\Element\RenderCallbackInterface') (Line: 870)
Drupal\Core\Render\Renderer->doCallback('#pre_render', Array, Array) (Line: 432)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 248)
Drupal\Core\Render\Renderer->render(Array) (Line: 706)
Drupal\views\Plugin\views\style\StylePluginBase->renderFields(Array) (Line: 572)
Drupal\views\Plugin\views\style\StylePluginBase->renderGrouping(Array, Array, 1) (Line: 463)
Drupal\views\Plugin\views\style\StylePluginBase->render() (Line: 2177)
Drupal\views\Plugin\views\display\DisplayPluginBase->render() (Line: 1592)
Drupal\views\ViewExecutable->render() (Line: 201)
Drupal\views\Plugin\views\display\Page->execute() (Line: 1689)
Drupal\views\ViewExecutable->executeDisplay('page_1', Array) (Line: 81)
Drupal\views\Element\View::preRenderViewElement(Array)
call_user_func_array(Array, Array) (Line: 113)
Drupal\Core\Render\Renderer->doTrustedCallback(Array, Array, 'Render #pre_render callbacks must be methods of a class that implements \Drupal\Core\Security\TrustedCallbackInterface or be an anonymous function. The callback was %s. See https://www.drupal.org/node/2966725', 'exception', 'Drupal\Core\Render\Element\RenderCallbackInterface') (Line: 870)
Drupal\Core\Render\Renderer->doCallback('#pre_render', Array, Array) (Line: 432)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 248)
Drupal\Core\Render\Renderer->render(Array, ) (Line: 238)
Drupal\Core\Render\MainContent\HtmlRenderer->Drupal\Core\Render\MainContent\{closure}() (Line: 638)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 239)
Drupal\Core\Render\MainContent\HtmlRenderer->prepare(Array, Object, Object) (Line: 128)
Drupal\Core\Render\MainContent\HtmlRenderer->renderResponse(Array, Object, Object) (Line: 90)
Drupal\Core\EventSubscriber\MainContentViewSubscriber->onViewRenderArray(Object, 'kernel.view', Object)
call_user_func(Array, Object, 'kernel.view', Object) (Line: 111)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.view') (Line: 186)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 76)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 53)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 28)
Drupal\Core\StackMiddleware\ContentLength->handle(Object, 1, 1) (Line: 32)
Drupal\big_pipe\StackMiddleware\ContentLength->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 36)
Drupal\Core\StackMiddleware\AjaxPageState->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\StackedHttpKernel->handle(Object, 1, 1) (Line: 741)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

List by Author: Rachel Thomas

Proof of the Kochen-Specker Theorem

In this appendix we give a gist of the proof of the Kochen-Specker Theorem.

The only way is up: constructing the Heron Tower

Looking out to Canary Wharf, to the arch at Wembley Stadium, and down onto the Gherkin, the 700 people working on the construction site of the Heron Tower in London had one of the best views in London. Plus was lucky enough to speak to two engineers involved in building the tower and asked how maths was involved in the construction of such an impressive addition to the London skyline.

How the velodrome found its form

The Velodrome, with its striking curved shape, was the first venue to be completed in the London Olympic Park. Plus talks to structural engineers Andrew Weir and Pete Winslow from Expedition Engineering, who were part of the design team for the Velodrome, about how mathematics helped create its iconic shape.

Biology's next microscope, mathematics' next physics

It is thought that the next great advances in biology and medicine will be discovered with mathematics. As biology stands on the brink of becoming a theoretical science, Thomas Fink asks if there is more to this collaboration than maths acting as biology's newest microscope. Will theoretical biology lead to new and exciting maths, just as theoretical physics did in the last two centuries? And is there a mathematically elegant story behind life?

A new phase in mathematics - the work of Stanislav Smirnov

The work of Fields Medallist Stanislav Smirnov will take mathematics and physics into a new phase with his mathematical proof of the understanding of phase transitions.

Lambda marks the spot — the biggest problem in theoretical physics

The mathematical maps in theoretical physics have been highly successful in guiding our understanding of the universe at the largest and smallest scales. Linking these two scales together is one of the golden goals of theoretical physics. But, at the very edges of our understanding of these fields, one of the most controversial areas of physics lies where these maps merge: the cosmological constant problem.

It's all in the detail

The computer animation used in movies and games is now so lifelike, it is very hard to believe that you are actually watching a surface built from simple shapes of triangles. Phil Dench tells Plus how he uses mathematics to help bring these models to life.

A disappearing number

Mathematics takes to the stage with A disappearing number, a work by Complicite, inspired by the mathematical collaboration of Hardy and Ramanujan. Rachel Thomas went to see the play, and explains some of the maths. You can also read her interview with Victoria Gould about how the show was created.

A new kind of singing star

The Sun is no longer singing solo and is now part of a stellar choir

Swimming in mathematics

The mathematics of foam coats Olympic swimming venue

Now you see it, now you don't

Mathematicians may make the "invisibility cloak" more powerful

Through the looking-glass

Some molecules - thalidomide, for example - come in both left and right handed versions, while others are indistinguishable from their reflections. Plus finds out about the role of mathematical symmetry in chemistry.

Error message

List by Author: Rachel Thomas