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How has mathematics gotten so abstract?
11–20 of 220 posts
Re: How has mathematics gotten so abstract?
#12I feel like a great deal more credit should be given to Cauchy and his school, but I understand the tale is long enough.
The Peano axioms are pretty nifty though. To get a better appreciation of the difficulty of formally constructing the integers as we know them, I recommend trying the Numbers Game in Lean found here: https://adam.math.hhu.de/
Re: How has mathematics gotten so abstract?
#13>Today, mathematics is regarded as an abstract science.
Pure mathematics is regarded as an abstract science, which it is by definition. Arnol'd argued vehemently and much more convincingly for the viewpoint that all mathematics is (and must be) linked to the natural sciences.
>On forums such as Stack Exchange, trained mathematicians may sneer at newcomers who ask for intuitive explanations of mathematical constructs.
Mathematicians use intuition routinely at all levels of investigation. This is captured for example by Tao's famous stages of rigour (https://terrytao.wordpress.com/career-advice/theres-more-to-...). Mathematicians require that their intuition is useful for mathematics: if intuition disagrees with rigour, the intuition must be discarded or modified so that it becomes a sharper, more useful razor. If intuition leads one to believe and pursue false mathematical statements, then it isn't (mathematical) intuition after all. Most beginners in mathematics do not have the knowledge to discern the difference (because mathematics is very subtle) and many experts lack the patience required to help navigate beginners through building (and appreciating the importance of) that intuition.
The next paragraph about how mathematics was closely coupled to reality for most of history and only recently with our understanding of infinite sets became too abstract is not really at all accurate of the history of mathematics. Euclid's Elements is 2300 years old and is presented in a completely abstract way.
The mainstream view in mathematics is that infinite sets, especially ones as pedestrian as the naturals or the reals, are not particularly weird after all. Once one develops the aforementioned mathematical intuition (that is, once one discards the naive, human-centric notion that our intuition about finite things should be the "correct" lens through which to understand infinite things, and instead allows our rigorous understanding of infinite sets to inform our intuition for what to expect) the confusion fades away like a mirage. That process occurs for all abstract parts of mathematics as one comes to appreciate them (expect, possibly, for things like spectral sequences).
Re: How has mathematics gotten so abstract?
#14This reminds of of that one time when I was on a date with a girl from the history department who somehow bemusedly sat through my entire mini-lecture on comparing infinite sets. Twenty years and three kids later, she'll still occasionally look me straight in the eye and declare "my infinity is bigger than your infinity."
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You would not. People love hearing about the things you care about as long as you can present them in interesting ways. Try it!
Re: How has mathematics gotten so abstract?
#15This reminds of of that one time when I was on a date with a girl from the history department who somehow bemusedly sat through my entire mini-lecture on comparing infinite sets. Twenty years and three kids later, she'll still occasionally look me straight in the eye and declare "my infinity is bigger than your infinity."
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I wouldn't go on Hinge if that's the default experience.
Re: How has mathematics gotten so abstract?
#16[flagged]
Could be him? https://en.wikipedia.org/wiki/Micha%C5%82_Zalewski
Re: How has mathematics gotten so abstract?
#17[flagged]
Did you bother to google his handle? While I don't know his pure mathematics credentials, he's nerd-famous enough to not warrant an introduction. In fact, you not recognizing it says something about you.
Re: How has mathematics gotten so abstract?
#18[flagged]
Did you bother to google his handle? While I don't know his pure mathematics credentials, he's nerd-famous enough to not warrant an introduction. In fact, you not recognizing it says something about you.
>he's nerd-famous enough to not warrant an introduction
What is nerd-famous supposed to be. He's at the center of some subjective in-group that exists in your head?
Re: How has mathematics gotten so abstract?
#19This reminds of of that one time when I was on a date with a girl from the history department who somehow bemusedly sat through my entire mini-lecture on comparing infinite sets. Twenty years and three kids later, she'll still occasionally look me straight in the eye and declare "my infinity is bigger than your infinity."
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Get this incel trolling out of here. No, all that would happen if your date weren’t interested in math/whatever you’re into is a polite message “I had a great time but I don’t think we have much in common” and leave it at that.
Re: How has mathematics gotten so abstract?
#20[flagged]
I'm curious how you managed to find nothing on lcamtuf. He's one of the most famous Polish hackers from the 90s, then one the best security researchers Google had. Even if you live under a rock, the substack has an "about" section.
If it wasn't for Michał I'd probably be a farmer today.