She chooses to think deeply and slowly about problems but I am sure she can think fast if she has to. You don't get gold medals at the IMO otherwise.

http://www.imo-official.org/participant_r.aspx?id=926

Einstein fit that bill, as well. Scientists that worked with him noted he was neither a fast thinker nor the best of mathematicians.

This isn't really true; scientists also praised Einstein for his deep mathematical intuition. His work on Brownian motion and general relativity was new and difficult mathematics (GR still is). GR is also startling for the mind-bending fundamental intuitions behind it. He asked mathematicians for help hammering out details, but 1) everyone does this and 2) mathematical rigor and abstraction wasn't nearly as well-established back then as it is now, and was difficult to grasp for many physicists and even mathematicians. For example it was several years before Minkowski established the connection between special relativity and the "shape" of spacetime, giving rigor to Einstein's intuition--but doing so is nowdays an easy exercise in undergraduate mathematics.

> Scientists that worked with him noted he was neither a fast thinker nor the best of mathematicians.

I thought this was mostly a myth. Do you have source for that?

I copied the quote from [1] however credible you find that source. (Though they provide references to several books at the end of their article.)

Also, Darwin:

"At no time am I a quick thinker or writer: whatever I have done in science has solely been by long pondering, patience, and industry." [2]

On a personal note, I entirely relate to the slow thinker. Most smart peers of mine are fast thinkers and I'll usually lose to them on puzzles and tricky math problems when it is a matter of speed, but then I'll solve problems that these same people give up on and claim too difficult if I can sit in a quiet room with my fists on my head.

I have a suspicion that fast thinking involves a developed ability to filter out (quickly) what seem like dead end avenues -- so the fast thinker can hone in on the promising avenues and get to a local maxima solution faster. But for some problems -- especially ones that require very non-traditional paths to solutions -- this filter fails and prunes away avenues that actually lead to a solution to that "impossible" problem or global maxima solution.

I realized a long time ago the danger in pruning away the "obvious" dead ends, so I think my slow thinking comes from a refusal to categorize anything as a dead end until it is provably so -- because of a worry I'll prune away the solution. A bunch of avenues will present and I'll need to consciously sort through them. So my filter is slow and requires me to retreat to that quiet room to go sort through all the possibilities. But then I'll come up with gold.

I have a theory that I'll put out here... that slow and fast thinking are developed tendencies not innate qualities. In my experience most of the smart people I know are fast thinkers. Which makes sense if this is developed, because there's an ego reward involved -- especially in our educational systems -- for developing that way. And the only reward for slow thinking is solving a hard problem, but as a kid in school, where's the external reward in that? And how often is the opportunity for solving really hard problems given? Basically what I'm saying is that I'd like to see more slow thinkers in the world. (I'm not kidding.)

[1] http://www.unmuseum.org/einstein.htm [2] http://www.criticalthinking.org/pages/the-questioning-mind-n...

As a fast thinker, everything you say here makes sense to me, especially about quickly pruning dead ends. I admire my slow-thinker friends for not doing that, and I've always considered slowing my thinking to be a top career goal.

As for whether it's a developed vs innate quality, I don't remember ever thinking differently and being trained to think the way I do because of my environment. I would agree that in our system fast thinkers are rewarded more, but that doesn't mean that our system develops fast thinkers at the expense of slow thinkers, or that its any less innate. It just means that slow thinkers have more difficulty being recognized earlier (hence "late bloomer" or missing the "precocious" label.

I definitely remember seeing that in one of Feynman's autobiographies like 'Surely You're Joking Mr. Feynman'

Einstein to Feynman: "Please explain things slowly"

Feynman seemed like a particularly quick thinker. I suspect a fair number of "geniuses" would need him to slow down.

It's interesting to compare the two approaches (and characters) of Feynman and his close colleague (with whom he shared the Nobel), Julian Schwinger. https://en.wikipedia.org/wiki/Julian_Schwinger#Schwinger_and...

You could call Schwinger "slow", but he "saw" very deeply. After all, he found and corrected problems with the Dirac equation.

Context, please. That means Einstein was a 99.99%ile fast thinker in a room of 99.999%ile fast thinkers.

"This is related to another comment about two types of genius. There are people who solve a problem the same way that you do, just much much faster. You can imagine doing the same work they had done, but rather than an hour or a day, you would have got to the same place after months of hard work and dead ends. These people are much like ourselves, only a lot quicker. Then there are the other people who show you a solution, and you have absolutely no idea how they even got started. Feynman fell into this latter group." [1]

"Upon starting high school, Feynman was quickly promoted into a higher math class and an unspecified school-administered IQ test estimated his IQ at 125—high, but "merely respectable" according to biographer James Gleick;"[2]

I think people with extremely high IQ tend to be "fast thinkers" and they seem to rely more on logical thinking while those who have sufficient IQ tend to be "deep thinkers" and rely more on intuition/epiphanies.[3]

John von Neumann would the "fast thinker" type of Genius.

[1] http://c2.com/cgi/wiki?FeynmanAlgorithm

[2] https://en.wikipedia.org/wiki/Richard_Feynman#CITEREFGleick1...

[3] “I never made one of my discoveries through the process of rational thinking” ― Albert Einstein

Well, my opinion is not entirely uninformed or off the cuff. I was briefly Director of Community Life for The TAG Project. I homeschooled my gifted-learning disabled sons. I attended a gifted conference and was a low-level presenter. I did plenty of reading on the subject for a time and participated in lots of discussions with other informed individuals in the gifted community, including some fairly important professionals in this niche field.

First of all, most IQ tests do not go above 140. So anything anywhere near 140 may only be telling you the person is at about the limits of what the test can measure. Even for those tests that do go above 140, it requires a qualified assessor to interpret it properly. The smartest kids often do not measure as being all that smart by standard measures. "Genius" is, basically by definition, someone who thinks differently from others. So measuring the kid who is radically different by standard measures has a track record of missing a lot.

In recent years, there is increasingly research into and available literature on the idea that gifted kids have different minds. They are not merely "more" of something, they are fundamentally different. The correlation of "speed = intelligence" is a rubric which assumes gifted kids are simply "more" of something. Yes, they do tend to be faster than average, even if they are slow compared to other gifted students, but it's really a lot more complicated than that and I think the emphasis on speed does a huge disservice to the gifted community.

The "fast = smart" paradigm is a really major metaphor for giftedness in the world. For example, Stephanie Tolan's essay "Is it a cheetah?" is very popular: http://www.stephanietolan.com/is_it_a_cheetah.htm I once wrote something of a polite rebuttal to that which used redwoods and gazelles as other metaphors. I am not terribly important in the world and it did not become popular (and is no longer online, unless it got captured on The Way Back Machine). I think the cheetah metaphor does a disservice to the gifted community in part because of the unstated assumption that smart people are all dangerous predators. Gazelles are just as fast and are not predators. Why not use that as a metaphor?

Anyway, I am quite busy today so I don't plan to argue this or dig up detailed supporting links. If you really want to look into it, HN's member who goes by the handle tokenadult is a good resource on the topics of intelligence and education. I believe his profile contains links to resources and his posting history, both comments and articles, is likely to be enlightening. (Though I have no idea if he would agree with any of my views above. He and I are not close. We haven't talked in quite a long time. But I have reason to believe he remains far more current on these subjects than I am.)

I actually agreed with everything you say. You can be a really great Genius, much like Feynman/Einstein without needing to have a stratospheric IQ like John Von Neumann.

Deep thinkers tend to be more original and there is actually a negative correlation between extremely high IQ and creativity.

Those profiles are probably just trying to make her seem more relatable.

Extremely fast thinking is the name of the game in the IMO and similar competitions. In fact, the emphasis is so much on speed that there are often doubts as to whether the medalists will also be good at research.

There's probably more kinds of geniuses than those that do well in speed math competitions. At least, I hope for all of our sake.

It may be worth clarifying the sort of "speed" we're talking about here.

An IMO takes place over two days. On each day the candidates get a question paper with three questions on it. They have 4.5 hours to attack the questions. The threshold for getting a gold medal might be roughly equivalent to getting five of the six problems more or less completely solved.

The questions are always of the form "prove X" -- maybe occasionally "prove or disprove X, whichever is possible" or "find quantity X, with proof"; but it's always a matter of finding proofs -- where X is something no more than a few lines long.

So it's "speed math" in comparison with actual academic mathematical research, which typically takes place on a timescale from weeks to years and where there's no guarantee that any human-accessible solution exists. But it's a whole lot slower than pretty much anything else these (roughly) 16-19-year-olds are being asked to do in mathematics.

And, empirically, it does turn out that people who do well in IMOs tend to do pretty well in mathematical research, and in other mathematical things they put their minds to. (But yes, of course there are kinds of genius that have nothing to do with mathematics, and kinds of impressiveness that have nothing to do with genius; and there are plenty of first-rate researchers who never took to IMO-like problem-solving.)

(Random example of an IMO question, from this year's IMO, to give an idea of what a typical X looks like: "For each positive integer n, the Bank of Cape Town issues coins of denomination 1/n. Given a finite collection of such coins (of not necessarily different denominations) with total value at most 99+1/2, prove that it is possible to split this collection into 100 or fewer groups, such that each group has total value at most 1.")

My point wasn't that there aren't multiple types, but that someone who wins both the IMO and the Fields Medal is exhibiting at least two "types" of genius at once -- normal thinking but at a much faster rate (IMO); slow thinking but at a much deeper level (Fields Medal).

Do you or anyone else have any further sources studying this split between "fast thinkers" and "deep thinkers"? I would be very interested in a way to find people who were "deep;" it seems like most of the technical interviewing techniques screen more for "fast" people.

You might wish to look at fewer applicants sporting advanced degrees and specifically hire roles that deep thinkers would naturally gravitate toward, degree or not.

As elsewhere mentioned, our educational system often ties success to fast thinking. I've always known I am not a fast thinker and, in fact, had often been the slowest thinker in my classes. This made school difficult and I struggled accordingly. Ultimately, I offset this by studying harder than my peers. For me, it has never been about reading the material and repeating, for example, some mathematics system from memory, but in truly understanding that system.

I consider myself a deep thinker that can easily connect concepts, graph relationships, and see the big picture. This is why I prefer to work as an architect, on security projects, and inevitably play the right stocks on the market. I suppose, anecdotally, if I'm any model, that deep thinkers might be better suited to certain roles and might naturally gravitate toward them.

Finally, and now a bit off-topic: The fact that deep thinkers might be equated with "late-bloomers" might have to do less with "figuring out what they're good at", and more to do with a society and a system which is prejudiced against them. If deep-thinkers were better nurtured and led through the educational system, they may not spend their thirties, or even 40's, learning how and where to apply their talents.

I think a better distinction are qualities of intelligence. For example a meticulous person will do well in a hard pattern matching puzzle, but ask them to do symbol substitution and they will be relatively slow and get a low score.

interesting. the "fast vs deep" comment intrigued me; i find i can go exceedingly deep when i can let things "simmer." to your comment, i had an intelligence test administered as a teen and the two outliers were basically symbol substation (< avg) and pattern matching (high).

It's a common pattern with engineering types. In programming you have to be highly detailed and accurate because computer languages are not forgiving, and you have to notice tricky patterns to fix bugs. It's called being meticulous officially I think. This is why you need someone trained to interpret your IQ test, you cant just feed them into a scantron.

There is a skill component to those things although. You could practice them a bit and improve your scores significantly. But is that really intelligence or just skill? It will always be a combination.

An entire book was written about it recently called Thinking Fast, and Slow.

It is a detailed 900 page exploration if a lifetime of research from the famous behavioral economist Daniel Kahneman on the topic