Russia's Conquering Zeros
by Masha Gessen
The following is taken from the article and this reminds me so much about my dd and her thoughts about Math research as she envisions it.
In the mathematical counterculture, math "was almost a hobby," recalls Sergei Gelfand. "So you could spend your time doing things that would not be useful to anyone for the nearest decade." Mathematicians called it "math for math's sake." There was no material reward in this—no tenure, no money, no apartments, no foreign travel; all they stood to gain was the respect of their peers.
Math not only held out the promise of intellectual work without state interference (if also without its support) but also something found nowhere else in late-Soviet society: a knowable singular truth. "If I had been free to choose any profession, I would have become a literary critic," says Georgii Shabat, a well-known Moscow mathematician. "But I wanted to work, not spend my life fighting the censors." The search for that truth could take long years—but in the late Soviet Union, time seemed to stand still.
American math culture has intellectual rigor but also suffers from allegations of favoritism, small-time competitiveness, occasional plagiarism scandals, as well as the usual tenure battles, funding pressures and administrative chores that characterize American academic life. This culture offers the kinds of opportunities for professional communication that a Soviet mathematician could hardly have dreamed of, but it doesn't foster the sort of luxurious, timeless creative work that was typical of the Soviet math counterculture.
And the following paragraph talks about the Russian Mathematician Grigori Perelman, who solved the Poincaré conjecture that was posed in 1904, and was regarded as one of the most difficult open problems until it was solved.
The entire article can be read here. Dd is so intrigued by this article that she is looking forward to finishing Masha Gessen's book, "Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century," a story of Grigory Perelman and the Poincaré Conjecture.
But this article is so relevant at so many other levels with respect to our family's current and future paths regarding our dd. Even though my dh found this article depressing (he is fully aware of how math research world works being a theoretical CS researcher) as he worries about dd's future as a successful mathematician in general, I could not help but feel good about letting my dd lead her own path. Just yesterday dh and I were chatting with a couple of other parents of very brilliant math kids on the purposes of doing math, math competitions and becoming a mathematician. This is something dh and I discuss a lot about; and this is also the topic that commonly comes up in our discussions with our close friends who have math competition oriented kids. And that is so different from what our dd wants to do in her life.
Dd wants to be a mathematician/ researcher and dreams about a place where she would just work on interesting and aesthetically pleasing problems while time would stand still. She wants to meet like minded mathematicians in such a place, where high level intellectual exchanges happen while they discover the beauty of math together. I am not sure if such a place exists in reality as she imagines it. But we have not stopped her from dreaming about it. Years ago when she exhausted all the K-12 offerings for math at age 7, we were advised to put her through math competitions as means of extending her math education and also to give her sometime to 'grow' to be ready for full time college.
Although math competitions work for many kids, dd thought differently. She chose to take college math courses and to work on math research problems simultaneously. She is a competitive kid who loves to win no doubt. She loves the 'rush' of doing something racing with the time and has proved to be good at it. Even in an every day activity of doing something, her competitive streak comes through while she races with her brother or someone else, whether it is in playing a board game or giving a quick correct answer in a college classroom. She did try out math competitions albeit very young with no prior training. She even amazed a couple of the mathematicians who train kids for math competitions with her unique thinking abilities and unusual solutions to some very difficult problems, which they felt some of the brilliant trained kids could not solve. She got opportunities to take advantage of some very esteemed math camps which we decided not to send her to because of her young age. Some such mathematicians have even come forward to work with her and train her for the competitions, which she did not want to pursue. We were told by many such mathematicians that if she chose to pursue that path of competition math she would be extremely good at it. But dd resisted doing such training for competitions and did not want to participate in such competitions. She strongly believed that it was a waste of time for her to go through such training as her heart was not in it. But she also recognized that it was the only means of meeting mathy, like minded kids. But their philosophies towards math were so different from that of hers. Instead of insisting on going through the training for competition route, we just let her be.
Having always been a child led learning family, we have hesitated to guide or lead dd (or ds for that matter) in any particular path. We wanted their natural inclination and interest to lead them where they wanted to go. We wanted dd to choose her path based on what she felt right about doing and told her to just follow her heart. May be my dh would have hoped that she may take to the competition route when time came, but I certainly did not bother much with it. So, when she decided math research was something she wanted to pursue and spend the time on even though she did not have much advance mathematical training in that area at that time, we let her do it.
She spent much of her time reading various high level math books, exploring math and attending plenty of math lectures at the Univs. She developed many contacts with famous mathematicians, wrote to them and solved problems that they sent her way. She was extremely happy pursuing this path. And every time the mathematicians who acted as her mentors upped the level of difficulty in the problems they sent her way each time she solved their previous ones. She had very interesting questions and conjectures that brought attention to her from wonderful mathematicians, who had similar philosophies towards math like her. She thrived in this environment. She works very hard on her math explorations and some of them are considered undergrad or even grad level problems.
Though she has wonderful mentors/profs with whom she gets to collaborate, and occasionally even gets to chat with her dad about her thoughts while she updates him about the new frontiers in advance math, she mostly spends time sitting alone for hours together in a peaceful state of 'flow' working on these interesting problems she chooses to work on, sometimes even forgetting to eat or shower. This phenomenon is common in our home, and it goes through its ups and downs. Unpredictable as to when and what and how she would want to do. She is not a kid who thrives on structure, but the lack of it.
She is a brilliant minded, sharp thinking kid and does best when let free with virtually no guidance or help with just time at her hands when it comes to her math problems she wants to do. They are not the most popular problems for a prize, but the most elegant ones that appeals to her aesthetic sense. She is choosy and has specific interests. When she is at such a state of flow, she hates interruptions and would much prefer to be left alone to her and in her world. It is not unusual for her to sit from 8am to 3 or 4 or even 5pm without moving from the spot..unless for nature calls or such induced breaks. I have experimented with this by not interrupting her and have been astonished at the level of long time focus she has shown on something. BUT I interrupt her thought process by giving forced breaks at times because it is not normal. Then at times, I would wonder what is really normal when it comes to this child?
And some days, I can see that she is just happier working at her stuff, and I let her be. I even let her eat her food at her table..often reminding her to take the next spoonful of food. When I interrupt her to let her run outside, there is no guarantee that she will be safe around the road. She has walked onto the middle of the street more than a few times without knowing that she was in the middle of the street. She was thinking oblivious to the world around her each of those times.
So, she could continue thinking even after the breaks we impose in her thought process. She he has told us that sometimes she can be thinking of something in her head while answering someone and doing entirely something different all at the same time! And no one comes to know of that thought process that keeps going in her head. At times, she rushes off to write something down regarding the problem she would be working on, right in the middle of conversation or talking...some break through, some new insight..I have had to explain to strangers and relatives that she does not mean disrespect when she does that, but just had to write something she suddenly thought of ...and it took a bit more getting used to her 'quirky' ways of working personally for me.
She has been successful with it so far, and it is her optimal zone of comfortable working and thinking. But this state of flow is something dh and I are very much familiar with and relate to. So does my ds. I see her extremely happy and excited to be able to spend the time in such long deep thinking. What we would think of 'hard work' is 'joyful' to her. And it amazes dh and I to see her enjoying it. Many of the problems she works hard on never leads her to proper proofs. The problems are very very very hard. Some of them are worked by very accomplished mathematicians and has been left unsolved. I never undermine her thoughts or efforts. She is not naive about the prospects of solving them either.
That is actually a key point I learned about her. She never thinks of solving, but thinks of the journey of solving it. So, she is extremely happy taking that journey and is excited about the unknown. She loves the journey. And she has this confidence in trying and working at it persistently that I admire and adore about her. There is one other thing I adore about her. I have witnessed her work hard at something for weeks and months only to see those proofs fall apart in the end. It has not stopped her from continuing to pursue it. It would even frustrate me. But It never crushes her down. She has the experience and sometimes laughs at it even; and at times chides herself for not listening to her gut feeling, showing very slight disappointment. But then she shrugs her shoulders and goes into it with even more vigor and excitement to find alternate paths or workable ways, without giving up. She is persistent, hard working, deeply focused and obsessed and totally in love with it. It is humbling to us parents to see her at work like this.
And personally, I learn so much from watching this innocent child at work on something she purely loves and celebrates for the sake of how she sees it. I wonder if this is what everyone of us alive today is after...and do not know how to get there ? She does not want to know the path to the answers to her problems.
She does not want help or short cuts to find it. She wants to find them. She wants to be in the 'math wilderness' and 'seek out answers' as means of taking the journey, while getting lost in the wilderness she says. She says she is bound to experience some amazing, beautiful things in that journey. And that is very exciting for her. She does not think of glory at the end of it, a ton of money or even a trophy at the end. It is sharing her joy of having created something beautiful that she takes her work to present as papers or share with fellow mathy kids. She says it is like sharing some treasure, an art, a beautiful music for the world to find out and admire together. This is the same kid who spent couple of hours explaining her math proofs to a Staples store copier guy who wanted to know what her proof was all about, as he noticed her making copies of her results to present in one of the presentations. She would spend time explaining to anyone who shows interest in finding about math that she finds beautiful.
She always wanted to work on open problems that are real hard, where she needs to create the tools in that journey to solve them. And she often says, 'Amma, I may only scratch the surface of this problem or sometimes only come to close to touch it or may even be awed at a distance with a total surrender and respect for it. But what an amazing feeling to go through such a process of trying to learn the depth of the problem and falling in love with it! Do you know what I mean? Does that makes sense to you? Do you think that is crazy?'
I am usually speechless listening to her. I am not a mathematician, but I know that feeling:). I tell her that it is wonderful she feels about it so. She sounds like a romantic, doesn't she? And also like the kind that would be considered a total misfit in this competitive tech marching fast paced world?
She says that competition math problem solving and training is not worthy of her time. She says she rather spend her time doing some math research explorations, and coining her own questions and solving them, no matter how long it takes. She considers math as means of solving 'God created' problems, as opposed to 'man created puzzles' and she tells her dad and me that math competitions are nothing but man-made math puzzles. Does that mean she has no respect for it? Actually no. She recognizes the fact that it is a wonderful opportunity for some kids, but she is not sure if any of it is helpful or even needed to become a great mathematician that she wants to be. And to her, it takes the time away from being on that path of becoming such a mathematician. Dh finds it hard to argue with that:)
Well, I must admit here that coming from a competitive Asian society and being proud of winning such competitions and hoarding trophies and gold medals, it was such a blow and an eye opener to hear our dd feel so strongly about it. She asks some interesting questions as to what happens to all the kids after winning the Olympiad competitions? How many stayed with math or did more for or in math research for the sake of math? How much of math is done by non-competition mathematicians? etc etc. These are deep, interesting and valid questions. I do not have all of the answers.
We know many wonderful mathematicians today did these competitions. Some turned totally away from it later in life. Some consider this as means of meeting mathy like minded friends. This post is more about sharing what my child feels about math and how she sees math, than about competition versus non-competition paths. And ofcourse, my dd also faces some questions from friends and family regarding her choice of wanting to do math. 'Why not become a doctor? Why do math which has no monetary benefits or even a high pay? There is no money in math!'
She feels very disappointed, disgusted and even angry at such questions. Poor relatives and friends! They do mean well and care for her and adore her very much. But they are ignorant at many levels. She tries to answer them politely. 'Because I love it very much! Don't you ever do something because you love something?'. Usually this does not stop their questions, but we have always diverted their attention to something else. And at times, we have tried explaining or letting dd explain it to them. Some get it. Some don't.
Though dd is only 11 and there is lifetime ahead of her to make her decisions and even change her mind, I feel strongly that she has the right attitude. It has served her well so far. And she is happy beyond words doing what she loves to do. I do not know where the future is going to take her, but we sure do enjoy watching her thrive in this life of doing something she loves. And I think we are going to enjoy her journey immensely as she discovers more and more about her path in finding something she always loves to do.
