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What is theoretical computer science?

(cacm.acm.org)
166 points levlaz | 2 comments | 18 Oct 24 06:04 UTC | HN request time: 0s | source
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hrkucuk ◴[18 Oct 24 07:40 UTC] No.41877157[source]▶
>“There is a grave danger that the subject will develop along the line of least resistance.”

What does von Neumann mean here? Why is it bad that it will develop along the line of least resistance? Does von Neumann advice that working on "harder" problems is more beneficial for TCS? Could not one argue that we should be solving away low hanging fruits first?

I am not sure if I am understanding von Neumann's quote nor this article properly. I would love to hear some simpler explanation (I am a new BSc. CS graduate).

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1. youoy ◴[18 Oct 24 07:58 UTC] No.41877257[source]▶
This is how I see it: you can work on mathematics from two different levels. There is more direct level, which is the formal system, and there is more indirect level which are the intuitions behind the formal system.

If you look at new theories (let's say you are starting to study topology, or group theory) they start from some definitions/axioms that seem to come from "nowhere", but they are in fact a product of working and perfectioning a language for the intuitions that we have in mind. Once we set for the correct descriptions, then there are a lot of consequences and new results that come from interaction almost entirely with the formal system.

The interactions with the formal system is the path of least resistance.

The power of mathematics is that once you figure out a correct formalization of the intuitions, using just the formal system allows you to get a lot of information. That is why sometimes people identify mathematics with just the formal system.

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2. tightbookkeeper ◴[18 Oct 24 09:33 UTC] No.41877714[source]▶
To take it one step further, mathematical ideas which do not nicely fit within one of the highly developed theories then feels underbaked and less attractive to other mathematicians.

Knuth thinking about algorithms led to all these research questions about combinatorics, that have turned out to be very interesting, but are much more messy and disjointed results.