different answer<\/a>. <\/p>\nWhat should we make of AI models that can outperform high school-age Olympiad competitors but cannot always add or subtract to primary school level? To understand this, it\u2019s helpful to think about what it means to be good at maths.<\/p>\n
The way maths is taught is by showing students a problem, demonstrating the method required to solve it and then assigning examples. Weaker students require numerous examples and sometimes end up simply memorising the method without understanding it. The strongest students need only one or two examples to master the concept and apply it to new problems.<\/p>\n
The ability to conceptualise and generalise distinguishes the best mathematicians. Good mathematicians solve hard problems; great ones find ways to make the hard problems easy.<\/p>\n
The strengths of AI models lie in their speed and ability to \u201cpractice\u201d at extremely high volumes. This means they can solve very difficult problems that bear some resemblance to things they have been shown before but may struggle when given something new. This is particularly a problem for theoretical maths. The number of examples available for training drops as you move towards more advanced problems.<\/p>\n
These are well-known issues with neural networks. They are great at interpolation (generating answers that are \u201cbetween\u201d things they\u2019ve seen before) and bad at extrapolation (generating answers that fall outside their training set).<\/p>\n
In maths, this is made extra difficult by problems that sound similar. Consider: \u201cWhat is the maximum number of cubes of volume 1 that you can fit in a cube of volume 64?\u201d and \u201cWhat is the maximum number of spheres of volume 1 that you can fit in a sphere of volume 64?\u201d. They sound alike but one is simple to solve (cubes fit together neatly in a 4x4x4 block), while the other is fiendish (spheres do not stack nicely).<\/p>\n
What this means is that AI use in applied mathematics and cosmology is still limited. We can take things we already know how to do and use AI to automate them. But so far, calculation has seen little advancement. <\/p>\n
It is possible, however, that more training will solve the problem without extrapolation ever being required. If AI models can be fed enough complex calculations they could perhaps solve problems that have so far eluded us without the need for any human-level inspiration.<\/p>\n
The question being asked in my field is: \u201cHow powerful is an extremely fast, extremely well-trained, unthinking mathematician?\u201d We are in the process of finding out. <\/p>\n","protected":false},"excerpt":{"rendered":"Stay informed with free updates Simply sign up to the Artificial intelligence myFT Digest — delivered directly to…\n","protected":false},"author":2,"featured_media":61652,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[554,733,4308,86,56,54,55],"class_list":["post-61651","post","type-post","status-publish","format-standard","has-post-thumbnail","category-artificial-intelligence","tag-ai","tag-artificial-intelligence","tag-artificialintelligence","tag-technology","tag-uk","tag-united-kingdom","tag-unitedkingdom"],"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/posts\/61651","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/comments?post=61651"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/posts\/61651\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/media\/61652"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/media?parent=61651"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/categories?post=61651"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/tags?post=61651"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}