8 ms·
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 thei
by magneticnorth 5y ago
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 https://en.wikipedia.org/wiki/Saharon_Shelah#Academic_career
- jjgreen 5y agoShelah'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).
- tux3 5y agoThat 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. =)
- mhh__ 5y agoI 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.
- Bayart 5y agoI'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.
- mhh__ 5y agoThey 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.
- dmix 5y agoI 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'.
- bakuninsbart 5y agoI 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.
- 5y ago
- jjgreen 5y agoI 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.
- Epa095 5y agoIt raises the question, it doesn't beg it (sorry for the boring off-topic comment). https://www.writersdigest.com/write-better-fiction/begging-the-question-how-to-use-it-correctly https://www.writersdigest.com/write-better-fiction/begging-t...
- tux3 5y agoThank you! I think I was actually corrected on that once before, but maybe this time it'll stick =)
- mhb 5y agoA nice substitute might be begets. It is so similar, I wonder if that is where the confusion arose to begin with.
- waterhouse 5y agoSee https://languagelog.ldc.upenn.edu/nll/?p=2290 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.
- DemocracyFTW 5y agoThis literally begs the question whether the prescriptive approach is to be preferred over the descriptive one.
- wallscratch 5y agoI 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.
- sorokod 5y agoIt is said about Saharon Shelah that colleagues are reluctant to share research problems with him since he solves them on the spot.
- OscarCunningham 5y agoCan you give an example paper? I want to see what you mean.
- jjgreen 5y agoPicked pretty-much at random, but typical of what I mean: https://arxiv.org/pdf/1802.01137.pdf 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/ https://shelah.logic.at/paper-list/