The generally very interesting blog called Languages of the World wrote the following about Burushaski: “Burushaski’s claim to fame is its isolate status. Put simply, it is not related to any other human language on the planet.”
Although one often encounters similar definitions of language isolates, it is a misleading simplification. A language isolate is a language that has not been proven to be related to any other human language on the planet.
In other words, before historical linguists started their work, all languages were technically speaking language isolates, and they have then slowly been demonstrated to be related to other languages. In some cases it was really hard – for instance, it was allegedly very difficult to show that Albanian was Indo-European because there are so many loanwords in that language.
In the case of Burushaski, some people believe it is related to the North Caucasian languages. This hasn’t been proven in a convincing way so far, but that could change at any time, and if it happened, Burushaski would immediately lose its isolate status, just as happened to Ket.