Don’t prematurely obsess on a single “big problem” or “big theory”
Looks like about 4 years after Tao posted this essay, (St.) John the Commenter shows up one Christmas Eve not long ago:<p>&quot;24 December, 2011 at 8:02 pm<p><pre><code>    John

    I have always “intuitively” known to follow this excellent advice.
    I use this kind of advice to know when to “give up” (temporarily) on a given approach to a particular problem and move on to other things. It is a non-obvious battle deciding whether one is wasting time repeating the same attack or being impatient by not pursuing a given approach long enough. Furthermore, an outside objective observer cannot always tell – unless they are experienced in one’s particular area of math. Same applies to any field.&quot;
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Continuing to scroll downward through the chronological parent comments, John encounters a comment Larry had posted to Tao not long before John had gotten there:<p>&quot;3 October, 2011 at 4:37 pm<p>Larry Freeman<p>Thank you very much for this well-written essay. I am guilty of the very thing that you warn against (I find myself working exclusively on impossible math problems: collatz conjecture, twin primes, Legendre conjecture) and I agree with each of your points.<p>The only thing that keeps me chasing these unbelievably difficult problems is the humility I feel when I realize:<p>(1) I’ve made no progress at all
(2) Any sign of progress is more often than not a sign of a mistake in my assumptions.
(3) I am learning number theory and enjoying it.<p>I am too old to make real progress in mathematics (I’m 40+) but working on the famous unsolved problems gives me a great respect for the brilliant mathematicians who have made progress in the past and helps me to acknowledge my own limitations.<p>Regards,<p>-Larry&quot;<p>This might have inspired John&#x27;s following parent comment a few minutes after his first comment:<p>&quot;24 December, 2011 at 8:09 pm<p>John<p>I meant to add: one of the great things about math, and one of the reasons I chose this field, is that one can do great math into old age, unlike fields like sports or ballet, where one has a very limited time that one can do those activities, because one’s body ages.<p>Thus, in math, one can always keep building and expanding on what one already has done and learned and inserting new research that comes along into one’s work.<p>I actually formally entered the math field relatively “late” (graduate school, after a period of work in my undergraduate major). I entered math because I needed to solve some extremely difficult applied math problems first before returning to work in my undergraduate major. I intended my foray into math to be just “temporary”, because I (in my naivete) expected to “quickly” solve the major applied math problems, say, in 4-5 years, and then “pop out” of math, and then pop back into work, applying all these wonderful results that I had proved for my math PhD. It’s been 23 years since I “entered math”, and I still have not popped out again, because the problem are just so overwhelmingly difficult, far more than in any other field.&quot;<p>There is some chance that John didn&#x27;t really mean to add all these personal details until after he had read Larry&#x27;s comment.<p>Less than 20 minutes later, my good friend Anonymous, surfing the entire internet as he usually does regardless of whether it is Christmas Eve, randomly stumbles upon John&#x27;s comment, when John is only the most recent among a handful of commenters to participate in years:<p>&quot;24 December, 2011 at 8:27 pm<p>Anonymous<p>@John, would you be kind enough to share the applied math problem that got you sucked into math in the first place? I am at the verge of leaving math and I feel a sense of relief after having solved several of the open problems in my field; one of them is still pending but I believe the ideas are in place. So I would like to put my experience in perspective of others.&quot;<p>Is it just my imagination, or could this be Tao?  And could he really have been on the verge of leaving math before 2012?<p>Anyway, less than 24 hours later, on Christmas Day, John proceeds to completely spill the beans to the anonymous perspective seeker:<p>&quot;25 December, 2011 at 1:22 pm<p>John<p>Yes, Anonymous. Ever since 7th grade, when I openly declared that I wanted to become an “organic synthesist” when I grew up, my dream was to become a mad scientist! Since then, I’ve learned of a new hope for a path to that dream: nanotechnology. And, my years in chemical engineering lab at school, at work in a chemical lab, tutoring others in math applied to science (linear optimization, statistics, probability), and my lab courses in biotechnology all point to one burning conclusion: the technical problems of moving atoms around in nanotechnology to where you want them to be won’t be solved until we have complete solutions and understanding of the nonlinear partial differential equations (e.g. Schrodinger) that govern those atoms. I am convinced now more than ever before in my life that this is true, as a result of my experiences and interations.&quot;<p>Now that&#x27;s problem-solving ambition.<p>This is where I could write paragraphs if not thousands of pages on the subject, I&#x27;ll spare you.
The quotes speak for themselves.<p>Over a lifetime, having some familiarity with these technologies and what is required to achieve breakthroughs, I would have to say that if I was a capitalist I would find it most worthwhile to invest in &quot;John&quot; to achieve the kind of partnership which could make as much money as anyone would like.<p>Plus, maybe John himself provided some inspiration for Tao to remain committed to math leadership ever since.<p>Happy Holidays to all.