Become a good mathematician without the "threshold" IQ?

[Rick77]

So I've read this "article"[ http://afiodorov.github.io/2015/12/04/terry-replies/ ] that really depressed me especially because I'm young. Apparently the threshold IQ is around 150, so does that mean someone has no chance?

 

[fresh_42]

First of all, an IQ measurement is nonsense. One gets varying results, depending on the kind of test, personal preferences and qualities. You can even practice those tests and get better at it. Does this mean you get smarter?
Secondly, you may wonder what disabled people are capable to do! Euler became blind and he still proved mathematical theorems. He only needed someone to write them down.
Furthermore it isn't true, that anyone's IQ (which way ever measured) is fixed. O.k., you cannot make a stupid person a genius, but training, experience and books, a lot of books, can change a lot!

Mathematics isn't something about IQs. It's very much the same as with everything else: practice, patience and diligence. You aren't supposed to be a genius. Curiosity is much more important, and the other attributes I mentioned. Of course not every runner can be a Usain Bolt, every physicist an Albert Einstein or every mathematician a Leonard Euler.

However, there is one important lesson to learn: Do not believe something, just because anyone has said so! The other way around makes you a good scientist: Wrong, until proven! In mathematics, you learn to read those proofs which are to convince you. In physics you do experiments.
What makes you think what you've read is right? It is not. And this has to become your standard assumption: it is wrong unless proven to you.

 

[Rick77]

First of all, an IQ measurement is nonsense. One gets varying results, depending on the kind of test, personal preferences and qualities. You can even practice those tests and get better at it. Does this mean you get smarter?
Secondly, you may wonder what disabled people are capable to do! Euler became blind and he still proved mathematical theorems. He only needed someone to write them down.
Furthermore it isn't true, that anyone's IQ (which way ever measured) is fixed. O.k., you cannot make a stupid person a genius, but training, experience and books, a lot of books, can change a lot!

Mathematics isn't something about IQs. It's very much the same as with everything else: practice, patience and diligence. You aren't supposed to be a genius. Curiosity is much more important, and the other attributes I mentioned. Of course not every runner can be a Usain Bolt, every physicist an Albert Einstein or every mathematician a Leonard Euler.

However, there is one important lesson to learn: Do not believe something, just because anyone has said so! The other way around makes you a good scientist: Wrong, until proven! In mathematics, you learn to read those proofs which are to convince you. In physics you do experiments.
What makes you think what you've read is right? It is not. And this has to become your standard assumption: it is wrong unless proven to you.

Thanks for the answer

 

[Dr. Courtney]

I tend to doubt the 150 threshold, but it depends on what you mean by "good mathematician." I tend to define "good" in terms of one's professional work product - satisfying the job requirements, which may or may not require publishing papers in the most esteemed math journals which get cited dozens of times each.

I've known lots of college math faculty who I regarded as very good by the above criteria whose IQs I would estimate at 115-145, with most from 115-130. But most of these tended to be faculty at teaching rather than "publish or perish" institutions (R1).

For a high school student, I would worry less about IQ. Work hard and shoot for an ACT score in the 30s if you want to become a mathematician. Not there yet? Keep working. I can give a lot of practical advice on how to improve your ACT Math score and get into the 30s. Success in math can be achieved even without the highest levels of intellectual gifting.

Just as exercise can make you stronger, hard work can make you smarter.

 

[TeethWhitener]

So I've read this "article"[ http://afiodorov.github.io/2015/12/04/terry-replies/ ] that really depressed me especially because I'm young. Apparently the threshold IQ is around 150, so does that mean someone has no chance?

Terry Tao's reply to the original poster is instructive: there are more and more math problems nowadays that require a "slow and steady" approach where one accumulates intuition across a broad swath of mathematical disciplines and methodically applies their techniques to the problem at hand, rather than a "brilliant flash of insight" approach that is maybe a more entertaining story to tell, but in practice happens only rarely.

Edit: Of course, Tao is himself a remarkable genius/child prodigy/etc., so maybe he's just stringing us along.

 

[StatGuy2000]

The discussion in the link provided by the OP (and the subsequent discussion here in this thread) somehow assumes that there is a consensus that IQ is a good measure of overall intelligence (or even intelligence with respect to mathematical ability). That is far from the case. Many others have argued (quite convincingly, in my personal opinion) that IQ is in fact a poor measure of something called "intelligence".

Consider the blog posts on this topic from physicist-turned-statistician Cosma Shalizi:

http://bactra.org/weblog/494.html

http://bactra.org/weblog/495.html

http://bactra.org/weblog/520.html

http://bactra.org/weblog/523.html

 

[Crek]

The reality is, to do much with mathematics or physics(theoretical) requires extraordinary ability. This isn't to say it's not possible to get a PhD without it but in my opinion, to do anything significant in the field requires genius level ability to the point it's probably not worth going into unless you do math 24/7. At this point I view math more as a hobby then as a career, I just hope to create a career that uses some of what I know without being forced to teach a bunch of incompetent students college algebra.

 

[StatGuy2000]

The reality is, to do much with mathematics or physics(theoretical) requires extraordinary ability. This isn't to say it's not possible to get a PhD without it but in my opinion, to do anything significant in the field requires genius level ability to the point it's probably not worth going into unless you do math 24/7. At this point I view math more as a hobby then as a career, I just hope to create a career that uses some of what I know without being forced to teach a bunch of incompetent students college algebra.

Crek, I do not agree with that premise, because you (like many others) assume that "extraordinary" ability is somehow an in-born or genetic trait. The fact is that to get to the stage where someone could be said to have such ability takes a tremendous amount of effort and hard work.

Sure, there are some people who may learn certain areas of knowledge more quickly than others, and for whom mathematics may come more naturally. But that does not mean that you need to be a genius to be able to make significant contributions. I would bet that most faculty members in math and physics departments are not geniuses.

I also find your arrogance towards other college students (calling them "incompetent", for example) to be offensive. In fact, every single one of your posts lately have been nothing but negative. This begs the question -- why are you even bothering to post here on PF, if you don't have anything positive to contribute?

 

[fresh_42]

Crek, I do not agree with that premise, because ...

Well said. I struggled to put it in an equally polite way.

 

[Logical Dog]

Like most things in life, you just have to have the passion for it. Presence of Other factors only help more.

If an online article about IQ can dissuade you from doing it, then you are not motivated enough for it. What good is high IQ whn you don't know how to prove statemrents, differentiate, do actual math first etc...? If you are happy doing and learning math, I am sure with anough hard work you can contribute something to the field. What helps the most in my opinion is being exposed to a variety of math and logic at an early age.

 

[TomServo]

The original link doesn't wourk for me

 

[Logical Dog]

The reality is, to do much with mathematics or physics(theoretical) requires extraordinary ability. This isn't to say it's not possible to get a PhD without it but in my opinion, to do anything significant in the field requires genius level ability to the point it's probably not worth going into unless you do math 24/7. At this point I view math more as a hobby then as a career, I just hope to create a career that uses some of what I know without being forced to teach a bunch of incompetent students college algebra.

Why? If you like mathematics you would enjoy teaching it to any group of people. :) The best maths book often start with a thank you note to the college students for their insights and opinions. I also think teaching is one of the best way to remain "fresh".

 

[radium]

Based on my experience and people I've talked to, this is the comment I have to make.

There are different types of intelligence and people have strengths in different areas. Every one has a unique thought process. Different problems require different skill sets. For example, it is very likely that Stephen Hawking has contributed so much to gravity even though it is difficult for him to move is because he has a special geometric insight that is very useful for the problems he's worked on (gravity is geometry in some sense). People who think this way may find other things unintuitive. I know lots of absolutely brilliant physicists who will readily admit when they don't understand something in area outside of their field. The goal is to identify problems for which you have special insight given your way of thinking.

 

[Crass_Oscillator]

The great computer scientist Richard Hamming had a great, inspiring talk on this:

 

[WWGD]

Like most things in life, you just have to have the passion for it. Presence of Other factors only help more.

If an online article about IQ can dissuade you from doing it, then you are not motivated enough for it. What good is high IQ whn you don't know how to prove statemrents, differentiate, do actual math first etc...? If you are happy doing and learning math, I am sure with anough hard work you can contribute something to the field. What helps the most in my opinion is being exposed to a variety of math and logic at an early age.

But somehow the level of passion is proportional/ postively-correlated with ability. You are more likely to want to spend a lot of limited resources: time, money, energy doing something you're good at and deprecate ( subconsciously) areas you're not naturally good at. Your mind is aware that it has limited resources and motivates you towards best areas to invest them in. Granted, hard work , focus, discipline matter but if those were fixed, I would still need some 15-20 years to become a good singer to Alicia Keys' 2-3 years.

 

[StatGuy2000]

But somehow the level of passion is proportional/ postively-correlated with ability. You are more likely to want to spend a lot of limited resources: time, money, energy doing something you're good at and deprecate ( subconsciously) areas you're not naturally good at. Your mind is aware that it has limited resources and motivates you towards best areas to invest them in. Granted, hard work , focus, discipline matter but if those were fixed, I would still need some 15-20 years to become a good singer to Alicia Keys' 2-3 years.

The assumption you are making here is that human abilities are somehow fixed and that these abilities are acquired in a linear progressive manner, which is a dubious assumption, given that it is by no means obvious what capabilities individuals possesses without some effort initially.

Also, people's capabilities can shift in a seemingly abrupt manner (e.g. people who struggle in, say, English becoming subsequently an accomplished writer)

 

[Dr. Courtney]

But somehow the level of passion is proportional/ postively-correlated with ability. You are more likely to want to spend a lot of limited resources: time, money, energy doing something you're good at and deprecate ( subconsciously) areas you're not naturally good at.

The assumption you are making here is that human abilities are somehow fixed and that these abilities are acquired in a linear progressive manner, which is a dubious assumption, given that it is by no means obvious what capabilities individuals possesses without some effort initially.

Good points. I can think of several areas in which my natural abilities are very limited that I've worked hard at - spending lots of time, energy, and money:

Music - 3 hours a week of practice has gotten me to a level where most church music teams are glad to have me on the bass guitar.

Tennis - Got my Universal Tennis Rating (UTR) up to 5 earlier this year in spite of a lack of athletic ability and formal training.

As a shooting instructor, I've also seen lots of students with little natural talent become pretty good through effort and hard work. Mediocre talents can and have won lots of local tournaments and even a couple NRA national championships.

My "rule of thumb" is that hard work and natural talent are equal contributors to success. Being in the top 50% in both will typically lead to a top 25% outcome. Being in the top 10% in both will lead to a top 1% outcome. Being in the top 50% in natural ability (the median) and top 10% in effort has an expected outcome in the top 5%. And so on.

Very few amateur musicians practice 3 hours per week for many years. Very few amateur shooters shoot thousands of rounds of practice ammo each year for many years. Very few math students spend an honest 3 hours outside of class preparing for each class hour. At an average to slightly above average level of natural gifting, much can be accomplished through "hustle" and hard work.

Now, there may well be psychological barriers to overcome for the human will to exert the needed levels of hustle and hard work in areas with modest natural gifting, but if those can be overcome, success is possible.

“If you don't have the ganas, I will give it to you, because I'm an expert.” - Jaime Escalante, Stand and Deliver

 

[gleem]

In Malcomb Gladwell's book "Outliers" he notes that to become accomplished in any endeavor one usually must devote a certain amount of time to achieve a level of competency. To attain expert ability in a field requires at least 10,000 hours devoted to that field in study and/or practice. As an example for a musicians who puts in 10000 hours can expect to attain competency of a virtuoso. Those who put in only 8000 hours may find employment as a professional musician. Those that put in at most 5000 hours teach music.

10000 hours is three hours a day for 9 years. How many hours are put in by scientists in studying and practicing to attain recognition in their field as an expert? How many hours does an Olympic hopeful devote to practice if he/she wants a gold medal? At least 10,000 hours.

Of course one must have the raw materials to work with to succeed with a given amount of work.

 

[WWGD]

Good points. I can think of several areas in which my natural abilities are very limited that I've worked hard at - spending lots of time, energy, and money:

Music - 3 hours a week of practice has gotten me to a level where most church music teams are glad to have me on the bass guitar.

Tennis - Got my Universal Tennis Rating (UTR) up to 5 earlier this year in spite of a lack of athletic ability and formal training.

As a shooting instructor, I've also seen lots of students with little natural talent become pretty good through effort and hard work. Mediocre talents can and have won lots of local tournaments and even a couple NRA national championships.

My "rule of thumb" is that hard work and natural talent are equal contributors to success. Being in the top 50% in both will typically lead to a top 25% outcome. Being in the top 10% in both will lead to a top 1% outcome. Being in the top 50% in natural ability (the median) and top 10% in effort has an expected outcome in the top 5%. And so on.

Very few amateur musicians practice 3 hours per week for many years. Very few amateur shooters shoot thousands of rounds of practice ammo each year for many years. Very few math students spend an honest 3 hours outside of class preparing for each class hour. At an average to slightly above average level of natural gifting, much can be accomplished through "hustle" and hard work.

Now, there may well be psychological barriers to overcome for the human will to exert the needed levels of hustle and hard work in areas with modest natural gifting, but if those can be overcome, success is possible.

“If you don't have the ganas, I will give it to you, because I'm an expert.” - Jaime Escalante, Stand and Deliver

What's Calcooloos, Esse ? ;). Loved the movie.

 

[WWGD]

The assumption you are making here is that human abilities are somehow fixed and that these abilities are acquired in a linear progressive manner, which is a dubious assumption, given that it is by no means obvious what capabilities individuals possesses without some effort initially.

Also, people's capabilities can shift in a seemingly abrupt manner (e.g. people who struggle in, say, English becoming subsequently an accomplished writer)

How often does that happen that people doing poorly in a given subject matter suddenly become proficient or very good at it? And I am not assumming fixedness, I am talking correlation: those with less talent are less likely to succeed. Do you disagree with that?

 

[Dr. Courtney]

How often does that happen that people doing poorly in a given subject matter suddenly become proficient or very good at it? And I am not assumming fixedness, I am talking correlation: those with less talent are less likely to succeed. Do you disagree with that?

But in the context of the OP, I think this is the wrong question. The right question is whether a natural gifting below the mean for a given field can be overcome with hard work. The right follow-up questions are how much work will likely be required to achieve the desired level of success with a given natural gifting and what other resources will likely be required.

I've seen lots of students fail to accomplish their goals, and they are usually tempted to ascribe their failure to a lack of natural gifting. This is sometimes a minor contributing factor. But the bigger factor is usually the lack of will to work hard enough.

I don't think I've ever said to a student, "You're not smart enough to do that." Better advice takes more of the form - this is how hard you're going to have to work and this is what it is likely going to take.

 

[Vanadium 50]

Um, everybody knows that this thread was a drive-by on the part of the OP, right? He came here 2+ years ago, asked his question, and never came back. I mean, you can keep arguing with yourselves if you want, but it's not helping the OP.

 

[WWGD]

Um, everybody knows that this thread was a drive-by on the part of the OP, right? He came here 2+ years ago, asked his question, and never came back. I mean, you can keep arguing with yourselves if you want, but it's not helping the OP.

Guess s/he has not figured out the effort part well-enough yet. Better be at that top 1% of talent.

 

[gleem]

The value of this thread and many more of this type is for those who might have posted a similar question had it not already been asked and some answers provided.

 

[WWGD]

@Dr. Courtney , what do you think of cases like Babe Ruth, who was so far ahead of everyone else? Top 0.1% talent and effort? He did start playing very early.

 

[Dr. Courtney]

Um, everybody knows that this thread was a drive-by on the part of the OP, right? He came here 2+ years ago, asked his question, and never came back. I mean, you can keep arguing with yourselves if you want, but it's not helping the OP.

My experience is that many more readers find internet advice as lurkers using search engines than the OPs. I like to address the OP and counter discouraging advice for their sake.

@Dr. Courtney , what do you think of cases like Babe Ruth, who was so far ahead of everyone else? Top 0.1% talent and effort? He did start playing very early.

Dunno about Ruth. But I've thought a lot about more modern cases like Roger Federer and Michael Jordan. 0.1% talent and effort, at least. It's rare to encounter students or athletes with true 0.1% talent. But I like to encourage them that if they add top 0.1% effort to that, they can likely have 1 in a million accomplishments and outcomes. Otherwise, they may just end up a Dennis Rodman equivalent.

But I also advise folks to work harder in areas with more demand and less supply of hard workers. There are way more athletes hoping for college tennis and basketball scholarships than will ever get them. In states like GA with the Hope/Zell Miller scholarship program, 10 extra hours a week on out of class academics is much more likely to get an academic scholarship than 10 extra hours a week on hoops or tennis. Average intelligence and top 10% of effort is about what it takes.

 

[StatGuy2000]

How often does that happen that people doing poorly in a given subject matter suddenly become proficient or very good at it?

More often than you think, at least based on my own anecdotal evidence.

And I am not assuming fixedness, I am talking correlation: those with less talent are less likely to succeed. Do you disagree with that?

I believe @Dr. Courtney has already addressed this in post #21. Let me add that what you refer to as "talent" isn't necessarily simply an innate trait (which is what you are assuming above), but something which can be and is often acquired through hard work and effort.

Let me ask you this. What do you attribute to whatever success you have achieved? Your genetics? Or your hard work?

 

[WWGD]

More often than you think, at least based on my own anecdotal evidence.
I believe @Dr. Courtney has already addressed this in post #21. Let me add that what you refer to as "talent" isn't necessarily simply an innate trait (which is what you are assuming above), but something which can be and is often acquired through hard work and effort.

Let me ask you this. What do you attribute to whatever success you have achieved? Your genetics? Or your hard work?

But we seem to be going in circles here: hard work definitely matters but talent gives you an extra edge. Like finishing a marathon faster by starting at the 10th mile instead of by mile 0. And, yes, the talent component is innate but often latent and must then be teased out. Like I said, no matter how hard I work, I will most likely never sing as well as Alicia Keys or many others, be a great chef, etc. , though possible do very well in other areas. I do believe in such a thing as having easier disposition towards certain activities.

 

[StatGuy2000]

But we seem to be going in circles here: hard work definitely matters but talent gives you an extra edge. Like finishing a marathon faster by starting at the 10th mile instead of by mile 0. And, yes, the talent component is innate but often latent and must then be teased out. Like I said, no matter how hard I work, I will most likely never sing as well as Alicia Keys or many others, be a great chef, etc. , though possible do very well in other areas. I do believe in such a thing as having easier disposition towards certain activities.

Again, from my reading of your posts, you (and many people with hereditarian views) seem to put far more stock in innate "talent" than I do in the intellectual or academic sphere, precisely because whatever "innate" predisposition is latent and is often impossible to disentangle from hard work, effort, & other environmental conditions.

The academic or intellectual sphere is different from your example of singing because singing talent is at least in part on physical characteristics (i.e. quality of someone's vocal chords). Whereas someone who is not afflicted with neurological or developmental disorders are capable of learning a vast of set of academic or cognitive skills.

 

[WWGD]

Again, from my reading of your posts, you (and many people with hereditarian views) seem to put far more stock in innate "talent" than I do in the intellectual or academic sphere, precisely because whatever "innate" predisposition is latent and is often impossible to disentangle from hard work, effort, & other environmental conditions.

The academic or intellectual sphere is different from your example of singing because singing talent is at least in part on physical characteristics (i.e. quality of someone's vocal chords). Whereas someone who is not afflicted with neurological or developmental disorders are capable of learning a vast of set of academic or cognitive skills.

Edit:Well, until someone brings up research it is little more than hearsay or personal opinions so we are stuck with this and I don't see it moving forward , so I will let you have the last word and I will bail out of this exchange. Edit : your claim about physical correlates does not hold as there are physical traits of the brain that correlate with IQ. But this is an extremely complex topic and we each have our opinion, neither of us seems to have convinced the other and I don't see what can be gained by continuing to exchange personal opinions.

 

[Vanadium 50]

Well, if we're writing for "posterity"...

• The very notion of a threshold IQ is unserious. Does anyone really think that with a 150 IQ one can be a successful mathematician but with a 149 one cannot?
• Does anyone really doubt that with a constant level of effort being smarter helps?
• Does anyone really doubt that with a constant level of intelligence more effort helps?

 

[StoneTemplePython]

Edit:Well, until someone brings up research it is little more than hearsay or personal opinions so we are stuck with this and I don't see it moving forward

I tried a year and a half ago, but I don't think it had much effect
https://www.physicsforums.com/threa...stress-and-the-human-cost.943817/post-5987052
As I recall, that issue of The Economist had some adjacent articles on notions of intelligence and how to estimate it from IQ to G to some other things.

 

[WWGD]

I tried a year and a half ago, but I don't think it had much effect
https://www.physicsforums.com/threa...stress-and-the-human-cost.943817/post-5987052
As I recall, that issue of The Economist had some adjacent articles on notions of intelligence and how to estimate it from IQ to G to some other things.

Like a large amount of topics, it's gone the way of culture wars. A sad comment on our society today that we have trouble disagreeing constructively on so many different topics. Edit: Baby Boomers did an amazing job of pushing technology forward but went backwards in terms of engaging in political, general debate.

 

[hmmm27]

The academic or intellectual sphere is different from your example of singing because singing talent is at least in part on physical characteristics (i.e. quality of someone's vocal chords).

Not really : a pleasant-sounding voice is nice to have, but almost totally irrelevant for a professional vocalist.

 

[Vanadium 50]

Not really : a pleasant-sounding voice is nice to have, but almost totally irrelevant for a professional vocalist.

Ethel Merman, Britney Spears...