(2003). I have a simple theory. Math is not a young man's game, but math at these levels is extremely demanding and all consuming of one's mind. As you get older life gets more complicated, you get a wife, kids, dog, etc. Your mind is no longer focused on one thing and one thing only. So it's exceptionally rare to see someone with a normal life do extraordinary discovery in mathematics past a certain age. Paul Erdős is often mentioned as a counterexample to the young mathematician. Yet, Erdős pretty much lived for mathematics and didn't really have a set place let alone a normal life with wife and kids. I'm not saying that this is the only contributing factor, but I'm willing to bet it's a big one.
The thing I find fascinating about both this article and now your comment is that regardless of who's game it is, it seems to be taken as fact that it's a MANS game. You said "you get a wife"...I suppose history isn't littered with too many breakthrough female mathematicians.
I believe the article followed Hardy's quote, and I followed the article lead. I realized after posting that it might be seen as male oriented but I believe the same is true for female mathematicians.
I'll happily look down on applied mathematics, but classifying Emmy Noether as only a physicist would be ridiculous, as a large part of her life's work was indeed pure mathematics. I can't imagine the abuse of history needed to assert otherwise.
And remember, even Hardy, most famous of the Purists, often slummed it with (hold your nose) physicists and on a few occasions even with (the horror) biologists.
I don't believe it's not about "not caring". I think it's more about having a finite number of productive brain-cycles per day, and what you spend them on (opportunity cost).
If you spend all day thinking about others, you won't get any math done. If you spend all day thinking about math, you won't be in tune with others. If you can balance things out properly, you can do both.
Sometimes it's necessary to go to one extreme for a long period of time. If you're working on a really hard problem, it might be best to isolate yourself from society for days/weeks/months at a time to figure it out. If a close family member is stricken with a major illness like cancer, it might be best to focus and spend your thoughts, time, and emotions entirely with them.
In reality it's usually a balancing act between different things. But you can understand why it's sometimes necessary to go to extremes.
I also think that in the adult life you search positive feedback in other critical things like life standard. When you are young it is enough to receive positive and easy feedback in your family or school. I recommend to read the Kasparov's book: how life imitates chess (not the best title) where he mention different chess player personalities and ages.
But we can't forget that there are huge brain changes when you are young.
In the same vein as Kasparov's book, there is this interview of Kramnik where he talks about the world champions before him [0]. It's interesting how he explains how different qualities can offset each other, for example, discipline and creativity.
I agree. Math seems to be a one man or two man show, so you need to be absolutely focused on what you are doing.
Businessmen can delegate and use the system set up in their young adult years to continue their trajectory. Franchising is an example that comes to mind.
I have always admired Paul Erdős, a really interesting life doing something he loved.
About 6 months ago I began writing a library[1] that focuses on topology (much of what was discussed in the article) and geospatial stats. I am by no means a math genius, and my library does nothing too novel from a mathematical perspective. Still, it has been nearly all consuming to grok the immense amount of math that goes into this sort of thing. I can only imagine the creative energy it must have taken to actually design these algorithms from scratch.
As far as I can tell, your library does topo_graphy_, not topo_logy_. Topology ignores such things as corners, distances, and convexity. That makes it hard to combine with GIS systems.
No, topology often focuses on things that are invariant under such things as corners, distances, and convexity, which can make it an extremely useful tool in a field awash in such concerns.
While many would classify the GP's library as one primarily concerned with computational geometry (but certainly not topography), there are large overlaps of computational geometry with computational topology. Many topology results won't be useful in an applied field like GIS, but other results will be extremely useful as they work regardless of the mess of real world measurements.
Classification of branches of mathematics is a losing game, anyway. You try to separate two bodies of work, you'll invariably find someone's extensive results that straddle the boundary.
Actually it deals with both. Primarily it deals with topology and statistics in the context of topography and geography. The concepts addressed by topology are essential to any GIS engine. There are actually several definitions of topology, and turf actually touches on most of them:
- basic topology like detecting whether or not a point lies within a complex polygon
- topological morphology, such as smoothing a line or polygon while maintaining boundaries (this is probably the most common definition in the GIS world)
- topological interpolation, such as estimating z values over a 3d mesh[1][2] (there are a number of methodologies here, and this represents probably the most interesting intersection of topology and statistics)
Also note that turf is geared towards GIS, but most of the underlying operations are not GIS specific and apply to geometry more generally. You will find many of the same algorithms in applications like game engines, for example.
I think the point is that none of these are topology in the mathematical sense. They're computational geometry. In my view that's still one of the most difficult fields of mathematics (precisely because the algorithms rely on extremely complicated data structures), but it's not topology.
If you are groking topology in the mathematical sense, you'd be talking about concepts like (co)homology and homotopy groups, and be doing quite a lot of commutative algebra. You definitely would not care about statistics and point location.
(co)homology and homotopy are specific to algebraic topology. There are several other types. Regardless, these sorts of discussions have convinced me that the semantics regarding these subjects are extremely muddy. I am by no means an expert, and tend to try to stick to the meanings conveyed by colleagues with more experience and/or wikipedia :)
My library is definitely not a topology library. I tend to describe it as a geospatial processing engine. My first comment was really only meant to speak to some overlap I noticed with the topology described in the article, and to convey my deep respect for the people who have a more full understanding of the low level mathematics involved (which it sounds like you might possess).
The code samples used to demonstrate that library loads a trees.geojson file with features like 'oak' and 'maple', so I think he definitely meant 'topography'. What makes you say it's a topology library?
See the authors comment above. The library does do a lot more than topology, but the see the sections titled: joins, measurement and transformation. These are all topological functions.
Similarly, I believe, due to the vast amount of information accumulated in all different fields in the last century or so, polymaths have simply ceased to exist. The last true polymath I know of was John von Neumann. I guess it just can't be done anymore.
On the other hand, it would seem that many of the top experts today are masters at mashing up the frontiers of multiple fields. Just think of all of the applications of Neuroscience + X (CS, Philosophy, Psychology, Chemistry, etc.). Sure, there are few (no?) people today that can claim mastery of 10 or 20 fields, but most of the cutting edge research does seem to require expert knowledge of 2 or 3.
I'd put Alan Kay forward as a living polymath. It's a shame that research has become siloed -- so many great discoveries came about because someone had insights perpendicular to their field.
Are you talking about Alan Kay as in https://en.wikipedia.org/wiki/Alan_Kay ? He doesn’t seem to have made any major contributions to physics, mathematics, the natural sciences or basically any other field, apart from software engineering.
Polymath needn't mean 'makes major contributions to multiple fields' (though, of course it, it can.) It means someone has deep knowledge across a wide array of subjects, and typically draws inspiration from fields which are orthogonal to their primary field of interest. In Kay's case, it's applying the concepts of biology, genetics, mathematics, and architecture, to computer science, to create Object Oriented Programming.
A major breakthrough in his primary field (computer science) came about because of a wide (rather than narrow) field of study.
In my view the simple explanation that there's more to learn before reaching the cutting edge seems credible.
Biology is another area. I live in a town where there's a lot of biology research, and there are start-up businesses, but they aren't formed by kids who skipped college to get rich. Instead, the typical start-up founder could be anywhere from 40 to 60. It takes a long time to learn biology.
Another possibility to consider is that math research takes more time now because it resembles more of a search than an inventive process. If proof is computer-aided, for instance, then an Edisonian approach could be applied to finding a proof for a theorem (or at least, finding important steps), resulting in discovery of proofs being a matter of time, even for the most brilliant mathematician.
Make no mistake, math research is very much an inventive process.
In particular, it's much more than just proving theorems. Mathematicians need to come up with ideas worth investigating, and that (in addition to writing proofs) often requires creativity.
I've thought about this for the last few months. I'm in my 30's and never really cared about math until the last couple years. I'm discovering that it has become somewhat easier now for me to understand and learn new math. I had the usual engineering calc set and hated it. But now that I actually have some goals associated with it I have been able to make progress. I've been particularly interested in ASR and AI/ML. I was deficient in the math needed for it but now I'm getting up to speed rapidly. I think the key is to have had some in-depth exposure to math earlier in life though.
I think ageism is implicit in modern Western culture. The Fields Medal has ageism built right into it: "a prize awarded to two, three, or four mathematicians not over 40 years of age." Source: http://en.wikipedia.org/wiki/Fields_Medal
However, skimming down the list of Abel Prize winners, those guys are no spring chickens, and do great work in mathematics well into their senior years.
Everything in this article is about youth, not being male, so I don't get why they chose to put "Man" in the title. Are there not any young women born as genius?
He is referencing a quote by G.H. Harding "No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game." Try reading the article before getting insulted.
Mathematics and mathematical physics have many accounts of brilliant female mathematicians. The first computer programmer was a woman (Ada Lovelace: http://en.wikipedia.org/wiki/Ada_Lovelace), at a time when programming was almost purely mathematical. In spite of serious obstacles throughout history, examples abound. My favorite contemporary example:
Quote: "Professor Lisa Randall studies theoretical particle physics and cosmology at Harvard University. Her research connects theoretical insights to puzzles in our current understanding of the properties and interactions of matter. She has developed and studied a wide variety of models to address these questions, the most prominent involving extra dimensions of space."
Only 5% of nobel prizes have gone to women, and this includes literature and peace prizes. I'm sure if you narrow it to pure STEM it's much lower.
Men have invented every major technological advance in history. If you look outside your window all the roads, all the buildings, cars, aeroplanes, cell phones, etc.
All men.
My theory is not that women are dumber, it's that the fight for survival is not there for women. They can just have a man pay their bills in exchange for sex.
Actually by seizing that advantage it makes women seem actually smarter..... and they live longer too.
>But in a groundbreaking study published in PNAS last week by Corinne Moss-Racusin and colleagues, that is exactly what was done. On Wednesday, Sean Carroll blogged about and brought to light the research from Yale that had scientists presented with application materials from a student applying for a lab manager position and who intended to go on to graduate school. Half the scientists were given the application with a male name attached, and half were given the exact same application with a female name attached. Results found that the “female” applicants were rated significantly lower than the “males” in competence, hireability, and whether the scientist would be willing to mentor the student. The scientists also offered lower starting salaries to the “female” applicants: $26,507.94 compared to $30,238.10.
We are not talking about equality of outcomes here; this result shows bias thwarts equality of opportunity.
Lol you do realize for every Grace Hopper and Ada Lovelace chestnut you pull out of the back of the drawer I could literally name hundreds and hundreds and hundreds of men who have done something similar? There's always a tiny few outliers in any study.
Once again I say look out your window. Everything invented and built by men.
And I used to agree with you in regards to institutionalized discrimination.
But the more I thought about it....it's VERY VERY hard to believe that there's some sort of international century long conspiracy of white men that get's together and represses women in every industry, career,country,time frame and scientific field EVER.
I'm not arguing that women are inferior in any way.
I just think that women aren't as ambitious as men due to ease of resource acquisition that they have built in to their bodies and it's really that simple.
Keep in mind the ratio of women to men in homeless shelters is like .000001 percent.
it's VERY VERY hard to believe that there's some sort of international century long conspiracy of white men that get's together and represses women in every industry, career,country,time frame and scientific field EVER.
Looking about there are many and varied ones and they seem to have been going a lot longer than that, not all of them are run by light skinned folk though.
Quite often their leaders wear elaborate hats, you must have seen them on the telly. Is not all they do, but it does seem to be a theme.
You must have seen them, they have loads of pointy buildings everywhere, with slightly different styles to show which team they are on.
It's also possible that the scientists correctly infer that, even conditional on having the same resume, female applicants were overall of a lower quality.
The study doesn't prove whether this disadvantage comes from people discriminating against women merely because they are women, or people correctly identifying that the women on average perform worse, even given the same resumes. It is still possible that given full information about the candidate, (not just the resume), women would not be disadvantaged.
> It's also possible that the scientists correctly infer that, even conditional on having the same resume, female applicants were overall of a lower quality.
Somehow you missed the point that, in the experiment, only the names were changed -- the resumes were identical, the applicants were identical, the level of experience and education were identical. Only the names were changed. The reviewers therefore judged the applicants only on the basis of gender. That's both wrong and illegal.
> The study doesn't prove whether this disadvantage comes from people discriminating against women merely because they are women ...
That is exactly what the study proves. Exactly. As in all good science, only one element was changed -- the name of the applicant. The reviewers changed their evaluation based solely on the applicant's gender, nothing else.
Let me clarify the the alternate explanations for this study:
The researchers are aware that women on average perform worse than men, even given the same resume. As a general principal, this is not ridiculous, e.g. a female boxer will perform worse than a male boxer, even given the same height and weight. You personally might believe that a resume so perfectly captures the qualities of a person, that the person's gender is no longer relevant once you have seen the rest of the resume. But that is just your opinion.
So the professors are discriminating against women, but not for its own sake, but because they believe that statistically, even given the same resume, the woman would on average perform worse. See http://en.wikipedia.org/wiki/Statistical_discrimination_%28e...
This kind of discrimination does not actually make women on average worse off, in the sense that it only penalizes them for their actual inferior performance, not for being women per se.
On the legality, I don't know if it is legal or not. I'm guessing it is illegal but in my opinion those laws are wrong anyway.
> You personally might believe that a resume so perfectly captures the qualities of a person, that the person's gender is no longer relevant once you have seen the rest of the resume. But that is just your opinion.
Which part of this are you not getting? THE EXACT SAME RESUME WAS PRESENTED, ONLY THE NAME WAS CHANGED. Consequently, the test subject's responses measured sexism, nothing else.
> I'm guessing it is illegal but in my opinion those laws are wrong anyway.
At this point anyone can see what is wrong -- you don't understand the topic of discussion.
It really depends on your definition of sexism, which is an ambiguous term.
Suppose it were true that given a woman and man with the same resume, the woman tended to perform worse. It would them be rational to assume that, given two otherwise identical resumes, the one with the female name represented a worse candidate. To act on this information is statistical discrimination. I highly recommend you read the article.
> It really depends on your definition of sexism, which is an ambiguous term.
Sexism is very clearly defined, so clearly that it can and does appear in the law, laws that, under our constitution, cannot exist if they contain any ambiguity.
I can't believe you don't get this. Researchers take a resume and present it in two forms -- for example, in one resume the name is "Andrew Jones". In the other, the name is "Andrea Jones". NOTHING ELSE IS CHANGED. One letter of one word is changed, and suddenly the applicant is unqualified. That is sexism defined.
> I highly recommend you read the article.
I read the article, you very clearly did not. Above you believed that the resumes differed, that they actually described different people with different qualifications. That wouldn't be science. In science, for maximum effect, you change as little as possible and measure the outcome.
The study measured, not reality, but people's attitude toward reality.
I'm giving an alternative explanation for why the female named resumes are rated worse by the professors.
I'm "pulling it from" the same place you pulled your preferred explanation (that female performance conditional on the same resume is the same, and so the worse ratings were due to professors preferring males, even given the same performance, or incorrectly expecting worse performance from the females).
The issue with your interpretation of the study is your selective appeal to evidence.
You would like to provide evidence for the fact that worse outcomes for females are due to discrimination. But the evidence you provided is consistent with both explanations (discrimination vs actually worse performance from females)
I asserted that both explanations are possible, which is an obvious fact to me, until it is shown that one of the explanations is wrong.
I didn't notice I was replying to you, not aestra, who implicitly explained the results of the study in the way I described, when they used that study as evidence that "sexism is alive and well". Even though in this particular study, the authors (incorrectly) ignored my alternate explanation, it is in fact often discussed in this context (see http://en.wikipedia.org/wiki/Statistical_discrimination).
And I am sick of your side of the argument swearing at your opponents while constantly playing the victim card. Fuck you.
I haven't said much here, barring taking the piss out of the magic man (he's crap at magic) and posting about Freeman Dyson doing his thing with the prisoners dilemma. There are always many perspectives you can take, to insist on binary debates is just forcing false choices. Calling me a cunt won't really change that.
As for why I asked you to stop being a tosser in the first place, I asked a question and immediately had you telling me what I supposedly think. That said, I really shouldn't have bothered asking you to stop, as to do that does seem to be something that is far wide of your abilities, given the evidence available here.
I'm having a really hard time convincing myself that you are not trolling here.
> they also don't have that drive to ascend to the top
Do you have any idea of what kind of barriers were in the way of those female prize winners and other academics like Marie Curie and Emmy Noether? They not only had to be world class in their fields, but had to do all their work in the face of constant sexist resistance. Look at what Curie and Noether had to put up with. They only got recognized for their achievements when a lot of their colleagues petitioned for their recognition. Noether had to lecture under an assumed name, for instance. If it hadn't been for the pressure exerted by some of their sympathetic peers, we might not know about their achievements as being THEIR achievements. Look at Rosalind Franklin, unrecognized for a long time and still mostly unrecognized. Do you think that they are the only ones, that there were not other women whose achievements were basically usurped by male colleagues, something possible due to the sexist environment they had to contend with?
You are maintaining that if women were as capable as men, they'd be equally represented, and are completely denying the remarkable barriers that they have to simultaneously overcome, and when we point to some women who managed to be world class in the face of these recognized barriers you claim that they are just outliers. First you say everything of importance has been done by men, and when counterexamples are pointed out you dismiss them as irrelevant. You are clearly a fanatic, nothing we can say will convince you otherwise.
I am not actually responding in order to convince you of anything, just to refute your claims for anyone who might read this in the future.
Still 1:100 ratio of women majoring in Math and Science.
Still a ratio of 1:100 Nobel prizes to women.
It's kind of hard to blame the 'sexist environment' of the past half century where women are free to do any thing they want yet nothing has changed....
So where does that leave your argument?
Maybe women just are wired differently than men.
Is that idea allowed into the 'women are victims' circle jerk?
> Men have invented every major technological advance in history.
That was your original statement. It has been refuted pretty well. Now you are changing your assertion without admitting it.
Actually, we still have a pretty sexist environment, and women aren't really free to do any thing they want. There's a pretence that they can do anything, but it isn't really true in many ways.
My argument is still perfectly sound. You are just ignoring the bits of it you don't like.
For all your talk about "facts" you seem to be particularly blind to the ones that have been offered to counter your vague arguments, both here and elsewhere in this thread: verifiable matters of historical record.
My argument is that women's lack of economic success is in part due to how they are wired and not some widespread culture of male repression.
>Actually, we still have a pretty sexist environment, and women aren't really free to do any thing they want. There's a pretence that they can do anything, but it isn't really true in many ways.
Wild speculation that {women|older people|Black people} are inherently less inclined/capable in a field, is baseless discrimination. Wild speculation that {men|younger people|White people} are inherently less inclined/capable in a field, is stimulating discussion. Just a heads up for when the downvotes come.
It's funny how so many of these HNers are so quick to jump the gun and join the "women are oppressed" circlejerk, and when someone disagrees, they call THEM sexist.
Do you all not remember high school? Don't you remember wondering why all the girls go for the football jocks and musicians? Don't fool yourself; engineers are boring. Engineering is isolating. That's why there are barely any female engineers.
You don't see people wondering why there aren't as many male kindergarten teachers.
In my opinion, if you agree with the 'women are victims' stance with regards to STEM, then you are sexist. It's basically a backhanded way of saying men are superior to women, when most women simply are just not interested in the field.
People seem to forget that men and women are fundamentally different. They have different interests and different goals in life. There is nothing wrong with that, and it doesn't need to be "fixed".
Here's a fact for you: There's tons of evidence in the testimony of MtF and FtM transgender people. A lot of MtFs simply lose interest in the sciences when they go on hormones.
