On mathematicians and mountains

Luca and Terry Tao have already reported the tragic loss of the brilliant probabilist Oded Schramm in a hiking accident.  I didn’t know Oded, but I knew some of his great results and was deeply saddened by the news.  My heartfelt condolences go out to his friends and family.

It was two years ago that we lost Misha Alekhnovich, who I did know, in a whitewater rafting accident.  Other mathematicians and scientists lost in similar ways have included Heinz Pagels, Jacques Herbrand, Raymond Paley, Krzysztof Galicki, and Erik Rauch.  The teenage Einstein very nearly died while hiking on a mountain near Zurich.  I have more than one irreplaceable colleague who’s repeatedly courted death on the ski slopes.

I’d like to issue a plea to any mathematicians and scientists who might be reading: please go easier on the extreme outdoor activities.  Let those who live for such things demonstrate their daring by gambling their lives; those who live for the ages can find safer recreations.  The world needs more nerds, not fewer.

43 Responses to “On mathematicians and mountains”

  1. Greg Kuperberg Says:

    I totally agree, moreover you said it very well. I only knew Schramm casually — I have one minor joint paper with him — but like a lot of people I feel a sense of grief.

    Pavel Urysohn, Witold Hurewicz, and Mikhail Goussarov are other important examples.

  2. Greg Kuperberg Says:

    Addendum: Urysohn is famous for Urysohn’s Lemma, which was one of the first non-trivial structural results in topology.

    Hurewicz is famous for the Hurewicz Theorem that relates homotopy groups and homology groups of topological spaces.

    Goussarov was one of the discoverers of finite-type invariants of knots. These are functions on the set of knots that have polynomial-type behavior, in the sense that some nth finite difference with respect to switching crossings vanishes.

    Finally another example is Stephen Paneitz. He was a representation theorist who studied invariants cones in Lie algebras, among other results. I cited that work in a paper, and it is very possible his work will be relevant to quantum information theory one day, since cone structures in vector spaces seem to come up a lot in that topic.

  3. Anonymous Says:

    Does a higher than expected percentage of mathematicians have the risk taking gene?

  4. Beetle B. Says:

    “Let those who live for such things demonstrate their daring by gambling their lives; those who live for the ages can find safer recreations. The world needs more nerds, not fewer.”

    I can’t say I agree. At the end of the day, scientists should have as much freedom to pursue their desires as the rest of us.

  5. Fernando Pereira Says:

    The untimely death of someone we know and value makes even the most rational of us grasp for explanations. If only he did not do this or that. But in my experience, very few of the people who seek the mountains, even professionals (I know quite a few as friends and guides), are there to “demonstrate their daring by gambling their lives.” We hike, climb, and ski because those particular challenges, beauties, and achievements are found nowhere else, and most of us are as careful as we know how. Things can go wrong in the mountains, but so can they go wrong on the road driving to work, or silently in our bodies.

  6. Greg Kuperberg Says:

    At the end of the day, scientists should have as much freedom to pursue their desires as the rest of us.

    I agree that we are all within our rights to do this. Even so, it’s perfectly reasonable to ask people to be careful. Nor would I mean it as a criticism of anybody. In Oded’s case in particular, I wouldn’t criticize him even for a second. It’s strictly a request to mathematicians who are still alive. My argument for it is: Sure, you’re perfectly entitled to recreate in any way that you like. But please consider how much we’ll miss your research if you encounter the worst.

  7. Greg Kuperberg Says:

    Does a higher than expected percentage of mathematicians have the risk taking gene?

    I do not have solid evidence in hand, but I suspect that the answer is no. I don’t think that it’s about mathematicians in particular. Most people trained in science have had good practice estimating probabilities, and usually a good sense of self-worth. So probably they are more likely to avoid risk than average.

    However, a cursory survey of Wikipedia suggests (again without any real science) a different pattern of risk. Half or more of all fatal accidents in developed countries are automobile accidents. But taking risks with a car is generally boring, and often simply unschooled. Hiking and swimming, on the other hand, are a lot of fun. So I would conjecture that among mathematicians and scientists who die in accidents, a larger fraction do so while experiencing nature.

    There are some great mathematicians who died from bad driving. I have heard that Frank Adams was one of them.

    Meanwhile I found yet another first-rate mathematician who died in an extreme nature sport: Jacques Herbrand.

  8. Greg Kuperberg Says:

    If I may change the subject temporarily to what nerds can do to improve American politics:

    I find Obama/Biden significantly more preferable now that McCain has picked Sarah Palin as his running mate. I won’t go into the reasons. Even so, there are other candidates that in my opinion are even more worthy than Barack Obama, even though they are running for smaller offices. One of them is Bill Foster, who is in a contested election. I almost never feel outright elated by a politician’s resume, but Foster does the trick for me, for the same reasons as Rush Holt.

    I also want to endorse the ultimate political math geek site, fivethirtyeight.com. Beyond the interesting election information at that site, I have also learned something about statistics from those guys.

  9. Scott Says:

    Greg: I completely agree; Bill Foster deserves the overwhelming support of the nerd community. (One thing I’d like to do is make up a list of Democrats running in House, Senate, and local races who are unusually good from a nerd perspective and who merit donations. Any other suggestions?)

    I’ve been checking fivethirtyeight.com compulsively, but I’m worried that Nate constantly seems to make optimistic assumptions about Obama/Biden, and to find reasons for downplaying bad news. And he doesn’t seem to account for the long history of ~7% of voters telling pollsters that they’ll vote for a black candidate and then voting for the white one. Thus, I fear that (though well-meaning) he may be lulling Democrats into a false complacency.

  10. Greg Kuperberg Says:

    One thing I’d like to do is make up a list of Democrats running in House, Senate, and local races who are unusually good from a nerd perspective and who merit donations. Any other suggestions?

    Almost anybody with a PhD in math or hard science, and in my view it doesn’t necessarily have to be a Democrat. So that means:

    Vern Ehlers (R House) – physics
    Bill Foster (D House) – physics
    Rush Holt (D House) – physics
    Jerry McNerney (D House) – applied math
    John Olver (D House) – chemistry
    Angela Merkel – wait, wrong country
    Janusz Onyszkiewicz – alas, also wrong country
    Ahmed Chalabi – maybe not such a good choice, but again wrong country

  11. XiXiDu Says:

    I agree as well, I would rather have those people alive doing research than dying in the field but where exactly do you draw the line. Do you wear a helmet when driving a car? It is feasible and much more secure! I wonder if Kurzweil aka “Mr. Live long enough to live forever” ever flys with a plane? What are the odds of taking 250 nutritional supplements making you live long enough to live forever compared to dying in a plane crash?

    But hey, it’s all up to what you want, everything else doesn’t matter at all! Most of us want to survive, but at what price? I guess the price could be pretty high if you knew that taking no risks now could make you live at least much longer in a more secure and exciting future. But do you know? How much time are you going to spend on reasoning about what you want? I guess you can think about it till the end of the universe if it has one. Or you just go outside doing extreme sport. But then you could as well just ignore those chest pain, it could be just a pulled muscle after all…for some reason you don’t. Elaborate or arbitrarily? Where do you draw the line…

  12. Scott Says:

    XiXiDu and Bettle: Obviously people can and will make their own choices. I’m just trying to get them to think through those choices a little more.

    I was scared to drive for many years—knowing the statistics as well as my own mediocre reflexes—and only started at 23, when I was at IAS in Princeton and would basically starve in the woods without a car. I still avoid driving when I don’t need to (it helps that I live in Cambridge and can usually walk or take the T). Safer, eco-friendly, and best of all I don’t have to park!

    I’m not the slightest bit afraid to fly commercial; the chance of dying on the drive to the airport is about 1,000 times greater. I would be leery about a two-seater that some dentist or entrepreneur flew as a hobby.

  13. Greg Kuperberg Says:

    where exactly do you draw the line.

    There won’t be any rigorous way to draw the line, of course, but I can think of an important litmus test: Do you weaken scientific risk assessment with personal bias or handwaving? If you’re trained as a scientist, then you have been trained to make rational personal decisions. It’s a waste to turn off your brain in order to have fun.

    As for driving, no you shouldn’t wear a helmet while driving a car. It would be a victory of procedure over probabilities. But there are other important ways to reduce the risks of driving, and it is true that about half of all accidental deaths are on the road.

  14. crb Says:

    Mahmoud Ahmadinejad – Civil Engineering

  15. Michael Bacon Says:

    People don’t change that much, they only get older. :)

    Once it’s clear the someone is capable of making special contributions to a particular field, it would be great if they would then start to exercise greater prudence in their personal behavior so that they might continue to make such contributions for as long as possible.

    Unfortunately, in most cases the behaviors and ways of thinking that got them to where they’re at just aren’t that easily changed. And saying that they should have thought and acted differently from the start just sort of begs the question: would that have made them different?

  16. Dave Bacon Says:

    et those who live for such things demonstrate their daring by gambling their lives; those who live for the ages can find safer recreations. The world needs more nerds, not fewer.

    But Scott you forget that being involved in an extreme sport is, according to all of the media I’ve seen, guaranteed to bump your odds of reproducing. I suggest that what the world needs is more adventures/skiers/hikers who are also nerds not less. So get off your lazy bum and start playing chicken with Boston traffic!

    (And see now you’ve made me write something very crass in light of a very tragic event. Death sucks and my condolences go out to all the friends and family of someone who sounds to me made the world a better place. )

  17. Scott Says:

    crb: If you read the speech that my friend Mahmoud gave at Columbia, he has a very strange definition of the word “science”:

      In our culture, the word “science” has been defined as “illumination.” In fact, the “science” means “brightness” and the real science is a science which rescues the human being from ignorance to his own benefit. In one of the widely accepted definitions of science, it is stated that it is the light which sheds to the hearts of those who have been selected by the Almighty; therefore, according to this definition, science is a divine gift, and the heart is where it resides. If we accept that “science” means “illumination,” then its scope supersedes the experimental sciences, and it includes every hidden and disclosed reality. One of the main harms inflicted against science is to limit it to experimental and physical sciences; this harm occurs even though it extends far beyond this scope.

    For this reason, it’s not clear if I can ask my nerd readers to send him money.

  18. Scott Says:

    But Scott you forget that being involved in an extreme sport is, according to all of the media I’ve seen, guaranteed to bump your odds of reproducing.

    If so, then that’s part of what ought to be changed about the world. (And there I go again, taking the route favored by George Bernard Shaw’s “unreasonable man”… :-) )

  19. Michael Bacon Says:

    ” . . . being involved in an extreme sport is, according to all of the media I’ve seen, guaranteed to bump your odds of reproducing.”

    Dave, I think you’re confusing causation with correlation — lots of men make that mistake ;)

  20. crb Says:

    Perhaps A.M. is a closet computability theorist :P

    Most programs have no meaning in the physical world, most are uncomputable, and we are very lucky to discover an interesting computation that halts.

    In our culture, the word “science” has been defined as “illumination.” In fact, the “science” means “brightness” and the real science is a science which rescues the human being from ignorance to his own benefit. In one of the widely accepted definitions of science, it is stated that it is the light which sheds to the hearts of those who have been selected by the Almighty; therefore, according to this definition, science is a divine gift, and the heart is where it resides. If we accept that “science” means “illumination,” then its scope supersedes the experimental sciences, and it includes every hidden and disclosed reality. One of the main harms inflicted against science is to limit it to experimental and physical sciences; this harm occurs even though it extends far beyond this scope.-A.M.

  21. Dylan Thurston Says:

    I am also quite saddened by the news about Oded Schramm. But I don’t think we should stop exercising as a result.

    Scott and Greg, I think you are committing the usual fallacy of only looking at the immediate, obvious risks of an activity, and not looking at its long-term benefits. Greg, some years ago you told me that for every minute you spend exercising (within reasonable bounds), you live two minutes longer on average.(*) This gain in life expectancy far outweighs the chance of an accident for most sports.

    I would urge scientists (and everyone else) not to take up hang gliding, however.

    (*) Do you happen to have a citation for this? I’ve found other data that are broadly consistent with that, but nothing so crisp.

  22. Dylan Thurston Says:

    And [Nate Silver] doesn’t seem to account for the long history of ~7% of voters telling pollsters that they’ll vote for a black candidate and then voting for the white one.

    He has addressed that issue, and explained why he doesn’t think it’s an issue. On The Monkey Cage they also had two different analyses (by political scientists) as well, explaining why it’s unlikely to be a factor in this election, both experimentally (it hasn’t been a factor since the early 1990′s in several elections) and theoretically.

  23. Scott Says:

    Dylan:

    (1) Obviously I wasn’t arguing against exercise! Just this summer I started an exercise regimen, and am very happy I did. Do any readers know of scientists or mathematicians who lost their lives swimming (in a pool), jogging, or using a treadmill or weight machine?

    (2) The fact that Silver seems so ready with explanations for anything that looks like bad news for Obama is precisely what makes me nervous. In particular, it seems entirely plausible to me that the Bradley effect would show up in the general but not in the Democratic primary. But who knows? We’re in fairly uncharted territory this year.

    (As a side note, I remember all too well the analysts predicting 80-90% for Gore in 2000…)

  24. Steven Says:

    “… Most people trained in science have had good practice estimating probabilities, and usually a good sense of self-worth. So probably they are more likely to avoid risk than average.”

    From my experience, scientists are really over-represented amongst rock and alpine climbers. For some reason the sport seems to attract analytical and introspective people. George Johnson wrote a nice article on climbing physicists in the NYTs several years back.

  25. Greg Kuperberg Says:

    Greg, some years ago you told me that for every minute you spend exercising (within reasonable bounds), you live two minutes longer on average.(*) This gain in life expectancy far outweighs the chance of an accident for most sports.

    You’re very right of course. But as Scott says, the issue here is the exceptions.

    I was at a conference on a Greek island last year with a lot of beach swimming. The island had fairly calm, fairly warm waters and a shallow slope, so it was easy to swim out to some distance. I saw several swimmers who were way the hell out there; they reminded me of Goussarov. I swam out to the safety bouy once — I rationalized that several people were out much further and spending much more time at it too. The water was maybe 12 feet deep at that distance and it was on the order of 100 yards out. This was already enough to give me the feeling that I was cutting off my options for no good reason.

    (*) Do you happen to have a citation for this? I’ve found other data that are broadly consistent with that, but nothing so crisp.”

    I think that it was a study of Harvard alumni and I think that I read about it in Harvard magazine, but I am not entirely sure on either count. It may have been this study, although the link is to the Gazette instead:

    http://www.hno.harvard.edu/gazette/2001/05.31/01-exercise.html

    The factor of two was a description of the health benefits of a medium amount of exercise. The study had a separate category of hard chargers, who for unclear reasons did not extend their life expectancy as much as the medium-exercise group. Or maybe it was four groups and the third group had the most gain, or something like that.

    Do any readers know of scientists or mathematicians who lost their lives swimming (in a pool), jogging, or using a treadmill or weight machine?

    Well, you have to admit that an exercycle or a treadmill runs you the risk of dying of boredom. That aside, I conjecture that it’s almost impossible for a sober adult to drown in a pool with a lifeguard watching. The statistics on this page do not quite prove that, but they are consistent with the conjecture:

    http://www.cdc.gov/mmwr/preview/mmwrhtml/mm5321a1.htm#tab

    As for jogging, you could of course get hit by a car. Otherwise the direct risk of death is surely very small.

    I think that there are four bicycle fatalities on record in the Davis area (not just within the city) since I moved here in 1996. In all four cases, the cyclist was hit by a motor vehicle.

  26. Greg Kuperberg Says:

    Sigh I posted a prepared comment with links and everything that got eaten. I don’t know if it is lost or in hiding.

  27. Fernando Pereira Says:

    Do you weaken scientific risk assessment with personal bias or handwaving? If you’re trained as a scientist, then you have been trained to make rational personal decisions. It’s a waste to turn off your brain in order to have fun. Scientific training, or training as a professional of any kind, has less effect on one’s decision making than we would like to believe, whether the decisions are about what to do driving on the road, climbing a mountain, or investing one’s savings. There are tons of literature on decision biases, from the popular Predictably Irrational (Dan Ariely) and Traffic (Tom Vanderbilt) to the very specialized Heuristic Traps in Recreational Avalanche Accidents. When you are standing there assessing that slope (or road intersection) for danger, you can miss important cues, you can overestimate your ability, you can just plain miscalculate by applying inapplicable heuristics (needed because the problems are always intractable). Is it that surprising that our decision-making processes are a pile of messy, imperfect hacks that can easily go wrong outside evolutionarily important situations?

  28. plam Says:

    While Douglas Adams was not a scientist or mathematician, he did have a heart attack while working out at a gym.

    I haven’t studied this question closely, but I suspect that the risk of driving to an outdoors activity can often outweigh the risk of the outdoors activity itself. It is a bit tricky to evaluate the risk precisely, because one’s judgment, skill, and willingness to take risks affects the risk of these activities; of course, a serac could also just fall on your head, which happens from time to time.

  29. Greg Egan Says:

    While Douglas Adams was not a scientist or mathematician, he did have a heart attack while working out at a gym.

    I was going to mention Adams myself in reply to Scott’s question (having a vague memory of hearing that he’d died on a treadmill), but then I looked at the account on Wikipedia:

    Adams died of a heart attack at the age of 49 on 11 May 2001, during the rest period of his regular workout at a private gym in Montecito, California. He had unknowingly suffered a gradual narrowing of the coronary arteries, which led at that moment to a myocardial infarction and a fatal cardiac arrhythmia.

    Obviously if he’d had his condition diagnosed he might have changed his exercise regime, but all else being equal he might just as easily have died running for a bus. The only moral of the Adams story is that regular check-ups with a physician are a good idea.

  30. Greg Kuperberg Says:

    I haven’t studied this question closely, but I suspect that the risk of driving to an outdoors activity can often outweigh the risk of the outdoors activity itself.

    This is usually true. When we were in Yellowstone we got a book called “Death in Yellowstone” that described the visitors who were eaten by bears, fell into the hot springs, etc. The book omitted car accidents because they were more than half of the cases, and they were boring.

    But it isn’t always true. Alekhnovich died doing something that really was pretty risky.

    Obviously if he’d had his condition diagnosed he might have changed his exercise regime

    Or not, because it could have happened when he got up in the morning. This could be the best example of Dylan’s point about short-term vs long-term risk. Exercise increases the risk of a heart attack locally, but decreases it globally if the cause is atherosclerosis. Atherosclerosis is a really big deal for many people that age, especially men, but the solution is statins and a strict diet.

    In fact atherosclerosis is the major reason that exercise is good for your health in the first place. Without that and diabetes, exercise is just a pastime. In fact it is just a pastime for the 5 percent or so of people who have strong genetic protection from heart disease and diabetes.

  31. A German Says:

    Also, Jop Sibeyn from Halle died while skiing on frozen water.

  32. Ian Durham Says:

    Jeezus H. Krist. Rauch was younger than me. Never knew him personally, but knew of him.

    On the other hand, the allure of mountains historically runs very deep in the physics and mathematics communities.

  33. David Z Says:

    I recall that some mathematics (I forget who now) used to mail a friend of his a postcard saying “I have proven the Reimann hypothesis!” before he took a trip overseas. He was certain that God wouldn’t let him live with the honour.

  34. David Z Says:

    …er, *die* rather.

  35. Cody Says:

    David, that was G.H. Hardy, I think I first read it in The Music of the Primes, by Marcus du Sautoy, which is an excellent book. Hardy used his postcard as an insurance policy, despite his atheism.

  36. Hopefully Anonymous Says:

    Sorry about the loss.
    It’s our social quirk that what amounts to our best supercomputers have so little protection. I think about Indiana Jones and the Las Crusade, how valuable a society would be that protects the well-being of brilliant problem solvers the way the Holy Grail was protected in that movie.

  37. Aghilmort Says:

    Boris Weisfeiler, missing in Chile since 1984.

  38. Jonathan Vos Post Says:

    Erik Rauch’s coauthor, NECSI head Yaneer Bar-Yam, asked if I would like to help rewrite some papers that are incomplete because of Eric’s tragic death. Yaneer and his father are both noted Physicists, before being pioneers in Complex Systems. I have chaired sessions for Yaneer at several ICCS (International Conferences on Complex Systems). Thank you, Scott, for putting Erik’s death in the ambient space of multiple mountain tragedy.

  39. Ryan Budney Says:

    It seems like half of our department is out either rock climbing or scaling some mountain every weekend. I haven’t noticed mathematicians dying at a greater rate than other people, but they seem to injure themselves in stranger ways than most people. I can’t quantify that. But I remember a few years ago getting an e-mail from someone at RIMS mentioning someone that I had been corresponding with fell off the side of mount Fuji while climbing it in winter and was in the hospital.

  40. Jonathan Vos Post Says:

    My closest call mountain climbing was when I was out, alone, on Paradise Glacier, on the south slope of Mount Rainier in Mount Rainier National Park in Washington, United States.

    A tremendous thunderstorm came out of nowhere (so far as my lightcone was concerned) and the ice that I was on reconfigured dramatically.

    No major injuries, perhaps due to sheer luck and my ability at the time to run at full speed down a mountain. As a husband, parent, coauthor, and schoolteacher, I have entirely quit mountain climbing, although I happily hike trails in the Angeles National Forest, which begins a quarter mile from my home.

    The National Park Service says that “Paradise is the snowiest place on Earth where snowfall is measured regularly.”[Mount Rainier National Park - Frequently Asked Questions (U.S. National Park Service)". National Park Service (created August 4, 2005 modified January 19, 2007). Retrieved on 2007-05-22.] 1,122 inches (93.5 ft, 28.5 m) of snow fell during the winter of 1971-1972, setting a world record for that year. The minimum annual snowfall at Paradise was 313 inches (26 ft, 8.0 m) in the winter of 1939-1940, and the maximum snowpack was 357 inches (30 ft, 9.1 m) in March, 1955.

    There’s a great sign on the road to there, which I keep meaning to use as the title of a science fiction story:

    “Halfway to Paradise.”

  41. KaoriBlue Says:

    I remember climbing Mount Rainier… and soaking my gloves… and it being cold and dark enough to put an ice pick through part of my hand without really registering it… and only later realizing that one of my gloves was soaked with something else. The summit made it all worthwhile though!

    Haha, I also have some fond memories exploring the trails off and around the Angeles Crest Highway. :-)

  42. Raoul Ohio Says:

    A related note; a lot of mathematicians and physicists enjoy flying planes, well beyond the bunny slope. Some have augered in, perhaps most famously David Schramm http://en.wikipedia.org/wiki/David_Schramm.

  43. John Sidles Says:

    A well-known maxim in medicine is “Never fly with a surgeon-pilot.” The reason is simple: the same high-confidence envelope-pushing personality that makes a good surgeon also makes a short-lived pilot.