Effective Strategies for Choosing a Research Topic

 
How to select a
research topic
 
Shweta Agrawal
IIT Madras
 
How to select a
research topic: A
theorist’s
 perspective
 
How to select a
research topic: A
theorist’s
 perspective
 
Drop modesty and say to yourself,
“Yes, I would like to do first-class
work.”
    
-Richard
Hamming
 
The most important thing before you
choose a problem…
Dropping Modesty
 
 Have the 
desire
 to do excellent work
 
 The 
faith
 that you can
 
 The 
willingness
 to put in what it takes (much toil,
many failures and frustration, much patience)
 
 Attitude that one starts with is important!
 
But this must be cultivated systematically…
 
THE TWO DIMENSIONS OF PROBLEM
CHOICE
 
1
 
(From essay by Uri Alon)
Feasibility Versus Interest
 
Easy-but-not-too-interesting
, a.k.a. ‘‘low-hanging
fruit.’’
 
Both difficult and have low interest
: hard equals
good?
 
Grand challenges
: tough problems with the
potential to considerably advance understanding.
 
Desirable: feasible and with high interest, likely to
extend our knowledge significantly.
Pareto principle of optimization theory
 
 If problem A is better on both axes (feasibility and interest)
than problem B, one can erase B from the diagram.
 
 Applying this criterion to all problems, one is left only with
problems for which there are no problems clearly better in
both feasibility and interest.
 
 These remaining problems are on the Pareto front
 
 Optimal problems move along the Pareto front as a function
of the life stages of the scientist.
 
Problem Choice changes with career stage
 
 Maintain healthy balance between 
hard and
reachable
 
 
Don’t prematurely obsess 
on a single “big problem”
or “big theory” – Terry Tao
 
 Try to work with other 
people
 
 
Do not be shy
 to ask for help if things are not
working out
 
Problem choice in early stages
 
These are things I learned the hard way
 
 When I started my postdoc, I worked essentially
alone for > 1 year almost exclusively on two big
problems
 
 One was solved by another group, one remains
open to this day (5 years later)
 
 I felt I was doing something wrong, didn’t discuss
 
 Lost confidence, came close to quitting
All eggs in one basket: Personal
 
Upside: Research was never so hard after that 
 
TAKE YOUR TIME
 
2
Taking the time
 
 It 
takes
 
time 
to find a good problem
 
 Do not be in a 
hurry 
to “get to work”. 
Savour
 the
process of finding a nice problem.
 
 Be 
creative
 in how you choose the problem. Don’t
rush for the first, most obvious question (it gets
crowded out there)
 
 Be original. What *you* like is important. Stay
committed 
to 
what is interesting
 to you.
 
 
WHAT IS INTERESTING?
 
3
What is interesting?
 
 In the early stages, 
if you want to be safe
, you can
tackle modest improvements over papers that
appeared in reputable venues
 
 As you 
gain confidence
, branch out to more creative
questions
 
 
Interesting = publishable? Who decides? 
What others
think is important but not as important as what you
think.
 
 
If we are 
genuinely interested
, then failures and
setbacks (inevitable and plentiful) do not seem so bad
 
 Once I got involved in a project because I confused interesting
(to me) with publishable
 
 Paper was rejected multiple times. Didn’t really like the question
but had to keep coming up with new ways to “sell” it.
 
 Another paper that took equally long to publish but I liked and
believed in it. Rewriting helped improve it. Satisfied in the end.
Interesting=Publishable? Personal
 
Don’t work on things just because you think they are
interesting to others.
 
There is confusion due to the mixing of
two voices—one is a loud voice of the
interests of those around us, in
conferences, in our department, etc.
The other is a faint voice in our breast,
that says, this is interesting to me.
Listening to our own idiosyncratic
voice leads to better science.
-Uri Alon
 
BE INSPIRED
 
4
 
 A concrete method I have is to maintain a stash of
papers that I have found 
innovative, inspiring and
cool
 
 I periodically look at these to 
rediscover what I love
about my research area. Keep adding to this stash.
 
When I 
feel inspired, I try to think
 of open directions
 
 Choose problems with a 
fresh mind
, e.g. morning
Being inspired while choosing a problem
 
 
 Useful to 
read abstracts
 of many papers, to know
landscape
 
 See many 
talks/slides
 to have high level idea of work
across the space
 
 Think 
wild
 
. Forget about  details, hurdles etc. Allow
the craziest of ideas. Listen to music. Have fun.
 
Seeking new problems
 
It is six in the morning. The house is
asleep. Nice music is playing. I prove
and conjecture.
 
-Paul Erdos
Then, stop being wild and lace up! 
 
 
 
 After the dreamy phase where all ideas are
welcome, 
play devil’s advocate 
and try to look at
why any one would make sense
 
 Do thorough 
literature survey
. Keep abreast.
 
 
Stop reading and start moving
. Knowing all the
details of all science done is unnecessary (and
impossible)
 
When I got (PhD) I knew almost
nothing about physics. But I did learn
one big thing: that no one knows
everything, and you don’t have to.
 
-Steven Weinberg
 
 
 My advice is to 
go for the messes 
- that’s where the
action is –Steven Weinberg
 
Once chosen, be 
diligent
. Don’t give up till you have
tried enough, and understand why you are not able to
make progress (eg techniques not enough?)
 
Even if you have to abandon a problem, make sure
you 
learn
 something from it. Quantify this and write it
down.
Going for the mess (and sticking on)
Keep at it
 
 
Talk
 about research to peers. You’ll get ideas.
 
 Attend and give many talks. 
Ask many questions.
This leads to new problems.
 
 
Be sceptical when choosing a problem
. Place any
question on the map of known results and check if it
is surprising.
 
 
 In crypto, we prove security against adversaries (modelled as
algorithms)
 
In one paper in 2011, I could only prove a weaker property than
I wanted. The adversary in my proof was limited
 
I kept trying to generalize the proof and failed each time
 
In 2016, it occurred to me, is it actually true that the proof can
be generalized?
 
Within half an hour, I had an attack against the scheme, if a
general adversary was considered
Being sceptical: Personal
 
Always ask: can what I am trying to prove true
actually be false 
?
 
 In choosing and later, try to 
keep the fun alive
 
 Should not become all about 
slog
 (though
you’ll need to work very hard)
 
 Work hard, but work 
smart
 
 
Get used to failure
. Keep learning.
Final Thoughts
 
Thank you!
 
References:
 
Richard Hamming: You and your research
Uri Alon: 
How to choose a good scientific problem
Steven Weinberg: Four Golden Lessons
 
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Choosing a research topic involves dropping modesty, nurturing a desire for excellence, and finding a balance between feasibility and interest. Consider grand challenges and the Pareto principle for optimal problem selection as you progress in your career.

  • Research
  • Topic Selection
  • Academic
  • Problem Choice
  • Career Development

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  1. How to select a research topic Shweta Agrawal IIT Madras

  2. How to select a research topic: A theorist s perspective

  3. How to select a research topic: A theorist s perspective

  4. The most important thing before you choose a problem Drop modesty and say to yourself, Yes, I would like to do first-class work. -Richard Hamming

  5. Dropping Modesty Have the desire to do excellent work The faith that you can The willingness to put in what it takes (much toil, many failures and frustration, much patience) Attitude that one starts with is important! But this must be cultivated systematically

  6. THE TWO DIMENSIONS OF PROBLEM CHOICE 1 (From essay by Uri Alon)

  7. Feasibility Versus Interest Easy-but-not-too-interesting, a.k.a. low-hanging fruit. Both difficult and have low interest: hard equals good? Grand challenges: tough problems with the potential to considerably advance understanding. Desirable: feasible and with high interest, likely to extend our knowledge significantly.

  8. Pareto principle of optimization theory If problem A is better on both axes (feasibility and interest) than problem B, one can erase B from the diagram. Applying this criterion to all problems, one is left only with problems for which there are no problems clearly better in both feasibility and interest. These remaining problems are on the Pareto front Optimal problems move along the Pareto front as a function of the life stages of the scientist.

  9. Problem Choice changes with career stage

  10. Problem choice in early stages Maintain healthy balance between hard and reachable Don t prematurely obsess on a single big problem or big theory Terry Tao Try to work with other people Do not be shy to ask for help if things are not working out These are things I learned the hard way

  11. All eggs in one basket: Personal When I started my postdoc, I worked essentially alone for > 1 year almost exclusively on two big problems One was solved by another group, one remains open to this day (5 years later) I felt I was doing something wrong, didn t discuss Lost confidence, came close to quitting Upside: Research was never so hard after that

  12. TAKE YOUR TIME 2

  13. Taking the time It takes time to find a good problem Do not be in a hurry to get to work . Savour the process of finding a nice problem. Be creative in how you choose the problem. Don t rush for the first, most obvious question (it gets crowded out there) Be original. What *you* like is important. Stay committed to what is interesting to you.

  14. WHAT IS INTERESTING? 3

  15. What is interesting? In the early stages, if you want to be safe, you can tackle modest improvements over papers that appeared in reputable venues As you gain confidence, branch out to more creative questions Interesting = publishable? Who decides? What others think is important but not as important as what you think. If we are genuinely interested, then failures and setbacks (inevitable and plentiful) do not seem so bad

  16. Interesting=Publishable? Personal Once I got involved in a project because I confused interesting (to me) with publishable Paper was rejected multiple times. Didn t really like the question but had to keep coming up with new ways to sell it. Another paper that took equally long to publish but I liked and believed in it. Rewriting helped improve it. Satisfied in the end. Don t work on things just because you think they are interesting to others.

  17. There is confusion due to the mixing of two voices one is a loud voice of the interests of those around us, in conferences, in our department, etc. The other is a faint voice in our breast, that says, this is interesting to me. Listening to our own idiosyncratic voice leads to better science. -Uri Alon

  18. BE INSPIRED 4

  19. Being inspired while choosing a problem A concrete method I have is to maintain a stash of papers that I have found innovative, inspiring and cool I periodically look at these to rediscover what I love about my research area. Keep adding to this stash. When I feel inspired, I try to think of open directions Choose problems with a fresh mind, e.g. morning

  20. Seeking new problems Useful to read abstracts of many papers, to know landscape See many talks/slides to have high level idea of work across the space Think wild . Forget about details, hurdles etc. Allow the craziest of ideas. Listen to music. Have fun.

  21. It is six in the morning. The house is asleep. Nice music is playing. I prove and conjecture. -Paul Erdos

  22. Then, stop being wild and lace up! After the dreamy phase where all ideas are welcome, play devil s advocate and try to look at why any one would make sense Do thorough literature survey. Keep abreast. Stop reading and start moving. Knowing all the details of all science done is unnecessary (and impossible)

  23. When I got (PhD) I knew almost nothing about physics. But I did learn one big thing: that no one knows everything, and you don t have to. -Steven Weinberg

  24. Going for the mess (and sticking on) My advice is to go for the messes - that s where the action is Steven Weinberg Once chosen, be diligent. Don t give up till you have tried enough, and understand why you are not able to make progress (eg techniques not enough?) Even if you have to abandon a problem, make sure you learn something from it. Quantify this and write it down.

  25. Keep at it Talk about research to peers. You ll get ideas. Attend and give many talks. Ask many questions. This leads to new problems. Be sceptical when choosing a problem. Place any question on the map of known results and check if it is surprising.

  26. Being sceptical: Personal In crypto, we prove security against adversaries (modelled as algorithms) In one paper in 2011, I could only prove a weaker property than I wanted. The adversary in my proof was limited I kept trying to generalize the proof and failed each time In 2016, it occurred to me, is it actually true that the proof can be generalized? Within half an hour, I had an attack against the scheme, if a general adversary was considered Always ask: can what I am trying to prove true actually be false ?

  27. Final Thoughts In choosing and later, try to keep the fun alive Should not become all about slog (though you ll need to work very hard) Work hard, but work smart Get used to failure. Keep learning.

  28. Thank you! References: Richard Hamming: You and your research Uri Alon: How to choose a good scientific problem Steven Weinberg: Four Golden Lessons

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