Max_Daniel

As a fellow former mathematician, I share your sense that "mathematics as poetry" seems like the most likely outcome, at least for pure maths and barring more fundamental AI-driven changes to the human condition (e.g., extinction, or humans being replaced by very different kinds of minds).

Some of your discussion reminded me of Field Medalist Bill Thurston's 1994 note "On Proof and Progress in Mathematics":

1. What is it that mathematicians accomplish?

[...]

Rather, as a more explicit (and leading) form of the question, I prefer

How do mathematicians advance

... (read more)

[Thoughts on what to do if there is an ontological mismatch between one's thinking and a tool]

• When I saw Jacob present a version of the OP in person, the discussion focused on cases where the correct response is to use a different tool, ideally one that matches the natural ontology of ones thinking. E.g. when using a whiteboard rather than a Google doc to express thoughts most naturally expressed as a mind map.
• But I think it's important that there are other cases where it can actually beneficial to 'learn how to think in a different ontology

... (read more)

[Thoughts on the term "ontology".]

• In philosophy, ontology refers to the subfield aiming to answer the question "Which things exist?".
• Perhaps as a consequence of this, hearing "ontology" makes me think of questions like: What are the primitives or building blocks here? E.g. in a spreadsheet, there would be cells; in a graph there would be vertices and edges etc.
• But I think the important things Jacob is talking about show up as answer to the different question of which relations there are between these primitives. E.g. the impor

... (read more)

Thank you for your feedback. I've added a paragraph at the top of the post that includes the definition of s-risk and refers readers already familiar with the concept to another article.