Is Math a Young Man's Game? (2003)
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There are quite a few female mathematicians who made important contributions. My wife wrote a top 10 of sort on my blog a few years ago: http://math-blog.com/2008/09/28/10-remarkable-female-mathema...
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.
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.
But we can't forget that there are huge brain changes when you are young.
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.
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.
> "Topology ignores such things as corners, distances, and convexity."
No, that's what topology is.
> "That makes it hard to combine with GIS systems."
No, GIS systems rely heavily on topology. Here are two definitions:
Topology: 1. the study of geometric properties and spatial relations unaffected by the continuous change of shape or size of figures.
Topography: 1. the arrangement of the natural and artificial physical features of an area.
- 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.
[1] http://en.wikipedia.org/wiki/Kriging [2] http://en.wikipedia.org/wiki/Contour_line
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.
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).
A major breakthrough in his primary field (computer science) came about because of a wide (rather than narrow) field of study.
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.
(edited for spelling)
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.
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.
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:
https://www.physics.harvard.edu/people/facpages/randall
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."
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.
The Nobel Prize is well known for being sexist.
http://news.nationalgeographic.com/news/2013/13/130519-women...
>Men have invented every major technological advance in history.
One counter example http://en.wikipedia.org/wiki/Grace_Hopper
Actually http://www.maximumpc.com/article/features/15_most_important_...
http://en.wikipedia.org/wiki/Timeline_of_women_in_mathematic...
Sexism is still alive and well
http://blogs.scientificamerican.com/unofficial-prognosis/201...
>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.
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.
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.
And each team has a book. You know.
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.
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.
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.
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.
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.
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.
Where exactly are you pulling this from?
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 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.
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.
Marie Curie [2] was awarded two Nobel prizes.
Emmy Noether [3] is known as the mother of modern algebra, a pretty important field, and part of the foundation of many applications today.
Some others of interest are Rosalind Franklin [4], Beatrice Schilling [5], and Barbara Liskov [6]
[1] http://en.wikipedia.org/wiki/Hedy_Lamarr
[2] http://en.wikipedia.org/wiki/Marie_Curie
[3] http://en.wikipedia.org/wiki/Emmy_Noether
[4] http://en.wikipedia.org/wiki/Rosalind_Franklin
That's a ratio of 100 to 1.
Now go look at the leaders in philosophy, business, politics,and basically every major field ever.
There will be the few women chestnuts but the ratio will be the same.
But go look in homeless shelters. Also mostly men.
Women have resource aquisition built into their bodies so they're never at the bottom but they also don't have that drive to ascend to the top.
> 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.
HAD to contend with....
In modern times women outnumber men in college.
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?
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.
>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.
Can't argue with that.
And you have completely failed to make the case for this.
> Can't argue with that.
You realize that I said that there's a pretence that they have the FREEDOM to do anything, not that they are intrinsically incapable it, don't you?
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 modern times women OUTNUMBER men in college yet the ration of women to men in STEM is abysmally low.
This isn't sexism this is factual. I'm trying to find an explanation besides: 'Science is filled with sexist pigs so that's why women avoid it.'
I'm just finding it harder to agree with the 'women are victims' stance the more I critically think about the situation.
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.
Do you think you can you guess what it is?
Because STEM is filled with 'sexist pigs' so women avoid it?
Or because women are wired differently?