But you seem to be using visualization software in your images. They didn't have that stuff when I was in school — fishfry

It's just fairly simple BASIC programming that I enjoy creating. I tried Pascal, Fortran, Mathematica, C++, and one or two others, but by the mid 1990s I returned to BASIC. I use Liberty Basic now. Microsoft's Visual 6 was excellent, but one morning I turned on my computer and it was gone. Instead Microsoft tried to get me to use some new programming language you had to employ at their servers. I've never quite forgiven them. I've written 3D programs, but haven't been happy with them. I'm a 2D guy.

Although I don't subscribe to mathematics being one object, when one looks at specific areas of the subject one can say that one object prevails, and there might be representations of that object that appear disparate. I have dabbled with Möbius transformations in the complex plane for years and still do not understand all the nuances of the subject. They form a group under composition, a procedure described below. Here are three representations: (a) geometric - rotations etc. of the Riemann sphere (b) the analytic form (c) the matrix form.
Question: what is the one object being represented?

Confused really why you would be in "literal shock" and why talk of having pushback. — ssu

I'm a little bit at a loss as to how to respond. 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. I can see that someone could use it to argue for woke math or decolonized math or whatever. So I abjure my former heresy. if it will help.

But you put some thought into your response, so I'll do my best to type in some words. Just please be aware that my heart's not in it. Not a hill I want to die on, not even a hill I want to get a hangnail on.

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

Yes I know these people. How bad has it gotten when Scientific American, of all outlets, publishes Modern Mathematics Confronts Its White, Patriarchal Past.

So I hear you loud and clear on this issue.

I truly don't think any of these people are waiting for the likes of me to give them aid and comfort with an anodyne remark like "Math is what mathematicians do." But if you disagree, I'll withdraw the remark. It's not going to help. Scientific American didn't call to ask my opinion before they published that article.

The conclusion and the counterargument isn't that "If then all mathematicians sleep, is sleeping then mathematics?", no, it's not so easy. — ssu

Well, math is what mathematicians do when they're doing math. An even more mindless slogan, therefore even more easily used by the enemies of rationality and merit, I suppose.

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

I can't do much about those folks. And I can't censor my opinions (and mindless slogans) just in case one of them overhears me and takes comfort in my words.

It's kind of like in politics. Sometimes there's a candidate with flaws. Some of their supporters deny the flaws entirely. Others admit the flaws but affirm their support for the candidate anyway. I'd be in the latter category. I'll tell the truth even if it undermines my own case. Perhaps I've done that here. So be it.

Hopefully you get my point. — ssu

Not entirely, that last paragraph went over my head a bit. I'll agree that I'd be hard pressed to give a definition of mathematics that transcended historical contingency.

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 can't separate math from its uses. If I was making the point that math can be political, I'd agree with myself.

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

Ok. Math is a historically contingent human activity. How is that any better than "math is what mathematicians do?" Maybe anti-racist math is the nex big paradigm.

“Grades and Test Scores Do Not Define
Us as Math Learners”: Cultivating Transformative Spaces for Anti-Racist Math Education [pdf link]

It's always the math "educators" and not the mathematicians promoting this stuff. Of course they started with a "land acknowledgment." I've noticed that they never give their real estate back, though.

So ok, you say I'm giving aid and comfort to these people. But how else should I say that math is a historically contingent human activity? Kuhn's paradigm theory says the same thing. One day someone comes along and changes everyone's view of the subject.

Kuhn is subject to the exact same criticism you level at what I said.

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 never gave any thought to "what math is." It just like what Justice Potter Stewart said about pornography. "I know it when I see it."

Well that's the best I can do today by way of response. But do tell me if you think Kuhn might be subject to your criticism, for noting that the nature of science changes radically from time to time.

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

Exactly what it was intended to be. How about my previous statement about a mathematician is one who scribbles on paper, curses, then wads the paper up and throws it into the trash. Nobody seemed offended by that. Folksy I guess.

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

That is a pretty bad article. It paints a picture of an entire profession based on a few incidents.

Thank you for the response. I don't think we have any real disagreement here and I think you got my point.

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!

With this short interlude to social discourse, I would like to go back to the actual topic of this thread.

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

One more slight digression from the original topic. I have been in this position. Rules of Affirmative Action applied and the dean asked for the top three candidates. There was a woman, but no minorities. The dean then placed a minority in with our recommendations. When the time came to decide to make an offer the dean picked the minority. It did not work out well in the long run.

I would like to go back to the actual topic of this thread. — ssu

May I suggest focusing on math objects having several representations (like my example four days ago) and speculating on what the object "really" is or looks like. Or where it lies in a metaphysical sense. To say math is one object is absurd IMO.