Why are there so many intellectuals (e.g. those in certain branches of mathematics and philosophy) thinking so hard about problems whose solutions have little to no real-world significance? Are all truths actually profound and important to arrive at?

The reason people think hard about problems that interest them is because the problems interest them. They don’t know if the solutions have “little to no real-world significance” (and neither do you), and they don’t care. They profoundly enjoy the journey, the learnings, and the creative process.

Most enjoyable human endeavors have “little to no real-world significance”. People climb mountains, play music, go to the beach, read, have sex, travel, keep flower gardens and study 16th-century poetry because we are curious creatures and voracious seekers of sublime joy.

In case what you really mean to ask is why we, as a society, allow people to pursue such fun activities instead of ensuring that everyone constantly contributes to what you deem to have real-world significance, well, we tried that too. Didn’t end very well.

In case what you really mean to ask is why we, as a society, choose to go even further and financially support such intellectual pursuits as the research of abstract mathematical problems with no real-life deliverables or real-world significance, well, there are several good reasons.

One, it’s incredibly cheap. Two, research mathematicians have proven to be amazingly effective teachers, partners and collaborators to engineers, chemists, physicists, economists, biologists, software engineers and many other practitioners of real life. Three, math turns out to be very useful, even pieces of it that were once considered not useful.

Inventors thrive in intellectual communities that span the practical and the abstract. Applied mathematicians thrive when surrounded by engineers and pure mathematicians. Students young and old are inspired by the dramatic discoveries, proofs and towers of abstraction which permeate the world of mathematics.

If you ever start a nation or design a country, I would warmly encourage you not to limit the spectrum of allowed vocations to what you regard as immediately beneficial and practical. Leave some room for poetry, fashion design and abstract math. Your world will be incredibly better for them.