
Don’t prematurely obsess on a single “big problem” or “big theory” - aburan28
https://terrytao.wordpress.com/career-advice/dont-prematurely-obsess-on-a-single-big-problem-or-big-theory/
======
gkafkg8y8
It's ok to try tackling a big problem, as long as you know when pause for a
while and come back to it later.

What if Ramanujan had been told by Hardy to stay home and stop working on big
things that he hadn't had sufficient experience in? While there will ever only
be one Ramanujan, he wouldn't have developed into what he did had he
restricted himself. He made a lot of mistakes, and that didn't kill his career
nor did it stop him from producing many great works.

Similarly, Bezos obsessed about a simple online bookstore website. Jobs
obsessed over details for a small number of devices. Torvalds obsessed over an
operating system he wrote. DHH obsessed over a web application framework open
source project for his company. If you obsess over something, it has a much
better chance for success.

If you believe in it, and you see a path to it, don't give up.

~~~
mathgenius
Ramanujan produced a constant stream of results and wasn't at all obsessed
with one big problem to solve.

Terrance Tao is talking about the "hide in the attic for 10 years working on
one problem" attitude. And this he warns against.

As for business development, I'm pretty sure Jobs/Bezos etc actually produced
something in fairly short order, ie. the MVP came out quickly. This approach
of release early, release often seems to be exactly what Tao would endorse.

~~~
joe_the_user
Yes, Ramanujan just floated around dealing with whatever number theories
inspired him, sometimes in a nearly mystical way so he's not a good example.

Andrew Wiles is a better example, since he hit in plain sight working on
Fermat's Last Theorem.

"He dedicated all of his research time to this problem for over six years in
near-total secrecy, covering up his efforts by releasing prior work in small
segments as separate papers and confiding only in his wife."

[https://en.wikipedia.org/wiki/Andrew_Wiles](https://en.wikipedia.org/wiki/Andrew_Wiles)

~~~
Ma8ee
Exactly. He proves the author's very well. Wiles was tenured, had published in
the field already, and made sure that he could continue publishing while
working on the Big Problem.

~~~
nwjtkjn
Tenured at Princeton, had already solved some fairly big problems in the
field, and it helped that FLT had recently been "reduced" to proving a
conjecture about elliptic curves which were already very much in Wiles's
wheelhouse.

Not to take away from his achievement, but I think it is not stressed enough
how much the proof depends on work from previous decades that a priori had
nothing to do with Fermat.

------
jiiam
A dear friend who works in harmonic analysis once added: "Don't even try to
tackle a problem on which Terry Tao is already working"

~~~
btdiehr
Terry Tao is a living legend

------
dmfdmf
I think the way I would phrase the advice is; If you are inspired or
challenged by the "big" problems keep an eye on them but work on other things
that are not directly or obviously related but _may be_ related. What Tao
warns against is a _direct assault_ on a big problem or theory as a career
path or plan. Like expeditions up Mt. Everest, that path is littered with
attempts that reached an impenetrable barrier and had to retreat or perish on
the mountain. If you think you've solved a big problem then your method should
also explain the failure of all the prior assaults to be credible.

Also relevant:
[https://www.youtube.com/watch?v=We760YM5-iM](https://www.youtube.com/watch?v=We760YM5-iM)

That said, don't give up on your dream of solving big problems, someone has to
do it and like Mt. Everest, every field has its _Ark of the Convenant_ or
_Holy Grail_ that challenges and inspires its members. If you are a genius all
bets are off and don't listen to me or Tao ;-)

------
amelius
Could it be that this is excellent advice for an individual, but for society
it may be better if some obsess over a single idea?

------
petters
Tao follows this advice well himself. He seems to be working on the millennium
problem of Navier-Stokes, but works on many other things simultaneously and
published partial results.

------
foobar16372883
There is a state of flow when the mind is completely preoccupied with an idea.
Where the idea itself takes over the mind at all time and in every place and
context.

Although context switches in good measure are useful to creative thought,
there's something to be said about a singular focus.

------
faragon
Tao's article reminds me Poincaré's "Science and Method" book (1908) where it
is explained how to split/address big tasks/problems over long periods of
time.

------
personjerry
That advice was spooky in mirroring startup founder advice: Have a strong
track record, have experience in the field, before you attempt the risk...

------
forgotpwtomain
Counter-example: Yitang Zhang's (recent) proof of a finite bound on gaps
between prime numbers.

~~~
bambax
From the article:

> _While it is true that several major problems have been solved, and several
> important theories introduced, by precisely such an obsessive approach, this
> has only worked out well when the mathematician involved had a proven track
> record of reliably producing significant papers in the area already; and had
> a secure career (e.g. a tenured position)._

~~~
hyperpape
Zhang was surprising precisely because he didn't have that track record:
[https://en.wikipedia.org/wiki/Yitang_Zhang](https://en.wikipedia.org/wiki/Yitang_Zhang).

------
alexmlamb2
This is excellent advice and I think it also applies to fields outside of
mathematics.

------
fuzzfactor
Looks like about 4 years after Tao posted this essay, (St.) John the Commenter
shows up one Christmas Eve not long ago:

"24 December, 2011 at 8:02 pm

    
    
        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."
    

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:

"3 October, 2011 at 4:37 pm

Larry Freeman

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.

The only thing that keeps me chasing these unbelievably difficult problems is
the humility I feel when I realize:

(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.

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.

Regards,

-Larry"

This might have inspired John's following parent comment a few minutes after
his first comment:

"24 December, 2011 at 8:09 pm

John

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.

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.

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."

There is some chance that John didn't really mean to add all these personal
details until after he had read Larry's comment.

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's comment, when John is only the most recent among
a handful of commenters to participate in years:

"24 December, 2011 at 8:27 pm

Anonymous

@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."

Is it just my imagination, or could this be Tao? And could he really have been
on the verge of leaving math before 2012?

Anyway, less than 24 hours later, on Christmas Day, John proceeds to
completely spill the beans to the anonymous perspective seeker:

"25 December, 2011 at 1:22 pm

John

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."

Now that's problem-solving ambition.

This is where I could write paragraphs if not thousands of pages on the
subject, I'll spare you. The quotes speak for themselves.

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 "John" to achieve the
kind of partnership which could make as much money as anyone would like.

Plus, maybe John himself provided some inspiration for Tao to remain committed
to math leadership ever since.

Happy Holidays to all.

~~~
GFK_of_xmaspast
> Is it just my imagination, or could this be Tao? And could he really have
> been on the verge of leaving math before 2012

That's a huge stretch.

~~~
mathperson
he won the fields medal in 2006. he's not perelman

------
spsgtn
I think the emphasis of the article is on the "obsess" verb, not on the "big"
adjective. Big problems and theories are a fundamental driver but obsessing is
not productive.

