I think about this subject a lot. Three key innovations we'll see in the "next wave" of search engines that flood in to replace stinky incumbents (won't name any names here)
1. New user interfaces. My effort, Glorp, attempts to transition from the "link dump" style of results page to something akin to Instagram. Faster to scan, fewer surprises, more friendly for kids and old folks. AR/VR will have some unusual needs. Audio - Alexa and Siri. We need search (in different forms) everywhere. [1]
2. New business models. Privacy is in, advertising is out. That changes everything about the model. We'll see engines with tons of niche features, like link collections, recorded search journeys, curated subject matter experts, family accounts with parental controls, and, most importantly, monthly fees.
3. New search mechanisms: ML embeddings. Search by image similarity, video similarity, subject matter similarity. Machine learning models transform different types of content into convenient embedding vectors. BERT gives you a few hundred floats to represent the meaning of a sentence. ImageNet, the same, for images. Once you begin to build search tooling around the notion of document embeddings, rather than just "input text," we'll be able to help users discover things in a much broader set of scenarios. [2]
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[1] https://glorp.co/Search/search%20engine%20user%20interfaces
[2] https://glorp.co/Search/search%20engine%20vector%20embedding...