The irony is that this is being argued by person with the best documented genius in the history of mathematics. His official IQ of 230 remains the highest officially measured IQ in the world. He taught himself to read by age 2. He was taking Calculus at age 7. He remains the youngest person for any level of medal in the International Mathematics Olympiad. That doesn't quite convey it. The youngest person to earn a bronze in that competition was 10. Silver was 11. Gold was 12. All three records were set by Terrence Tao, who then didn't bother competing any more.
His success is comparable to any person in the history of mathematics. Yes I am including Euler, Gauss, and Erdös. Euler possibly covered a bigger breadth of math. Gauss created more fields. Erdös solved more problems. And Tao has made more progress in more hard problems that had stumped everyone else.
The early mastery of swearing I picked up between backseat driving (that is, listening to my Scottish mother's running commentary on other drivers) and my spongelike absorption of Canadian broadcast media, earned my parents a stern reproach from the ultra-bourgeois kindergarten they sent me off.
The IQ figure of 230 can't be calculated on the usual scale with a mean of 100 and a standard deviation of 15, because if so it would mean that a world with our current population only had a 1 in 57 million chance of containing someone as smart as him. How could we possibly know enough about population statistics to know such a thing? Especially given that we do in fact have him in our world.
Not only that but standard tests don't even reach reach the point where you can distinguish people near the top. If you have, for example, Raven's Advanced Progressive Matrices, you're dealing only with 48 questions. I vaguely remember that making four mistakes at the age of 17 means an IQ somewhere in the mid-150s (with a standard deviation of 15). If you can only distinguish three more values above 150s, I don't think you can reasonably reach even 200, not to mention 230.
You are right that no adult test will give an IQ that high.
However the original definition of IQ was in tests for children, and it was measured as mental age divided by physical age. Those tests are still used for children, and it IS possible for a 6 year old to get an official IQ of 230 on a test like the Stanford-Binet.
Which is exactly what Terry Tao did at the age of 6. Comparisons to adult tests may be problematic. But it remains an officially recorded IQ from a standard test.
I think what he meant was that if Tao indeed has an IQ of 230, then on average one seven-billion-people-world out of every 57 million such (random) worlds contains one person as smart as Tao, or, that you need to sample something like 400 quadrillion people to find one such person. So your "122" figure doesn't seem to have any meaning here (at least to me).
I think the parent's point is that you would need 50 something millions worlds like ours to find a single person with such a high IQ score.
I haven't checked the maths, but I know the Gaussian distribution is falling fast past a few standard deviation, so such a result would not surprise me.
I admit I'm not very informed about what IQ denotes, but wouldn't such a probability need to include the population of the world? Is that a parameter in the calculation of IQ?
It was developed as a ratio between mental age and physical age, times 100. So if you performed as expected, your IQ was 100. It was originally developed as a way of finding people who were behind, literally "retarded". However it also proved useful as a way of finding people who are intelligent as well.
After IQ tests were adopted in school systems, we found that they were approximately normally distributed with a mean of 100 (by definition), and a standard deviation of 15-16. For a variety of reasons (including identifying military recruits to train for specialized roles), there was a desire to have ability tests aimed at young adults. We developed those and scaled them to be explicitly normal with a mean of 100 and standard deviation of 15 or 16 (depending on the test). We also found that childhood IQ is a fairly good predictor of your later adult abilities, and therefore many of those tests are ALSO called IQ, even though there is no quotient involved.
On the adult tests, the tests do not scale out to IQ 230, nor is it likely that anyone is that many standard deviations out. But on the child tests, there is no problem scaling it. And it turns out that, in practice, the tails are heavier for the original type of IQ test. Which means that it is more common to find a 6 year old who performs at a 14 year old's ability, than a person who is over 8 standard deviations out.
Terry Tao had his IQ officially measured on a childhood test, not an adult one. However there has been no test since that is able to reliability measure his ability, particularly in math.
Consider, at 7, his SAT score put him well within the top 1% of college-bound kids.
At 10, his performance on the International Math Olympiad meant that he was literally in the top handful of high school students in the world.
Yeah, we don't have properly scaled tests for that.
I'd add on top of that that these days adult IQ is instead defined to have a normal distribution with mean 100 and standard deviation 15. This is achieved by 'grading it on a curve'.
That's why my above comment was explaining why the 230 figure couldn't possibly make sense under the modern definition.
However the Stanford-Binet test is still used for children. And in young children can still produce extremely high IQ scores.
Also note that while usually the standard deviation is made to be 15 these days, there are still tests, like the Binet and OLSAT, where the standard deviation is 16. That's why I said that the standard deviation depends on the test.
Yes, I used the world population figure when I was calculating that probability. But the world population size is not used in the definition of IQ itself.
Echoing others, hyperlexia is a thing, and reading by age 2 isn't really all that special. I was reading by age two and a half, and my own kid was reading just before turning two. I'm no genius, while she's definitely sharp but not gifted.
Calculus at seven I can believe, but teaching himself reading at 2 sounds like something that goes against what we know about biological and social development of the child.
And official IQs of 230 and 300 sounds like someone doesn't understand what IQ is or the meaningfulness of measuring/quantifying such in a standardised way.
Obviously the person may be exceptional, and I do not mean to take anything away from Terence in his work that i'm clearly unqualified to comment on (it wouldn't surprise me if a bit of digging shows him unconnected to such claims), but we shouldn't just accept such things as given. Extraordinary claims require extraordinary evidence...
Reading at 2 is well-attested by multiple sources.
The IQ was a case of going back to the original kind of IQ test for children, mental age divided by physical age. At the age of 6 he performed at a level to be expected of a 14 year old on the Stanford-Binet test. At the extremes of these tests, the bell curve approximation. So yes, his IQ was measured that high. But it is not strictly comparable to adult IQ tests.
It should be noted that Terrence Tao's early achievements were well documented because he met Dr Miraca Gross of New South Wales at age 3, who was running a longitudinal study of Australian gifted children. Tao, of course, wound up as the star of the approximately 60 children in the study.
I must reiterate, I don't doubt Terence's abilities, what I doubt are repetition of borderline mythical tales without extraordinary evidence (albeit,I accept someone might say Terrance is the extraordinary evidence).
sure, we have many attestations of speed reading too, and of course there will be attestations of people trying to sell a particular child or education method (or indeed scam).
And I've seen some very convincing performances (and yes, 2 year olds can pick up some basic symbolism, recognition, and repetition). but they lack the ability to comprehend or extend past their specifically repeated contexts. if you film only the contexts of their true positive successes, you can almost sell it, but their errors in extension to anything but rote quickly reveals their comprehension of what they're capable of shouldn't be confused with literacy/numeracy.
different issues abound with attempts to measure or quantify IQs in the extreme ranges at all, let alone in children for which there will be almost no standard applicable method, and it's interpretation is even dodgier.
I mean, another cynical man might say, obviously someone who has lived a life like Terrance must have been given remarkable opportunities. since he clearly did not introduce himself to the gifted study at age 3, and given that we do not have standardised testing at such an age someone was likely a driving force behind him in his youth. the obvious candidate would be his parents, who partake in strong educational and repetitive training, but in the context of the pedagogy of Australian education of the time, would also have to had a very strong narrative needed to overcome some of the dominant "hold them back" attitude of the time.
I mean, we see the same thing with Beethoven and the like. everyone is so focused on the prodigious properties of the person in their later life, critical thinking and skeptical inquiry tends to go out the window. we want to explain greatness through some inherent difference, rather than say the alternative: maybe Terrence is great because of some innate ability. but primarily it is almost certainly the opportunities afforded to him via his circumstances combined with the work and practices and momentum of his parents and his family and then in later life, of himself.
relatively non-scientific hocus-pocus like "taught oneself to read at age 2" literally would go against almost all knowledge of language or child development theories. yet otherwise intelligent people accept such old wives tales without much critical thought.
Teaching a (bright) kid reading at age two may be possible by my experience. At that age, with a lot of talking to grown-ups or listening to stories, kids can have a surprisingly immense vocabulary. But "teaching himself" is a little bit too much for my taste.
I have a child that started reading at 5. It was very motivated and learned the basics in a couple of weeks. It really gets much simpler once they understand the basics. But to get there, we had to invest a couple of hours (say 5-10h total) into fundamental pronunciation and character recognition. Someone has to be there for the child to tell them the difference between d and b, or l and I, or e and a, and so on.
Now here's the catch: For someone in the position of teaching a motivated, intelligent child, it may actually feel like the child is teaching itself. But that's presumably skewed by our own school/college/university experience of learning stuff we were actually not that interested in.
I bought my kids iPads and educational apps from Originator which taught them letters and numbers. Granted, papa lizard has given them very good genes but the result was them knowing the English alphabet and numbers past 100 at 2-3 and reading at 5. And English is not even our first language.
Those iPads were the highest ROI of parenting so far. Please give your children high quality apps.
Sorry for semi-off-topic reply, but would be very interested in any other recommendations you may have, have been looking for high quality resources too.
The outcomes depend on how much and when the students were accelerated in school.
ETA:
The two extremes:
“… 17 of the 60 young people were radically accelerated. None has regrets. Indeed, several say they would probably have preferred to accelerate still further or to have started earlier…. The majority entered college between ages 11 and 15. Several won scholarships to attend prestigious universi- ties in Australia or overseas. All have graduated with extremely high grades and, in most cases, university prizes for exemplary achieve- ment. All 17 are characterized by a passionate love of learning and almost all have gone on to obtain their Ph.D.s.”
“The remaining 33 young people were retained, for the duration of their schooling,… Two dropped out of high school and a number have dropped out of university. Several more have had ongoing difficul- ties at university,…”
Based on this HN comment [1] it appears the participants have been anonymized. It also quotes some of Terrence Tao’s education and makes a claim there was someone else who may have equaled Tao in math ability, but did not have the educational support structure to recognize and nurture it.
It's great to see the positive outcomes of acceleration. I saw so many kids burn out on accelerated programs, and have generally become cautious about them.
It's also nice to know that 2 years was enough for positive lives even for the "genius" children, which sets a sort of upper bound!
As a parent I’ve come to believe a lot of the stories about how so and so was playing golf or skiing or playing piano by 3 are very biased retrospectives. My kid was playing notes on harmonica at 18 months. Could he carry a tune? Of course not, but if one day he turned out to be a musical genius I could brag he has been playing instruments since he was an infant. See the careful embellishment?
A kid who has memorized some sight words or some books can certainly claim “reading”, with just enough truth there for the tale to take hold when they do well later in life.
In many cases I'd agree with you. But in his case, he had come to the attention of researchers into high IQ by the age of 3, and the stories were recorded when they were still fairly fresh.
Yeah there's a considerable difference between "my kid is a genius among other kids" (probably what a lot of parents feel about their children) and "my kid is a genius even when compared to adults."
for the record I've got a son who is going on three now and I'm finding the developmental aspect fascinating. my wife is also studying some childhood development atm. I assumed he'll run
risks of being my "problematically gifted" given his parents :P But i have a very skeptical mind, it pays the bills.
I've observed in my research (and in real life) many various impressive renditions of what i call "stupid toddler tricks". i saw a 1 year old count to 20. my own kids take books to bed at 2 and "reads" them to himself.
could the kid do math? could my kid read? No. of course not. you probe a little bit deeper and all the trappings of what we adults call cognisance fall away. the one year old has no idea what they were reciting. my kid repeats (albeit poorly) what he heard us say when . "reading",but a little bit of digging reveals the limits of his comprehension. kids use the pictures and other hints hints as cues, they're (the clever bastards),they have a brilliant verbal/aural ability at such an age, and they can have some kind of basic symbolic ability and rote repetition. And you
can get them to do amazing things if you record them doing the trick but don't dig any deeper into their mental processes.
I'm guessing that people who are downvoting don't understand child mental development, have a vastly simpler definition of reading than myself, or don't understand how many layers of development are required to arrive at actual reading that have to be passed first. i do think you could quickly show such a trick to a well meaning person and get the legend started however...
If the two year old in question knows their alphabet, upper & lower case, knows most of the sounds the letters make, and can sound out unfamiliar words and sight read the rest, I don't really see what's controversial about calling that "reading". It's not a stupid toddler trick or a mark of genius, either.
If we're going to add comprehension requirements on top of that, then what passes as reading is pretty abysmal even for some adults.
Googling it, it seems like the claim that he taught himself to read when he was "a little over two" (ie not literally 24 months) has been repeated among multiple reputable news sources (New York Time, SMH, The Age).
No comment on the IQ.
>Calculus at seven I can believe, but teaching himself reading at 2 sounds like something that goes against what we know about biological and social development of the child.
It doesn't seem too far-fetched, to be honest. Back when my wife worked in child-care, she knew this one kid who was speaking in multi-word sentences at 9 months old. Most kids don't reach this milestone until they're 2 1/2. Kids can and do surprise you.
I'm only addressing teaching himself to read at two:
Check out "How Teach your baby to read" by Glen Doman.
He makes the case that it is pretty much an inmate ability if encouraged correctly.
The method has been around long enough to have some backing and witness, but it doesn't actually seem to confer much long term advantage.
I ended up not using it with my kids after feedback from a friend and some further reading.
My understanding is that for most people intelligence isn't a result of starting early, but rather having the brain finish late - i.e. remaining plastic longer.
I wasn't prepared for how innate verbal language, specifically stories, are. My kid would come home from preschool and accurately recite ten minute long books, full of unknown words, the same way I idly hum a tune. It was a lightbulb moment for me- I had always wondered how oral tradition could possibly hold up over centuries, but my god we're wired for it.
People seem to interpret my comments as some kind of tall-poppy syndrome or ignorance, but I actually believe that a lot of these mathematical abilities do generate at about the age that Terrence was said to display them (even if we accept he was early and prodigious).
if someone told you that they developed sight before they physically developed eyes, surely you'd pause for thought. But make similar claims concerning the neurological development or mental faculties in prodigies at a young age and suddenly everyone's critical thinking switches off.
I've actually read the study which involved Terrence before this thread, and I'll repeat it again: nothing I'm saying is trying to take away from his accomplishments or current abilities.
The far more plausible story is simply that he had two highly educated parents, one of whom was a math teacher, he has some innate ability, and his parents specifically focused on him and taught and pushed him in math from an early age, then they went about accessing opportunities for him to learn and continue his development at an abnormally early age and they additionally got him special access to educational resources, educators and equipment.
If anything, the video and further research confirms my early conclusions, but my point is really quite fundamental and has little to do with Terence's abilities or current day achievements: I don't believe a 2 year old can teach themselves to read (or at least to anything approximating what a skeptical person would call reading). I think anyone who's had dealing with kids and understands development would say that claim at least SMELLS of bullshit if it isn't actually so.
well, firstly, the claim can be broken down into two parts: taught himself, and reading at two.
I won't address the first because the discussion will get too long if you think that's genuinely how children learn, even geniuses.
on the later, because the basic foundations of math can be found in (at least some) ten year old minds. what the common man believes is possible in math is mainly influenced by cultural exposure and the order in which we learn it. But there's really only 3 - 4 meta-concepts that underlie all of math, and the rest is about exposure/experimentation, syntax and terminology. Terrence himself I believe says as much and if you read through the accounts of interviews with Terrence at a young age it's apparent that's how his mind is working (and explains the concepts he understands, the mistakes he makes, and those areas he hasn't had exposure to).
whereas the cognitive layers required for reading take time to develop in the child's brain, and you first have to wait for the verbal/aural language systems to develop the actual language structure first, then tack on some symbolic representation for letters, then understand composition for words, then attach words to their meanings, etc. You can skip some of those bits to perform party tricks (I.e rote symbolic recognition and repetition of aural sounds on cue), but this does not reading make. Reading we believe, from a cognitive science point of view, we think is a kind of a kind of kludge on top of later developed brain mechanics, whereas it's aural/verbal language that appears as an almost innate developmental ability around that age. (I say innate, but you still have to be exposed to other humans interacting and speaking for a young mind to learn the language).
Adults underestimate toddlers. I 'taught' my daughter to read some words at the age of 1. She could learn around 3 per week. Two weeks to learn to recognize them without any context. It's just a matter of providing the opportunity, and taking advantage of their curiosity.
I also think it's odd to put Tao next to Gauss and Euler. Maybe he's one of the best mathematicians right now but that's different from being the same calibre as the most influential people in the field ever.
Gauss and Euler had the advantage of living among a much smaller population of mathematicians, and when much low hanging fruit had not yet been discovered. If they were born today they would not reach the same level as Tao.
Yes, they made a lot of contributions because of the time they lived in (right after calculus was invented but before modern mathematics). Still, you have no way of knowing what they would be able to contribute today and that whole hypothetical is kind of pointless anyway.
That is baseless comment. Their achievements are low hanging fruits but only by today's standards. You can say the same thing practically for anybody. Einstein discovered relativity because low hanging fruit. von Neumann did all the amazing works because low hanging fruits.
And how can you say they would not reach the same level as Tao? You are indicating that being truly genius is some modern phenomenon. May be 100 years down the line, even Tao will proabably be downplayed and kids will be learning advance calculas before they turn 10.
It's mostly a question of population sizes. The world population in their age was around 15% of what it is now, and only a fraction of those people would have had access to enough of an education to be noticed as a top mathematician. So it would be astonishing if their top mathematicians beat our own.
an iq of 230 probably does not exist . it is impossible to devise a test accurate enough measure such a high iq .More likely there are probably a hundred people in the world who can be considered the smartest, including Terrance Tao and other prodigies. And that German guy who recently got a Field's Medal.
He said to do math, not first-rate math. I have witnessed plenty of seemingly merely above-average-IQ people make interesting, novel contributions to math. Complex analysis, infinite series, matrices, stuff like that.They don't get much media coverage but produce interesting results and produce high quality math..that is probably what he was getting at.
-read the req. literature
-find an interesting problem, something u want to learn more about
Without even reading a single word of it, the non-irony is in your characterization. He taught himself. Ultimately we all taught ourselves and our peers and mentees. Intelligence is mostly rooted in curiosity and attention, not some innate capacity. People who are perceived to be at the lower end of that capacity often inform those who aren’t, and vice versa.
i would wager a lot of money that no one here has the capacity to approach John von Neumann, Srinivasa Ramanujan or Terence Tao in a single lifetime of unlimited curiosity and attention.
In https://terrytao.wordpress.com/career-advice/does-one-have-t... he argues that you do not have to be a genius to do first rate mathematics.
The irony is that this is being argued by person with the best documented genius in the history of mathematics. His official IQ of 230 remains the highest officially measured IQ in the world. He taught himself to read by age 2. He was taking Calculus at age 7. He remains the youngest person for any level of medal in the International Mathematics Olympiad. That doesn't quite convey it. The youngest person to earn a bronze in that competition was 10. Silver was 11. Gold was 12. All three records were set by Terrence Tao, who then didn't bother competing any more.
See https://newsroom.ucla.edu/releases/Terence-Tao-Mozart-of-Mat... for some more of his accomplishments.
His success is comparable to any person in the history of mathematics. Yes I am including Euler, Gauss, and Erdös. Euler possibly covered a bigger breadth of math. Gauss created more fields. Erdös solved more problems. And Tao has made more progress in more hard problems that had stumped everyone else.