It's still meritocratic even with dramatic genetic differences between individuals. A peer comment mentioned an anecdote of Terence nearly failing his orals because he ended spending all of his time playing Civ instead of studying anything.
It's basically the Gattaca story. Somebody can have the most brilliant mind in the world, but without actually applying it, they're not going to do great in life. If you give a person of average intellect Tao's life of dedication and work ethic, then he's going to end up a world class mathematician. He probably won't end up at the top of the top, as that's going to be reserved for those that hit the mega-lottery of genetics + dedication, but will also have no problem leaving his mark on this world and living a comfortable life.
I seriously doubt a person with average intellect can become a world class mathematician, let alone a decent one. Just on grid. I have seen people in college that were tremendously hard working fail math classes and just not understand it. At some point saying they should just try harder is cruel.
The logic in my claim is that the overwhelming majority of people will reach nowhere even remotely near to their genetic potential in literally anything. You can see this in any endeavor where performance can be objectively measured - chess is the obvious one. A 2000 rated player is not much more than a strong amateur, but that already leaves one in like the 90th+ percentile for a game that millions of people work and study at.
It's not like the other 90% of people lack the intelligence or whatever else to be much stronger than they are, but it requires extensive dedication, work, and suffering that many just uninterested in tolerating for the sake of improving at a single domain. I think your example largely proves the point. Anybody of average intelligence can obviously excel at undergraduate math if they're willing to dedicate themselves to it, but many people aren't. If somebody was failing at math it's probably because they were just treating it like you might e.g. literature, and trying to do cram sessions relatively shortly before each exam, whereas by the time somebody gets to stuff like diff eq math starts turning more into a puzzle game that requires developing things on a subconscious/intuitive level.
This was not undergraduate math in my case, but I still don't agree.
I don't think anyone of average intelligence can excel at undergraduate math. It of course depends on the degree and the school. Can anyone with average intelligence excel at an undergraduate math course in community college for their psychology degree? Probably yes. But an undergraduate math course at oxford as part of a maths degree? Not for sure not.
I think you are severely underestimating how much intelligence factors in how fast and even what at all you can learn. Take the opposite end of the spectrum. The US army rejects candidates with an IQ of ~85 or lower. Because they have found this group cannot contribute meaningfully. Let that sink in. Just a drop of 15 IQ points means the US army has decided you cannot be effectively taught anything to a minimum degree of competence. Now consider that the average IQ of a mathematician is 130 (https://realiqtest.webflow.io/posts/iq-by-occupation-a-compr...).
I'm speaking of math majors, or fields with a heavy math requirement, of course. Diff eq is not required anywhere, as far as I know at least, for non-technical majors. As for the army, I wouldn't just hand-wave away soldiering. You're talking about people being put in high pressure situations with ever-shifting dynamics, potentially against a human adversary, where lives are at stake. And they think everybody except the bottom ~32% of society is fit for this task.
I'd certainly expect an average person who dedicates his life to mathematics to end up with a higher than average IQ largely because while IQ is a useful measure, it's not an independent g factor. Studying mathematics is going to absolutely help train your brain in many areas that are also beneficial for performance in IQ exams. So for instance, some studies have shown that each additional year of education, relative to a fixed base, can causally contribute 1-5 additional IQ points. [1] So our person in question would almost certainly expect to see a significant and measurable IQ increase.
And FWIW I'm rather on the opposite extreme of those who argue for some sort of tabula rasa. I fully acknowledge dramatic innate differences between individuals, but I'm largely arguing that such differences only become major factors for people who approach their genetic potential in something, which most people will never get even remotely near, simply because the amount of dedication and sacrifice it takes is something that very few people are willing to accept.
Well the central post that the commenter made about the army’s iq requirement is trivially fact checked to be untrue. The army doesn’t administer iq tests as part of screening. They do asvab which tests _knowledge_ which you can study for. They have correlated outcomes in that a high IQ usually means a high asvab but they aren’t identical (you can for instance top out an asvab test and practice shows meaningful improvement whereas there is no top iq and if you can practice for it the test is flawed.)
"Dedication and work ethic" is almost certainly nonsense here. Some people do the activity a lot without having any ethic or dedication - they like it.
He stopped playing video games, presumably in part because of this event. [1] Many, if not most of us, would instead just let our professional life dip a bit and try to roll back the gaming a bit. Going completely cold turkey is a person with a special sort of dedication and ethic.
There is zero, absolutely zero chance of the 50th percentile IQ becoming a world class mathematician. People who say this have no idea exactly how smart these guys are.
It seems like a bit of a pointless and unanswerable argument about semantics, the only bit is the irritating "ohh if it's SOOO EASY" about something that was definitely framed not to be easy.
If your cutoff of "world class mathematician" is a few hundred or thousand people, then no chance. If their cutoff is "earn a comfortable living" and the top 10% of the world is 800,000,000 people most of whom don't study mathematics, then can an average intellect with an obsession for math end up working a job a normal person might call 'mathematician' by working on AutoCAD or 3D rendering game engine or industrial statistics and process control or economics or vehicle aerodynamics and be in the top 10% of the world in mathematical ability? Possibly yes. And you can adjust the numbers and criterion to get a yes or no whichever way you like.
>you can adjust the numbers and criterion to get a yes or no whichever way you like.
Good idea, I'll do that :)
>can an average intellect with an obsession for math end up
>working on AutoCAD or 3D rendering game engine or industrial statistics and process control or economics or vehicle aerodynamics and be in the top 10% of the world in mathematical ability?
I think this does happen quite a bit and the need for strong math in these difficult areas is so great that there will never be enough people as briliant as Tao to fill the positions.
That's so far outside the mainstream anyway, most systems are going to screen the rare person like that out without understanding why.
Now what happens when those having top 10% of ability are very excellent themselves, but cases come up that would yield only to a Tao level of "natural-born" problem-solver?
A mathematician is someone who creates or advances math. Not someone who uses math. If you don't understand how the word is used, that's your problem, not a problem with the statement.
mathematician /măth″ə-mə-tĭsh′ən/
A person skilled or learned in mathematics.
One versed in mathematics.
An expert on mathematics.
The American Heritage® Dictionary of the English Language, 5th Edition • More at Wordnik
None of the definitions require creating or advancing mathematics.
People in the field would never, ever call someone "versed in mathematics" as being a mathematician.
I don't even buy that regular people call someone who is "versed in mathematics" a "mathematician".
If you met a 30 year old person and asked what they do and they said "I'm an athlete" - do you take the dictionary definition there too? Most people will assume they mean a professional athlete.
> absolutely zero chance of the 50th percentile IQ becoming a world class mathematician.
Good, we don't need billions of them anyway.
I wish modern society would quit focusing on individual intelligence over collective intelligence. We can take something like the microprocessor, for example. The smart group that designed the microprocessor was not the same group that designed the software nor the group the built the parts nor the group the assembled the device. However, every group is equally important.
It's basically the Gattaca story. Somebody can have the most brilliant mind in the world, but without actually applying it, they're not going to do great in life. If you give a person of average intellect Tao's life of dedication and work ethic, then he's going to end up a world class mathematician. He probably won't end up at the top of the top, as that's going to be reserved for those that hit the mega-lottery of genetics + dedication, but will also have no problem leaving his mark on this world and living a comfortable life.