Rationality advice from Terry Tao

Via a link on IRC, I stumbled upon the blog of the mathematician Terry Tao. I noticed that several of his posts contain useful rationality advice, part of it overlapping with content that has been covered here. Most of the posts remind us of things that are kind of obvious, but I don't think that's necessarily a bad thing: we often need reminders of the things that are obvious.

Advance warning: the posts are pretty well interlinked, in Wikipedia/TVTropes fashion. I currently have 15 tabs open from the site.

Some posts of note:

Be sceptical of your own work. If you unexpectedly find a problem solving itself almost effortlessly, and you can’t quite see why, you should try to analyse your solution more sceptically. Most of the time, the process for solving a major problem is a lot more complex and time-consuming.

Use the wastebasket. Not every idea leads to a success, and not every first draft forms a good template for the final draft. Know when to start over from scratch, know when you should be persistent, and do keep copies around of even the failed attempts.

Learn the limitations of your tools. Knowing what your tools cannot do is just as important as knowing what they can do.

Learn and relearn your field. Simply learning the statement and proof of a problem doesn't guarantee understanding: you should test your understanding, using methods such as finding alternate proofs and trying to generalize the argument.

Write down what you've done. Write down sketches of any interesting arguments you come across - not necessarily at a publication level of quality, but detailed enough that you can forget about the details and reconstruct them later on.

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If you unexpectedly find a problem solving itself almost effortlessly, and you can’t quite see why, you should try to analyse your solution more sceptically. Most of the time, the process for solving a major problem is a lot more complex and time-consuming.

I would add that if you unexpectedly find a problem being extremely hard to solve, you should react the same way. Devote a little time to trying to solve it under the assumption that a simple solution exists. It works surprisingly often (i.e., more often than never).

It would be good to summarize your selected links in your post - perhaps a sentence each. They are good posts, but clicking through to them is inconvenient.

Edit: Five bonus points for anyone who sees something wrong with the above.

The links are a sentence fragment describing the conclusion, and you linked a site that I am just proactive enough to mouse over and see the convenient name in the bar at the bottom of the webpage without summarizing it? Hmm, I'd link to a programming blog that gets more in-depth about user lazyness instead of a less wrong post, is the inbred community links what's wrong?

No, it was simply that I criticized Kaj_Sotala for posting links without summarizing by posting a link I didn't summarize. You're right that it's not as big a deal for people familiar with the post from the title, but...

(p.s. the "inconvenient" link describes how a trivial inconvenience - like finding an internet proxy or sending an email before posting - can act quite effectively as a major barrier to an action. Implied is that following the links to see what Kaj_Sotala is reviewing positively is a similar inconvenience, and therefore might lead to the post being unfairly ignored.)

Wow, rationality notes from maybe the most brilliant thinker of our times! I would not have believed the Terry Tao has time to write blogs while churning out all those deep results with apparent ease...

I am impressed, Definitely a treat!

Wow, rationality notes from maybe the most brilliant thinker of our times!

Congratulations on eliminating all the other candidates so easily!

I challange you to name your candidates... ;)

There are an awful lot of great thinkers, but really rare are those kind of human beings that appear to belong to a different species.

Well, I know very little about Terry Tao, so I'm going to say everyone else who's ever won a Fields Medal.

Not all Fields medalists are made equal... :)

Really: It's just a side effect that he got the Fields medal.

I don't know him personally, but I know several (unrelated) people personally who worked with him, and based on their stories + information available on the internet I was equally impressed by him before this medal event...

That guy simply has an impeccable record of achievements from age two on (disregarding a lot of other prizes)

  • age 2: Teaching himself arithmetics (from Sesame Streets)
  • 8: Scoring 760 on SAT in Mathamatics
  • 10: Winning bronze medal at International Mathematical Olympiad
  • 13: Winning gold medal at International Mathematical Olympiad
  • 17: Master in Mathematics
  • 20: PhD
  • 24: Full Professor at UCLA
  • 31: Fields Medal
  • 34(now) 140+ publications and 9 books in various different fields of mathematics, like: harmonic analysis, partial differential equations, geometric combinatorics, arithmetic combinatorics, analytic number theory, algebraic combinatorics and representation theory.