Feynman is not my hero

There has been some discussion going around about the character of physics heavyweight Richard Feynman, and whether we should really be treating him as an idol when he has such a well-documented history of terrible behavior towards women. Matthew Francis has an excellent post on Galileo's Pendulum dealing with the implications of this kind of hero-worship, as does Janet Stemwedel of Doing Good Science.

In Stemwedel's article, she makes a point that really resonates with me:

"You may be intending to convey the message that this was an interesting guy who made some important contributions to science, but the message that people may take away is that great scientific achievement totally outweighs sexism, racism, and other petty problems.

But people aren’t actually resultant vectors. If you’re a target of the racism, sexism, and other petty problems, you may not feel like they should be overlooked or forgiven on the strength of the scientific achievement."

I am one of these people.

Early in my undergraduate studies, I was hired by a member of my university's faculty to do a video editing job for a set fee. when I got the material I was supposed to be working with, it was in such poor condition that I realized I could not do what I was hired to do in the time frame allotted, and so I told him I needed more time (and thus more money). He flew into a rage and refused to pay me for the work I had already done, demanding to know my home address so that he could "come over right now and get his equipment back" - this demand was made at 11:30pm. I told him that I would instead meet him the next day at a coffee shop, and when I did, he leaned in and screamed in my face - yelling about how I was "unprofessional" and (I remember this most vividly) calling me a "stupid little girl". At the top of his lungs, in a popular cafe near campus. I remember that mixed in amongst the shock, fear, and embarrassment that I felt upon being treated this way, was relief that I had not told him where I lived the night before. I ended up taking a leave of absence from school due to the stress of dealing with him (and the money issues resulting from not getting paid for my work.) He now runs a research lab.

A few years later, I worked at a major tech company where a customer threatened me physically and threatened my job (he was a lawyer, he was friends with my boss, he was important and I was expendable, etc.) I was a top ranked employee with a relatively long work history, and there were witnesses. I was told by management that I'd have to continue working with him. Fun times. I ended up leaving that job, too.

I have had men in academia disparage me to others, and dismiss both my interests and accomplishments as trivial. I regularly deal with comments like "PRO TIP: Mute the video, sit back, and admire the cute girl" regarding my outreach work. I have had jobs (multiple) where I was harassed and propositioned by my own boss. I have been on dates (again, multiple) with men in both tech and academia that resemble this account. (Trigger warning) I have had men on Twitter and Facebook threaten to rape me, kidnap me, and tell me they hoped I would die, all because I'm a woman who talks about math (and is really not into nerd wish-fulfillment).

And there is a whole lot more that I don't feel safe sharing. Think about that for a minute.

So why am I even sharing this much? Because this is where I'm coming from. Today, in 2014.

Because every time I hear someone in my department or in one of my classes go on about how Feynman was so awesome I mean he was kind of a jerk to women but whatever, I file him (and it is almost always a him) away as someone who would have sided against me in every single one of the situations I've mentioned. Every time I see a joking tweet or post about how Feynman's second wife divorced him because she didn't like that he was always doing calculus in his head, while totally ignoring the fact that the divorce papers indicate that he would fly into a rage, attack her, and break furniture whenever she interrupted said mental calculus, my world gets a little bit smaller.

Now, that may not be totally fair to every Feynman fan out there, but let me tell you, life as a woman in phenomenally male-dominated fields is pretty damned unfair. I put people into boxes about stuff like this - not because I think all of the people who hero-worship Feynman (and countless other mathematicians/scientists with similar track records) approve of how he treated women, but because there are actually some that do. As in, there are people today who think that lying to women and treating them like prizes to be won is totally fine. And some of them are researchers, professors, PhD candidates. And I know from personal experience that if I found myself once again in a situation where a prominent man was abusing his power, there would be people who would bend over backwards to protect his reputation, to the detriment of mine. That is the ugly side of hero worship. People like me get the message that great scientific achievement will totally outweigh reprehensible and hurtful behavior towards, well, people like me.

Feynman did amazing work, it's true. Talking openly about the uglier aspects of his life doesn't diminish that. But glossing over his reprehensible behavior towards women, or trying to explain it away, alienates those of us who have had to struggle with that same behavior from our own friends and colleagues.

And there's more of us than you'd think.

A Mathematical History Tour

(One of my favorite series in Scientific American  was James Burke's "Connections" (Later collected into the book Circles). This is a sort of homage to those, for math enthusiasts. There will be more.)

*Note: An earlier version stated that Archimedes was from Seneca, which was in error. Archimedes is from Syracuse. And I live in Ithaca, New York, which is south of Syracuse and east of Seneca Lake (both in New York). Hence my confusion! Mea culpa. (and thanks to Chris Maslanka for pointing it out.)

In 1906, Danish historian J.L Heiberg was inspecting a religious text from the thirteenth century, when he made an astonishing discovery – the traces of mathematical symbols that could be seen on the parchment were from the lost works of Archimedes of Syracuse. Archimedes was a third-century Greek mathematician who was known for his work in mechanics, and for the legend of his death (one account says that he was working on a mathematical problem during the siege of Seneca when a Roman soldier burst in to his study – Archimedes yelled out “don’t disturb my diagrams!” and the soldier responded by running him through with his sword. Seems a tad aggressive, if you ask me. Maybe the soldier had math anxiety.) In the thirteenth century, a manuscript containing transcriptions of Archimedes' work was scraped and washed to make a Christian liturgical text. (This was a pretty common practice in the early middle ages, since parchment was so expensive - these recycled texts are called palimpsests.) Often, traces of the original text would still be visible, and historians could restore the original text - so, nearly 700 years later, the Archimedes palimpsest was recognized for what it was, and the underlying text was translated. 

Among other works, the palimpsest contains a manuscript called “On the Sphere and the Cylinder.” In it, Archimedes gives a method for finding the surface area of a sphere which uses a technique that closely resembles a modern technique (Riemann summation) named after nineteenth century mathematician Bernhard Riemann – famous for the Riemann Hypothesis, one of six (originally seven) unsolved problems in mathematics for which the Clay Mathematics Institute offers a $1,000,000 prize for a proof or solution. You would think, given his inclusion on such a list, that he was one of those precocious whiz children that wowed their teachers with mathematical insights from the time he was a child, and (at least in this case) you would be right. However, Riemann initially went to university to study theology, and had to be convinced to drop it for mathematics by mathematical heavyweight Carl Friedrich Gauss. 

This is itself impressive, as Gauss, though an extremely prolific and influential mathematician, reportedly hated teaching and thus took on very few students in his life. Gauss was a perfectionist of the highest order, often failing to publish important mathematical results until after he died they were perfectly polished. As a result, mathematicians with exciting new discoveries in the field were often disappointed to find that Gauss had already proved their results (though I do wonder whether some of that was just talk on Gauss’s part – he tended to exaggerate his claims of priority in his correspondence). In one such case – that of Russian mathematician Nicolai Lobachevsky, and his work in non-euclidean geometry – Gauss claimed to have known of the results for 54 years! He even goes so far as to write in correspondence that “there was nothing materially new for me in Lobachevsky's paper.” (I raise my eyebrow at that claim, since Gauss reportedly collected all of Lobachevsky’s known work, and then taught himself Russian in order to read it. You don’t do all of that for “nothing materially new.”)

Lobachevsky’s name was also (perhaps unfortunately) immortalized by Tom Lehrer, a satirical singer-songwriter active in the 1950s and 60s. (Lehrer holds a special place in the hearts and minds of scientists everywhere for the song "The Elements", where he set the names of the chemical elements to the tune of the "Major-General's Song" from Gilbert and Sullivan's Pirates of Penzance.) Trained as a mathematician, Lehrer wrote many songs with mathematical themes, and “Lobachevsky” was one of these. It tells the story of a mathematician who climbed his way to the top of his field by plagiarizing the work of others, and then publishing before they could claim credit – this unnamed mathematician claims to have learned this skill from Lobachevsky (even though there is no evidence that Lobachevsky ever did such a thing):

Let no one else's work evade your eyes
Remember why the good Lord made your eyes
So don't shade your eyes
But plagiarize, plagiarize, plagiarize!
(Only be sure always to call it, please, "research.")

And ever since I meet this man
My life is not the same
And Nicolai Ivanovich Lobachevsky is his name! 

Lehrer is, as of this writing, still around, though he hasn’t written new music in decades. I would say that he’s 86 years old, but he prefers to calculate his age in Centigrade (so he’d say he’s 30, despite being born in 1928). The Centigrade system was developed (as a measure of temperature, not age!) by Swedish astronomer Anders Celsius, who travelled with Pierre Louis Maupertuis on an expedition to Lapland to determine the exact shape of the earth. The success of this expedition led to Maupertuis being tapped to run the Prussian Royal Academy of Sciences alongside a partially blind Swiss mathematician named Leonhard Euler. Euler, like Gauss, was an intensely prolific and formidable mathematician – his work covered (among other things) calculus, optics, fluid dynamics, astronomy, and even music theory. Euler tackled (and proved) Fermat’s Little Theorem, which Pierre de Fermat had stated without proving it himself (this was a bad habit of Fermat’s – one other theorem of his, found in the margins of a book after his death, took mathematicians over 350 years to prove). 

Just before he died, Fermat published a paper on analytic curves, which included a type of logarithmic spiral that became known as the Fermat spiral. Fermat spirals can be found as patterns in the heads of sunflowers, and is closely related to the Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.( For a long time, it had been noticed that these numbers were important in nature, but only relatively recently has it been understood that this is due to efficiency during the growth process of plants.)

This sequence was also studied extensively by French Mathematician Edouard Lucas, who, in his spare time, developed mathematical puzzles. The most famous of these was called the Tower of Hanoi – which, according to a paper published in 2010, can be solved by a species of Argentine ants using non-linear dynamics.  (Yes, ants. Doing non-linear dynamics. I find that to be a humbling thought, since I can barely keep up with my laundry.) Unfortunately, in 1891 Lucas attended a banquet that would spell his doom - while he was there, a waiter dropped a dining plate and one of the pieces bounced up and cut Lucas’s cheek. This being Europe in the late 1800s, Lucas died within the week due to a form of septicemia*. (Bummer.) 

Lucas was well regarded, and his obituary was printed in Popular Science Monthly the following January. This same issue featured a delightfully enthusiastic article entitled “The Aviator Flying-Machine” by one Gustave Trouvé, who was heralding the end of balloon flight – “let us always keep in mind that we shall thank it as soon as possible for its services and show it the door”  – and the start of a new era of heavier-than-air flying machines, like… mechanical birds. Don’t laugh – apparently, the study and design of mechanical birds was an important part of aeronautics research at one time. So much so, in fact, that aviation pioneer (and mentor to the Wright brothers) Octave Chanute not only reproduced Trouvé’s design for a mechanical bird in his book Progress in Flying Machines, but devoted a considerable section of the book to calculating speed and horsepower of various birds: 

"Napier assumed that a swallow weighing 0.58 oz. must beat his wings 2,100 times a minute while going 33 ½ miles per hour, in order to progress and sustain his weight, and that it therefore expended 1/13 of a horse power. In point of fact, the bird only beats about 360 times a minute, and is chiefly sustained by the vertical component of the air pressure on the under side of the wings and body… "

(Note: I have read the book cover to cover, and was disappointed to find that there was no mention of African vs. European, or laden vs. unladen swallows. Surely a great scientific opportunity was missed.) 

In this same book, Chanute describes the work of Sir George Cayley, an English aviation pioneer. This Cayley was the distant cousin of Arthur Cayley, a professor credited with founding the modern British school of pure mathematics. One of the many abstract concepts Arthur Cayley worked with were the quaternions, an algebraic group first described by Irish mathematician William Rowan Hamilton in 1843. Or, at least, the description was first published by Hamilton – a review of Gauss’s unpublished work shows that he worked on something similar as early as 1819. (I’m assuming that if he had been paying attention, he would have undoubtedly told Hamilton that he knew about the math behind the quaternions for 50 years or so, and there was nothing materially new in Hamilton's work. Remember Lobachevsky? Gauss was kind a of jerk like that.)

In fact, one of the precious few to receive unqualified praise from Gauss was an obscure French mathematician named Monsieur LeBlanc – in a letter to a colleague, Gauss writes that LeBlanc had studied Gauss’s works in number theory “with a true passion… and has sent me occasional very respectable communications about them.”  Gauss corresponded with Monsieur LeBlanc for three years before discovering that LeBlanc was actually a woman named Sophie Germain – upon discovering this, he wrote a letter to Germain, in which he expresses his admiration: 

"When a person of the sex which, according to our customs and prejudices, must encounter infinitely more difficulties than men to familiarize herself with these thorny problems, succeeds nevertheless… then without doubt she must have the noblest courage, quite extraordinary talents, and a superior genius."

Germain did indeed have a great deal of courage and determination – she began to study mathematics as a young woman, confined to her family’s house during the French Revolution. Her family did not approve – going so far as to put out her fire (and even take away her clothing!) in order to force her sleep instead of study. She thwarted them by wrapping herself in blankets, and, waiting until everyone had gone to bed, studying by candlelight. What inspired her to pursue mathematics with such passion? She had read an account of the early death of a Greek mathematician who was killed by a Roman soldier – none other than Archimedes of Syracuse.

*According to his obituary, Lucas died of erysipelas, which was also commonly known as "Saint Anthony's Fire." Thanks to @OnThisDayinMath for this bit of info.

References (for anyone who wants them)

Chanute, Octave. Progress in Flying Machines. Toronto, CA: General Publishing Company,
Ltd., 1997.

Edwards, Harold M. Fermat's Last Theorem: A Genetic Introduction to Algebraic Number
. New York, NY: Springer Verlag, 1977.

Fellmann, Emil A., Gautschi, E., and Gautschi, Walter. Leonhard Euler. Basel, Switzerland:
Burkhauser Verlag, 2007.

Knoebel, Art. Mathematical Masterpieces: Further Chronicles by the Explorers. New York, NY:
Springer Verlag, 2007.

Osen, Lynn M. Women in Mathematics. Boston, MA: Massachusetts Institute of Technology,

Pickover, Clifford. Archimedes to Hawking: Laws of Science and the Great Minds Behind Them.
New York, NY: Oxford University Press, 2008.

Reid, Chris R., Sumpter, David J.T., and Beekman, Madeleine. “Optimisation in a natural
system: Argentine ants solve the Towers of Hanoi.” The Journal of Experimental 
. January 1, 2011.

Stillwell, John. Mathematics and its History. New York, NY: Springer Verlag, 2010. 

Trouvé, Gustave. “The Aviator Flying-Machine.” Popular Science Monthly vol. 40. January


And now for a completely different rant...

I noticed that there was a juicy little tidbit in Nature that had my Twitter feed all a-flutter today. Apparently the editors of Nature saw fit to publish in their correspondence section a missive from one Lukas Koube, and, well, I think I'll begin by reproducing it here:


Publish on the basis of quality, not gender

The publication of research papers should be based on quality and merit, so the gender balance of authors is not relevant in the same way as it might be for commissioned writers (see Nature 504, 188; 2013). Neither is the disproportionate number of male reviewers evidence of gender bias.

Having young children may prevent a scientist from spending as much time publishing, applying for grants and advancing their career as some of their colleagues. Because it is usually women who stay at home with their children, journals end up with more male authors on research articles. The effect is exacerbated in fast-moving fields, in which taking even a year out threatens to leave a researcher far behind.

This means that there are likely to be more men in the pool of potential referees.

Lukas Koube Sherman, Texas, USA.

Oh my. I have so many thoughts on this.

So, let's get started, shall we?

1. "The publication of research papers should be based on quality and merit"

This is one of those assertions that looks great on paper, which is why so many people use it as a highbrow way of telling those of us trying to come up with solutions to the gender disparity in scientific fields to shut up. The first problem with this assertion is that while publication should be based on quality and merit, reality (read: academic politics) quite often gets in the way. How do I know this? I know this because publication involves people. People can be idealistic, and work tirelessly towards lofty ideals such as this one, but they can just as often be lazy, petty, vindictive, and nepotistic. Publications like Nature often get hundreds of submissions a week, and assuming that every single editor and reviewer is upholding this goal above all else (and indeed is even able to tell when they are not doing so) is an astonishing display of naiveté.

Secondly, this statement assumes that "quality" and "merit" are objectively defined, allowing editors to rank submissions from best to worst in a clear-cut, mutually agreed upon manner, and to the satisfaction of all.

Um, nope. Nope nope nope.

These values are subjective, and "quality" and "merit" are most often defined by those in positions of power. As an example, take the game Cards Against Humanity. (Yeah, I'm going there. you can substitute Apples to Apples in this example if that's more your thing.) You don't win a round of CAH by popular vote - there's just one judge. Your entry could have the entire room in stitches, but the judge has ultimate veto power. And if the judge doesn't appreciate it as much as everyone else does, well then tough crackers for you. (I once played a round of Apples to Apples wherein we were all trying to match the adjective "beautiful". I played "Canada". Was it the funniest entry? No. The most accurate? No. Was the judge for that round Canadian? Yes. I won.)

2. "the gender balance of authors is not relevant in the same way as it might be for commissioned writers"

I agree. Yes. The gender balance of authors isn't relevant in the same way as it is for commissioned writers. However, I take issue with your assumption that this means it isn't relevant at all. There are a ton of factors that contribute to gender disparity in publication. There are biases woven through our education system, affecting women in high school, college, graduate school, and beyond. Those of us who are working to address gender disparity in the sciences know that what we are up against is a Hydra with many, many heads. That's why we don't say things like "the publication of research papers should be based on quality and merit" and then declare the problem fixed, patting ourselves on the back for a job well done. Bias of any form is, and always has been, an incredibly complicated issue.

3. "Because it is usually women who stay at home with their children..."

And this is where I seethe with rage. There are studies showing that having children affects women's careers negatively, while the effect on men's careers can actually be positive. The major reason behind this is because of the prevalence of this belief that you yourself hold: women are usually the ones taking care of the children. Not only is this assumption often inaccurate when it comes to women with strong careers, but the attitude that women can either have children or be scientists, but not both, while men can do both easily (Because hey! He probably has a stay-at-home wife to do all the time-consuming child-rearing for him, amirite?!) is exactly the kind of biased thinking that we are working to address. Remember that Hydra? That's one of its heads.

Doing a quick search on Google, I find that this is not the first time you've completely missed the point when people make arguments about the representation of women in male-dominated groups. Also, pro tip: when your argument can basically be restated as "Things are the way they are because that's the way they are!" then you haven't actually made an argument.

And finally, I want to thank you, Lukas. Thank you for submitting such a shining example of dude-butting-in-to-mansplain-without-any-proper-research I have seen in a while. It's comments like yours that do my work for me.

Good articles on math fear

There are some great articles/blog posts floating around that are tackling the same subject as my video - please check out this article written by Ben Orlin, a high school math teacher, about his own struggles in a college math course. While you're at it, you should go read his entire blog - www.mathwithbaddrawings.com - because he is such an entertaining writer. This passage particularly struck me (emphasis mine):

I manifested every symptom that I now see in my own students:

Muddled half-comprehension. Fear of asking questions. Shyness about getting the teacher’s help. Badgering a friend instead. Copying homework. Excuses; blaming others. Procrastination. Anxiety about public failure. Terror of the teacher’s judgment. Feeling incurably stupid. Not wanting to admit any of it.

It’s surprisingly hard to write about this, even now. Mathematical failure—much like romantic failure—leaves us raw and vulnerable. It demands excuses.

I tell my story to illustrate that failure isn’t about a lack of “natural intelligence,” whatever that is. Instead, failure is born from a messy combination of bad circumstances: high anxiety, low motivation, gaps in background knowledge.

Most of all, we fail because, when the moment comes to confront our shortcomings and open ourselves up to teachers and peers, we panic and deploy our defenses instead.

This is so true! And I think that many of us are more likely to react this way to mathematics because there is a myth in our world that math is only for the "special" or "gifted." that is simply untrue! Take this article that appeared today in the Atlantic, The Myth of 'I'm Bad at Math' - The authors make several points I've tried to make myself (albeit in a much more polished, let's-get-this-actually-published kind of way, as opposed to my rant-on-YouTube method). Ultimately, math is something that rewards hard work. So keep working!             


A Math Major Talks About Fear

I believe that STEM fieldsbenefit from the inclusion of people with "non-traditional" backgrounds, and I cringe when I see people justify keeping them out. And I cringe when I see people justify keeping themselves out.

And I know (boy, do I know) that feeling like a failure in math does not mean you are a failure in math.

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