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Is mathematics mostly chaos or mostly order?

(www.quantamagazine.org)
116 points baruchel | 1 comments | 20 Jun 25 15:21 UTC | HN request time: 0.001s | source
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revskill ◴[24 Jun 25 07:09 UTC] No.44363585[source]▶
We need a word-less world of math where all meaning is derived from figures. WOrds are confusing.

"If you can't describe the meaning using only pencils and compass, you don't mean it"

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novaRom ◴[24 Jun 25 07:19 UTC] No.44363632[source]▶
And especially when we mix different categories. Like saying about any infinity as about an object is misleading, because it's rather a process
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Sharlin ◴[24 Jun 25 07:29 UTC] No.44363700[source]▶
Infinities (transfinite cardinals) in the sense used by the article are absolutely objects. We’re not talking about infinite sums or other sequences and their limits. (And limits aren’t really “processes” either – the limit of the sequence 0.9, 0.99, 0.999, … is exactly 1, as a well-known example which nonetheless is controversial among people who don’t know what limits are.)
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random_ta ◴[24 Jun 25 08:22 UTC] No.44363966{3}[source]▶
Sure, if you accept reifying concepts into objects as valid. But that is a gateway to misery.
replies(1): >>44365492 #
1. Sharlin ◴[24 Jun 25 12:33 UTC] No.44365492{4}[source]▶
What's the difference? How is the concept of a transfinite cardinal less of an object than, say, the concept of a set? Or a real number? All are well enough defined that you can do useful math with them, and that's really all that matters.