Filed under: Mathematics, Quest Log, Random Thoughts | Tags: learning, Mathematics, working
I spent the last two days reviewing and delving deeper into some details on the construction of Galois representation from modular forms. It was a refreshing getaway from the occasional frustrations and disappointments one experiences while conducting new research. Learning new things in mathematics is not as much a challenge nowadays as it was when I began. I suppose I can take pride and comfort in the knowledge that I have grown in mathematical maturity. Everyone needs to return to his or her comfort zone once in awhile to refuel and rekindle the desire and aspiration for improvement, and learning stuff that is well-known and widely accepted is my safe harbor and my favorite retreat.
On the other hand, spending too much time learning new ideas may not be a good thing. It is not just the time commitment, but learning everything that comes my way tends to dilute my focus and make me extremely scattered-brained. So much so that it breeds “mathematical greed”, something that I was seriously plagued by during the early years of my graduate career. I was literally spending every waking moment trying to do something math related, and it was an unsustainable lifestyle that I now learned to shy away from on most days.
For better or worse, I am pleased and grateful that I can still stay away from the internet for a good number of hours and focus on learning things. Even though my merits as a mathematician mostly depend on my ability to conduct new research, I still take great joy and comfort in learning things.
Recently I have been going back to my seven-day-a-week work schedule. It is difficult to gauge your work effort when you don’t have the usual 9-to-5 job. Being mostly in control of my own time, the boundary between my personal life and my work life is extremely blurry. In fact, it is virtually non-existence until recently, when I stopped taking all my math work back home (but soon enough I know I am going to do that again, say, this evening.)
What bothers me, however, is not the amount of time I spent on research work and the lack of a perhaps more “normal” life; instead, it is the unproductive time spent in the office that makes me squinch. For some reason (probably the recent addition of tech-toys to my everyday life), my mind is not as apt at controlling my actions as it used to be. Trifle things like checking Amazon.com’s Goldbox are being quite the hurdle to jump over and continue my research work.
I think it’s time for a good look at the mirror. I need my disciplined self back.
Filed under: Mathematics, Moderation and Balance, Self Improvement | Tags: Mathematics, mind-body connection, observations, physical effects, vitamin, work
You probably know that taking too much vitamin B2 turns your urine bright yellow. It turns out that there is one additional side effect on me.
After returning from the holiday break, I felt lethargic and unmotivated. So I fooled around with my diet a bit, and decided to resume taking Twin Lab’s Daily One Caps multivitamin to boost my energy and stamina. I bought these a year ago when the vitamin B content in these pills was still extraordinarily high. Although these are just multivitamin supplements, the physical effects were much more acute compared to the Centrum brand.
As unbelievable as it may sound, taking these riboflavin-loaded vitamin pills made me unusually moody about things that have no emotional bearing. Just several minutes, I was trying to write up some mathematical computations, but slowly sad memories begin to drift through my mind. I remembered the years of hardship laboring over the tons of mathematical texts that I have to digest, and my eyes begin to swell up. It was not distracting; quite the opposite, remembering these bitter sweet moments made me more focused and resolute on the work at hand, and bestowed me with a sense of purpose and a desire to give all my being to mathematics. Please tell me that I am not crazy.
What did the Twin Lab guys put in their pills anyway?
Filed under: Mathematics, Random Thoughts | Tags: focus, Mathematics, productivity, research
Although I brought several research papers and a book on ergodic theory back home over the holiday break, the only bit of mathematics I did was reading some parts of Yuri Manin‘s delightful book, “Mathematics as Metaphor“.
All this means that shifting back into research mode is going to be a bit of a challenge. Indeed, the five some hours spent by my desk did not yield any fruit. Of course, solid effort does not always lead to real progress, but it is still disappointing when you spent the day giving a counter-example.
I need to regain my focus again. When research is going well, my writing improves too, and let us hope this will happen soon.
Filed under: Mathematics
In contrast to the spur of interest in mathematical research that I underwent just weeks ago, the past several days marked a sharp decline in my mathematical productivity. Part of the problem is that I pushed myself too hard on the 10K run last Friday. For two straight days, I was suffering from various symptoms of a cold. Runny nose, low body temperature, light-headedness, and other irritations compromised my focus and my performance.
The real source of the problem, however, is probably that I am running out of good ideas. Viable and original ideas are the driving force behind an active and exciting piece of research. Just as much as life survives on water, mathematical research survives on ideas. My own research was clearly under nourished in the last couple of days.
The million-dollar question is then: How does one keep the well of ideas from drying up? One simple way is to avoid exhausting all ideas at once. Save some for the next day, and if luck has it, then the untapped ideas may give birth to other ideas. Also, a change of scenery is frequently helpful. I had some of my best ideas when I switched from sitting at a desk to riding on my bike to Princeton. It is a fascinating experience how the human mind works. Lastly, it may be worthwhile to just keep on going even if you feel short on ideas. There are several occasions when overcoming the initial impedance to mathematical work paid off handsomely. Do what you must do, and take it easy when things are really stuck. Remember, a relaxed mind is a creative mind.
Tuesday, October 14, 2008
Filed under: Mathematics
Today meeting with my advisor marked a turning point in my life as a graduate student in mathematics. Many grudges and hard feelings deep inside have evaporated with the one and a half hours of discussion on my thesis research.
I look forward to a productive semester. Now it’s time to go full-throttle ahead.
Thursday, September 18, 2008
For two days now I have adopted a different method to mathematical research. Rather than trying to get everything as precise and rigorous as possible from the start, I learned to sketch a flow chart (in a sense) of the logical structure and formulate a plan of attack to solve the problem at hand. This makes doing math a lot more fun compared to my past approach of polish every argument to my standard of perfection as they are worked out.
Of course, although my new way of doing math is a lot less stressful and a lot more lively and exciting, it also compromised the depth of my thoughts. The easy pace means I am not pushing my brain to think hard and fast, and in turn, I feel my “mental muscles” are growing weak from underuse. To avoid from drowning in a comfort zone, I will still need to do hard and fast mental training. This could take the form of working out exercises, serious and intense reading, quizzes, etc.
Mathematics is in many ways similar to athletics, it takes a lot of hard training and some talent to be good. Build up my mental power.
Tuesday, August 12, 2008
It is difficult to balance physical training and mental work. After two months of incremental physical training, I find myself unable to persevere when it comes to serious mathematics. I am losing the passion that I once had for learning and reading.
Yet this spells something more physiological than psychological. I believe if I cut back (which I eventually will) on exercise, then I will have more energy for studying. I have experienced this change in my behavior around four years ago, and I expect to witness it in the near future.
A well-rested Johnson is a happy Johnson.
Wednesday, July 16, 2008
“The value of compassion cannot be over-emphasized. Anyone can criticize. It takes a true believer to be compassionate. No greater burden can be borne by an individual than to know no one cares or understands.”
–Arthur H. Stainback; author
Filed under: Mathematics
5 hours and 17 minutes of math. I haven’t felt so at ease doing mathematics for a long time now. Although I didn’t do any active research, this is still a good sign. I felt drawn to mathematics again. I felt eager to explore the possibilities outline in the books.
It’s time to make the final sprint toward the finish line.
Thursday, June 19, 2008
