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Hilda Geiringer Reshaped Mathematics (bbc.com)
70 points by sonabinu 16 days ago | hide | past | web | favorite | 54 comments



While I don't doubt that Geiringer did a lot of important work, I'm a little frustrated with how difficult it is to read about that work itself.

Look at a Wikipedia article about a relatively obscure mathematician, say, Robert Remak:

https://en.wikipedia.org/wiki/Robert_Remak_(mathematician)

Right away it says what fields he worked in and mentions some of his results. The rest of the article goes into a bit more depth about his work and then finishes off with a paragraph about the tragedy in his life.

Compare now with Hilda Geiringer's article:

https://en.wikipedia.org/wiki/Hilda_Geiringer

Her work is described in very vague strokes, "two variable Fourier series" and then mentions statistics, probability, and plasticity... so, what did she do exactly? These are very broad fields! The article does mention the Geiringer equations, but there's no corresponding Wikipedia article about them.

The majority of Geiringer's article is instead taken up by the fact that she was a Jewish woman with relatively very little attention given to her mathematics.

To be clear, I'm not saying that this is a Wikipedia-exclusive phenomenon. The BBC article is also rather "soft", as a popular article must be out of necessity, but for minorities, sometimes they (we?) must deal being talked about in nothing but soft articles. The geek feminism wiki calls this the unicorn law:

https://geekfeminism.wikia.org/wiki/Unicorn_Law


For some reason some people are incredibly hostile to this suggestion, but I think the BBC has dumbed down pretty drastically over the years - and this can be pretty easily verified by comparing their output from decades past with today's. Older popular science TV programmes sometimes even had - shock horror! - in depth discussion of actual mathematical equations. By contrast, I watched a Brian Cox space series recently in which I recall a single mention of maths, and that was a few animated formulae floating around a beautifully rendered planetary scene as graphics without real explanation, whilst some dreamy ambient synth music played in the background. There's a massive difference in style, content, sophistication of ideas presented, and density of information. The new stuff poses as educational, but delivers very little proper detail.

Apart from that, I think that surely it would have served this woman's memory far better to tell us the details of what she achieved, and how her work has been built on, rather than making her victimhood the main thrust. I'll bet she'd have preferred to be remembered as a mathematician rather than a victim.


(Public) TV used to be much more intellectual in several countries (including my own, Hungary). Partially because there weren't so many alternatives to compete with. The managers could afford to not care about dumbing it down and people watched it in lieu of more gratifying things.

Clickbait and instant gratification is now the norm and if you don't keep up, you just won't be able to attract enough viewers. Now theoretically publicly funded channels and publications could just ignore viewership/readership numbers, but their management style has also become much more commercial.

"Who wants to be a millionaire" used to be incredibly popular in many countries (it was huge in Hungary). In that show sometimes half a minute is just a person thinking in silence, staring at some question about medieval history or about an opera. How many people would watch this nowadays?


Thing is there were plenty of programmes on TV when I was younger that would have had a tiny viewership even back then, and were shown as they fulfilled the required 'boring but worthy' percentage of the BBC's output - these have almost all disappeared to be replaced by facsimiles that pretend to be the same thing but are nothing close.


There is some evidence that women scientists are being selectively excluded from Wikipedia. As one researcher put it, ‘Women academics are twice as likely to be nominated for deletion as you would expect from the proportion of women among Wikipedia biographies.’

Some sources: https://www.chemistryworld.com/news/female-scientists-pages-... https://www.nature.com/articles/d41586-018-05947-8

That doesn't directly explain why the articles that are there would be so shy on information, but it does suggest that people won't spend a lot of work on a topic for which deletion may occur, discouraging people from making improvements.


That could also be explained by feminists aiming to list as many female academics as possible, so perhaps they are also likely to list many who are less noteworthy.

It would be surprising if there was really a bias to delete entries about women, as actually Wikipedia is assumed to be under SJW control.


Talking about minorities is an extension of the human drive to find one's place among other people, which is an extremely high priority in almost everyone's lives. As a result, far more people are interested in talking about minorities (which fulfills a basic drive) than are interested in talking about math. So much so that a very significant fraction of articles related to math or any other topic that otherwise doesn't get a lot of light in the public arena are motivated by the social desire.


"for minorities, sometimes they (we?) must deal being talked about in nothing but soft articles"

Rather than "deal", they could take it upon themselves to improve those articles. Who should be responsible for doing that? You yourself, upon seeing such a "soft" article, could try to improve it. Or send a shout out to the feminist mathematicians reddit group that undoubtedly exists.

Also, comparing your links, the entry for Geiringer appears to be much longer and more detailed. I can not discern from the Remak article what exactly he worked on, either. It mentions "embeddings" and "CM-fields" - how is that better than "Fourier series" and "plasticity"? Maybe you view those articles in a biased way?

Also, "unicorn law"? What the serious fuck? They now count it as oppression that they get invited to talk about "women in open source"?


Fourier series and plasticity are very broad fields. They're almost top-level classifications in the MSC subject index. Remak's article mentions topics that are much more specific. Although to the uninitiated it may sound just as obscure, saying someone worked on complex multiplication fields tells a mathematician much more than saying they worked on Fourier series.

The unicorn law isn't oppression; it's just tiring and an annoyance. We are all more than our genders and ethnicities, so it gets tiring to only get asked about those.

I don't understand why this makes you angry enough to curse. Do you understand why?


She may be cool, but she didn't "reshape Mathematics". Wish such articles would come without so much hyperbole.

And as for missed geniuses, there are many missed male geniuses, too, many famously so (even Einstein didn't get a position as a professor at first). They suggest only women are overlooked, which is untrue.

There are also examples of female mathematicians even further back being fostered by famous mathematicians.


> She may be cool, but she didn't "reshape Mathematics".

You missed the pun.


No I get it, her formula is about ideal shapes (of bridges). It is still misleading. They could have written "who reshaped bridges".

I suppose Grothendieck reshaped Mathematics - he invented a new way of looking at things, that made it possible to prove a host of new things.

In a sense perhaps every mathematical result reshapes mathematics. But they used it here to inflate her importance, to make it seem outrageous that she was supposedly forgotten. As if many Mathematicians are being remembered in general.


[flagged]


That's not the point. The point is that it is a lie to claim she was forgotten because she was a woman.


if we are talking about female mathematicians don't forget Emmy Noether: https://en.wikipedia.org/wiki/Emmy_Noether


She's one of the few true aliens I regard as up there with von Neumann and Einstein, who have some kind of ridiculous direct line of communication with the fabric of reality.


You're doing a bit of a disservice to Newton and Maxwell there, surely. And lots of Einstein's work was derivative of others.


Special Relativity was completely ripped off from Henri Poincaré and Hendrik Lorentz (but then they were not German and the physics establishment was dominated by Germans at the time).

Einstein's 1921 Nobel prize pointedly ignores Relativity and was awarded for his work on the photoelectric effect, a backhanded slap if there were none.


We are talking about a migrant Jewish female mathematician who was discriminated against trying to start a career in the USA in mid-1940s.


Who did not reshape mathematics, unlike Emmy Noether.


Yes. When I read the headline, I thought it was going to be about Noether. Even then, I'd argue she reshaped physics, not mathematics itself, unlike, say, Galois or Gödel.


Emmy Noether had a comparable background and had her problems with academia, too


Yes, Emmy Noether was a pure genius (one of the greatest mathematician of all time), and was never named full professor (even though she had Hilbert support).


This title isn't very good. At least name the person.


"Reshaped Mathematics" is quite an exageration.


I think it's a pun with plasticity, a field where she did work in.


BBC has a way of doing this with titles. They start with a very broad title and then narrow it as the story ages.


Summary: Woman contributes to mathematics; can't find appropriate academic position because she isn't a man.

As far as the article goes there is a bit about her contribution which is over inflated to, "reshaped maths". This is used as a jumping off point to talk about how she can't find the same work her male counterparts would, skills being equal. Finding out that professors were mostly men in the early to mid 20th century is hardly noteworthy but the article spends some time on it. Finally a bit of commentary by the author about missed opportunities because people other than white men have ideas, too.

The last seems to be the point, but it reads as an attempt to find misery and highlight it, rather than perhaps remembering the woman and her contribution. The contribution the author is really interested in is the failure and the opportunity it presents to make a trite statement about equality of opportunity. All with a click bait title.


If the BBC is trying to build a case that female mathematicians were treated poorly 70 years ago compared to their male counterparts, they would somehow need to show that there wasn't a similar supply of men who made an obscure but significant contribution only to get coldly treated by the establishment (somehow I think there's no shortage). We must be careful to not fall prey to example-ism, building cases out of salient examples instead of evenly sampled trends.


Let's not fall into denialism here. There's absolutely no doubt that being a Jewish woman mathematician in the 1930s was doubly difficult than being a male Jewish mathematician -- double the discrimination. Calling Geiringer's situation "example-ism" is up there with doubting the sky is blue because I said I saw blue skies in Italy one time.


An interesting comparison would be with Srinivasa Ramanujan. Male but non-white, and from a poor background. Also Emmy Noether, also Jewish, German and female, whose contributions to both mathematics and physics are much more significant, fundamental even.

Also, I doubt her being Jewish was a factor of academic discrimination, as opposed to the more general Nazi persecution she endured. We're not talking about Moses Mendelssohn breaking through glass ceilings in the 18th Century but the 20th by when Jewish intellectuals like Hilbert or Einstein (or more controversially, Fritz Haber) held a commanding place in science and academia.


I have never seen any evidence that women were discriminated against in 1930s mathematics other than specific stories about women being treated coldly by the establishment. I have certainly never seen anyone compare their cold treatment to the ambient coldness.

Look at it this way. If I told you every time a coin came up heads, how many reports would it take for you to conclude that it was biased? The right answer is "the conclusion may never be reached," because I'm not allowing you to tally up the number of times it came up tails. Likewise, despite the huge number of stories about women being denied appointments despite having made significant contributions, no conclusion can be drawn until there is some indication that the effect is unique to women.

Another important point is that even if the 1930s were awful and sexist, there may have been islands of relatively fair people. So in the interest of remembing them as they deserve, it is best to check each social group individually for evidence of their bad behavior, so that you don't end up remembering the one admissions committee that wasn't sexist as just another bias enforcement team.


> I have never seen any evidence that women were discriminated against in 1930s mathematics other than specific stories about women being treated coldly by the establishment.

So you've seen no evidence of discrimination... other than specific stories of discrimination? What do you think discrimination in academia looks like? A giant sign on the front door of the university that says "NO GIRLS ALLOWED"?

Geiringer was the first woman professor of Mathematics in Germany but she probably wasn't the first woman in Germany who was qualified to hold that position.


There is no number of specific stories that should convince anyone, unless there is also some indication that they are being evenly sampled! You would have to compare all of the stories of men who were denied appointments to make a conclusion. To get a probability from a count, you have to divide by something.


I mean, isn't the fact that there were virtually no women in academia back in the time a convincing enough proof in itself that there was, indeed, discrimination?


Discrimination on the part of gatekeepers isn't the only thing that can keep minorities out. A culture that tells them not to try doing it because it isn't their assigned role, a fear of being the only one of their group among a majority of another group, and earlier discrimination that prevents them from getting qualifications but isn't the fault of the gatekeeper could all be responsible. Given the information I know and what has been brought up in this discussion, University mathematicians could have been perfectly willing to hire women.


This is just the good old pipeline fallacy all over again.


The fact you like to call it fallacy doesn't make it one.


How do you know that last part? What was the state of education in Germany at that time? What was considered the qualifications for professorship at that time? How many people of any gender had those qualifications? Do you have any specific knowledge about any of this?


[flagged]


I think you completely didn't get the point of his comment.

Say you are a woman and you made an important contribution to mathematics. Now would you want it such that every article written about you did not focus on your achievement, but instead focused on your inability to get an academic position?

Lots of people know the work of Emmy Noether. Do they know know it only because she managed to get academic positions? Had she never got one do you think it would be appropriate to know she was a genius, but never talk about her contributions?


I think I did and from the way the commenter doubled down without acknowledging his disrespect of Hilda's contributions, I'd say my take was spot on.

I'd say you missed the bias in his comment. Had he been more altruistic in his take, I'd say you gave thoughtful feedback.


OK - Let me respond to your original comment:

LanceH said:

> there is a bit about her contribution which is over inflated

to which you said:

> Why do you diminish this woman contributions to mathematics?

LanceH didn't. He acknowledges her contributions elsewhere in the comment. He is saying that characterizing it as "reshaping mathematics" is likely an exaggeration. At the very least, the BBC article doesn't give an indication of how she did this, and doesn't back the stance. Even a great contribution to the theory of plasticity is not one that reshapes mathematics. It's an extraordinary claim. While in academia, I worked with people who made incredible contributions to a sub-sub discipline of physics. Within the sub-sub discipline they are recognized as the leaders/pioneers of the field. Yet they are unknown to most physicists, and no one (including they themselves) would dare make a claim that they "reshaped physics". Mathematics is a broader discipline and it takes even more to reshape it than it does physics.

LanceH said:

> to make a trite statement about equality of opportunity

To which you responded:

> Are you saying equal opportunity is trite?

LanceH wasn't. What was being said is that writing an article pointing out how few opportunities women had at the time is trite (definition: "boring from much use : not fresh or original"). If they want to write yet another article documenting this, that is fine. But they should title the article to reflect it.

A famous blind programmer once complained of the same phenomenon: That articles written about him focus more on his blindness than on his achievements. I don't know how Hilda would feel about this article, but I would not be happy if I made an achievement and all that is written about me is related to my gender/race/disability and not the work I've done.


OK - Let me respond to all your biases:

> He is saying that characterizing it as "reshaping mathematics" is likely an exaggeration

No, it's not and actually reading the article points out how Hilda Geiringer helped change the course of mathematics. The author may have used flowery language but is not "wrong" or an "exaggeration" as you or the other commenter claim.

The title of the article is fine. You take umbrage that the article also points out something else along the way...

> What was being said is that writing an article pointing out how few opportunities women had at the time is trite

So again, you're saying articles the use of the past as an example of why discrimination and equal opportunity in STEM fields are important topics is trite. How trite of you ;)

It's amazing how easily men can call exemplifying past gender discrimination to highlight why it's not a good thing as "trite".

After all, racism was solved by the civil rights movement right? No need to revisit the past as that would be... trite ;)

As I said before, had the original commenter been a bit more neutral in his take, I would have given your original defense of his argument more salt (that and I probably wouldn't have commented in the first place).


> No, it's not and actually reading the article points out how Hilda Geiringer helped change the course of mathematics.

Since people are saying the article doesn't, and you are saying it does, it behooves you to demonstrate this. Where is the article demonstrating this? I see only an impact to one small subdiscipline of engineering. I see other achievements in math, but nothing indicating the impact those had.

> You take umbrage that the article also points out something else along the way...

Blatantly false. I take umbrage that the article is about her exclusion from the community, and it along the way points out she made some contribution, and that the title of the article does not reflect this. Had the title been "Yet another example of an accomplished woman in mathematics who was denied X, Y and Z" I would have been fine.

> It's amazing how easily men can call exemplifying past gender discrimination to highlight why it's not a good thing as "trite".

It's amazing you draw conclusions about people's gender.

> After all, racism was solved by the civil rights movement right? No need to revisit the past as that would be... trite ;)

Throwing in non-sequiturs is not helpful.

And frankly, I do not think you understand what "trite" means. It doesn't mean irrelevant or not worthy of discussion.

> As I said before, had the original commenter been a bit more neutral in his take, I would have given your original defense of his argument more salt (that and I probably wouldn't have commented in the first place).

And as is often the case in such discussions, this seems to be more about you than about LanceH or me. Why would you even tell me/others your criterion for what you would give more salt to? We are not in an arena aimed to satisfy your perspective, and you are not doing an adequate job of backing your perspective. Furthermore you are avoiding addressing the comments/arguments made to you, and have not even attempted to acknowledge that you understand the counterarguments.


>Since people are saying the article doesn't, and you are saying it does, it behooves you to demonstrate this.

The article stands on its own and I don't have anything to prove to you. It's funny because while I don't think it's a very well written article, I will (and did) highlight biased within critiques.

> Blatantly false.

This made me laugh, thank you. Again your bias is showing through and I stand by my original comment on this aspect of language.

>It's amazing you draw conclusions about people's gender.

Bravo! Spoken like a true alt-right "warrior" mocking liberals with "did you just assume my gender?". Good re-phrasing though.

Now I'm not saying you are, but the tone is unmistakable my friend ;)

>Throwing in non-sequiturs is not helpful.

Ahhh but it was a relevant comparison to your position. You may not like it, but you framed the gendered example the exact way.

>And frankly, I do not think you understand what "trite" means. It doesn't mean irrelevant or not worthy of discussion.

I used the word exactly how you defined it in your comment. Again you may not like the comparison, but it's your own framing looking back at you. ;)

>And as is often the case in such discussions, this seems to be more about you than about LanceH or me. Why would you even tell me/others your criterion for what you would give more salt to?

So providing context for others regarding the sentiment of original comment is all about me. Interesting analysis.

>We are not in an arena aimed to satisfy your perspective, and you are not doing an adequate job of backing your perspective. Furthermore you are avoiding addressing the comments/arguments made to you, and have not even attempted to acknowledge that you understand the counterarguments

Oh I understand your position well enough. It's a decent job, a bit dressed up, but it succumbs under any positive pressure. I'm glad to hear you and your friend are close, and seem share the same biases. Thank you for exemplifying them in your own words.

And also thank you for attempting to clarify the original commenters words as I initially thought it was well meaning, this past comment a little less so.


I'm sorry, but all I see in your comment is:

"I do not want to defend my stance. My positions are obvious so no explanation is needed from my side"

"I see bias everywhere, but I won't do anything to try to understand how what I see may not be a bias."

"I will attribute intentions to the person I am speaking with and make assumptions about who the person behind the computer is. I will view what (s)he says through that lens that I have chosen to wear. I will not supply any avenue for that person to point out defects in the lens."

"Thanks for trying."

There is no substance here, so nothing I can respond to.


The dude is deliberately misquoting my "As far as the article goes there is a bit about her contribution which is over inflated to, "reshaped maths"." He leaves off the 'to, "reshaped maths" at the end, changing the meaning entirely.

He's trolling hard.


No deliberate misquote. No troll. I was just pointing out what seemed to be bias in you comment.

Again, the article was badly written. We just differ in opinion on the substance and therein lies the rub I suppose.

In our highly charged social climate this is not surprising.

I wish you well.


This has been fun and a good chuckle. I needed that so, again, thank you.

Let me fix this for you for your own edification:

"Please don't refuse to explain your position to me even though I've already proven I won't hear a word you say! I promise I won't listen again."

"I can't see my own biases so I can't understand anyone explaining them to me. Please don't try to explain them, it's upsetting!"

"I hate it when people peg me with my own words! Just let me use my anonymity to help you ignore my everything I've just said!" waves hands

"I resent it when people try to be nice or acknowledge my attempts at communication after I've insulted them, I won't let you!"

Oh and your last insult is a real gem... :)

"Since I lack real substance in my positions, I cannot see or acknowledge any substance from any alternate point of view"

As as side note, brick walls are fun conversation only if you're interested in hearing an echo ;)

(Of course that all depends on the acoustics of the space as well but I digress)

Regardless of it all I'll say it again, had the original commentor been more altruistic in his take, I'd say you gave thoughtful feedback. I had thought your comments were well-meant initially in regards to clarifying that commenter. I had even acknowledged some ideas (we agree the article was not well written even if we differ on the substance). However by your words it's shown that wasn't your real intention - you being more interested in defending the negative bias of the comment (and it was negative) than the underlying content of the comment.

I do wish you well.


I have more respect for her and her work than to use her as a prop for a poorly made point, which is what the author has done.

> Your comment seems dismissive and full of bias.

I stand entirely behind my dismissal of this article.


>"there is a bit about her contribution which is over inflated"

I guess your comment read as dismissive and disrespectful of the mathematician and the idea of equal opportunity on multiple levels.

And while I don't think it was a "great" article, I stand entirely behind my dismissal of your comment.


Explain why you're misquoting me. You even stop the quote mid clause. I can only construe this as a deliberate misrepresentation of what I said.

I disagreed with the article, which is quite clear in the literal words I wrote. You chose to attack me instead.


[flagged]


Yes, but should white men have all of the opportunities though? That's the point of the article.


Classic HN baiting; I predict the comments will be over 50% meta-commentary about the title's inaccuracy and possibly something about the principle of highlighting female mathematicians, a sizeable chunk on suggestions for female mathematicians with a larger impact, and very little about Geiringer, her mathematics and her legacy...


It's incredibly unfortunate that you're correct, but I'm also not surprised.

Topics like these on HN inevitability devolve into complaints about the media or attempting to divert discussion into something entirely different (like missed male geniuses). Nevermind the pun people missed in the article title as they immediately jumped to attempt to discredit the entire thing.




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