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Comment by paulpauper | Hacker News Reader

seems like unsolved problems are being solved at a breakneck speed

https://www.google.com/search?q=site%3Ahttps%3A%2F%2Fwww.qua...

I love this series of Quanta's. They have truly excellent coverage of real, modern mathematics results of the type that are very hard to explain outside of their own field.

Speaking as a former mathematician, I don't think problems are being solved any faster lately, but we hear about it more outside of academia because this is something that Quanta has started covering.

As an example, you could look only at Saharon Shelah, one of the co-authors of this result and a giant in the fields of model theory and set theory. He has spent a career settling long-standing open problems, including Whitehead's problem and Morley's problem. Until this Quanta series, Shelah's work didn't get much coverage outside mathematics as far as I know, but results of this caliber are not atypical for him. https://en.wikipedia.org/wiki/Saharon_Shelah#Academic_career

Shelah's productivity is astonishing, but he uses the worst notation possible, his preprints are practically unreadable as a result (not that I'm clever enough to understand them).

That begs the question of whether the unorthodox notation is a catalyzer for the results he gets, just a coincidence, or if just thinking differently in general is the reason for both. =)

I think notation is completely misunderstood by some fields, and that physics in particular really shows the benefits of it (i.e. With tensors and feynman diagrams we can nearly stop ourselves from writing down the wrong answer through notation), but academics are just as idiosyncratic as everyone else so I'd guess something more human.

I've got terrible mathematical education, but Feynman diagrams are something even a clown like myself can easily wrap his head around. They're really an exceedingly clever device, end "clever" doesn't do it justice.

They don't even have to be Feynman diagrams - theoretical (rather than mathematical) physicists are usually pretty lazy. We make up notation for us rather than the reader. Mathematicians, I find, are a lot worse but still bearable. Engineers though, oh boy, seem to actively enjoy using notation to obscure the material in the books I have read.

I bought ~5 different kindle books on logic as a prerequisite for understanding another book I originally bought on Probability Theory (E. T. Jaynes). Every logic book I bought used a different notation and none of them matched the notation used in the book I wanted to read either, which is how I ended up with 5 of them.

You'd think something as straight forward as (boolean) logic would converge on a standard notation. But I'm not familiar with the mathematics field to really criticize this. Regardless I found it to be a large barrier-to-entry which over complicated something when I was hoping to find direct analogies not needing constant 'translation'.

I agree. What I saw with the mathematics students during our Bachelors (I did CS, so adjacent, but still far away) was that they would have a really hard time in the beginning coming from school, but after a few semesters they would transcend notations and it would then become mostly a thing of preference. The thing is that all of these guys were already really talented and engaged in mathematics, and it was still quite hard combined with the fundamental difference of how we do mathematics in university compared to school.

That gives me some motivation to power through them until I get used to the notation. Thanks.

In programming language theory there is a unified notation for operational semantics, but most papers use nonstandard and/or incorrect interpretations of the notation. It’s a glorious minefield when you go to try to implement the papers — you inevitably end up talking to the authors & helping them debug issues, even years later.

I suspect that he has some alternate level of perception, sees the beauty of the underlying mathematical structures directly without seeing the ugliness of the notation that distracts dull-witted mortals like me.

It raises the question, it doesn't beg it (sorry for the boring off-topic comment). https://www.writersdigest.com/write-better-fiction/begging-t...

Thank you! I think I was actually corrected on that once before, but maybe this time it'll stick =)

A nice substitute might be begets. It is so similar, I wonder if that is where the confusion arose to begin with.

See https://languagelog.ldc.upenn.edu/nll/?p=2290 for some details. I would summarize by saying, there were words involved (i.e. the Latin "petitio" and Greek "αἰτεῖσθαι") that have multiple meanings (a modern analogue being "plead", which can mean "ask"/"beg", but can also mean "plead to the court [some statement of fact]"—i.e. to make a claim), and the word "beg" comes from a translator selecting one of the wrong meanings. Also, "the question" is really a poor choice to mean "the original point to be proven"/"the conclusion"/"the point in question".

I am strongly against prescriptivism telling people that a bad translation that makes no sense is correct. I recommend "assuming the conclusion" as a correct name.

This literally begs the question whether the prescriptive approach is to be preferred over the descriptive one.

I feel like at this point common usage has moved so far away from this that it’s almost not worth trying to reel it back in.

It is said about Saharon Shelah that colleagues are reluctant to share research problems with him since he solves them on the spot.

Can you give an example paper? I want to see what you mean.

Picked pretty-much at random, but typical of what I mean: https://arxiv.org/pdf/1802.01137.pdf

The use of the filled club ♣ makes the whole thing look like it's been sneezed on by someone who's just come off a shift in a coal-mine.

There are 1087 published research papers here if you'd like to browse ... https://shelah.logic.at/paper-list/

Ah, how to feel totally inadequate...

Shelah is a powerhouse, in fairness. A 10x mathematician.

> Articles in preparation (104 items)

Holy crap. I've got about a dozen articles in preparation. Not a one of them is in Shelah's league

I'm reminded how Newton invented modern physics after spending a year(?) in seclusion because of the pest raging in London and I wonder if something similar has been going on with the Covid lockdowns.

I wonder if computers have something to do with this.

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