But you seem to be using visualization software in your images. They didn't have that stuff when I was in school — fishfry
Confused really why you would be in "literal shock" and why talk of having pushback. — ssu
The statement "Math is what mathematicians do" can be interpreted totally differently by for example social sciences. Totally differently what you mean. I do understand your point, but what I'm trying to say here that all do not share your perspective and they will use a totally different discourse. — ssu
The conclusion and the counterargument isn't that "If then all mathematicians sleep, is sleeping then mathematics?", no, it's not so easy. — ssu
It's that if mathematics is just what mathematicians do, then we just can just focus on the mathematicians as group and in their social behavior and interactions and workings as a group. Because what mathematicians do is what is mathematics, we can take out any consideration of things like mathematics itself or the philosophy of math. What the schools of math disagree on isn't important. I'll repeat it: all you need is to look at mathematicians as a group of people and the behavior and interactions. And in the end some can then talk about "decolonization of mathematics", because the study will notice that it's all about "dead white European males". This is just the way some people think. — ssu
Hopefully you get my point. — ssu
Cryptography and secure communications are important, and it's quite math related. And Wall Street uses quants, quantitative analysts, who do also know their math. Would then mathematics be capitalist? Of course not. I myself disagree with these kinds of interpretations. — ssu
You don't have to, it's all quite simple. Thomas Kuhn came up with the term "scientific paradigm" and note that Kuhn isn't any revolutionary and he doestn't at all question science itself. He's basically a historian of science. It's simply a well thought and researched book that states that basically everybody everybody is a child of their own time, even scientists too. And so is the scientific community, it has these overall beliefs until some important discoveries change the underlying views of the community. And that's basically it. — ssu
For the philosophy of mathematics or the to the question of just what math is, Kuhnian paradigms don't give any answer and actually aren't important. What is important is the questions in mathematics... that perhaps in the end can get a response like a Kuhnian paradigm shift. So hopefully you still think that way, not only probably. — ssu
I find myself defending a hill that I'm definitely not willing to die on. If it made a difference to anyone, I'd gladly deny, renounce, disavow, and forswear my earlier claim that "Math is what mathematicians do." It was a throwaway line, a triviality, a piece of fluff — fishfry
Yes I know these people. How bad has it gotten when Scientific American, of all outlets, publishes Modern Mathematics Confronts Its White, Patriarchal Past. — fishfry
Well, that article basically states what this is about: attempt to get job positions. What better way is there to accuse a field of study, mathematics, to itself be "white and patriachial", or whatever. But it works. What can the head of a mathematics department say when accused that there are too few if any women or minorities represented in the staff? Stop hiring your male buddies and follow the implemented DEI rules!How bad has it gotten when Scientific American, of all outlets, publishes Modern Mathematics Confronts Its White, Patriarchal Past. — fishfry
What can the head of a mathematics department say when accused that there are too few if any women or minorities represented in the staff? Stop hiring your male buddies and follow the implemented DEI rules! — ssu
I would like to go back to the actual topic of this thread. — ssu
I think the one issue in mathematics is that defining a "mathematical object" can be difficult if there are equivalencies, multiple ways of representation of the "object". There's a whole field of mathematics just looking at these similarities, category theory. — ssu
Let's try an example to clarify this idea:Yes, the similarities don't define the object, however. Is an "object" its' representation picked at random? Or, is there a more metaphysical meaning of the one object having representations? Is there an Object Theory? Just thinking of a way this thread might proceed. — jgill
Question from the stands: are individual numbers considered objects? — Wayfarer
What would be the mathematical object behind/described by the "well ordering theorem" — ssu
Ok, I perhaps I could have better defined the axiom of choice, but in the latter you get the point.You're conflating non-equivalent theorems. — TonesInDeepFreeze
That basically was my question. And I think comes to this thread's main question, because mathematics is quite connected.This brings up an interesting question: If two things are equivalent, A<->B, does that mean they represent the same math object? — jgill
If two things are equivalent, A<->B, does that mean they represent the same math object?
Mathematics thrives on going to extremes whenever it can. Since the “compromise” we sketched above has “mathematical objects determined by the network of relationships they enjoy with all the other objects of their species,” perhaps we can go to extremes within this compromise, by taking the following further step. Subjugate the role of the mathematical object to the role of its network of relationships—or, a
further extreme—simply replace the mathematical object by this network. This may seem like an impossible balancing act. But one of the elegant–and
surprising—accomplishments of category theory is that it performs this act, and does it with ease.
He ends up advocating (maybe just "showing the benefits of" is a better term) of an approach grounded in category theory. — Count Timothy von Icarus
This is a very interesting paper on the subject. Thank you, @Count Timothy von Icarus! :grin: :up:Barry Mazur has a really neat paper on this question, and at least parts of it are quite accessible. He ends up advocating (maybe just "showing the benefits of" is a better term) of an approach grounded in category theory. — Count Timothy von Icarus
Too bad that the basics of category theory aren't taught in school. But then again, the educational system doesn't care much about the philosophy of mathematics or the foundations of mathematics. — ssu
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