The Math Gift Myth | Hacker News Reader

The Math Gift Myth

devlinsangle.blogspot.com

37 pointsaqsalose13 comments

I realized in my math undergraduate studies that mathematicians have merely "sat" with the material longer. Sure, some people seem to click with certain topics reliably faster than average (even than their apparent peers). But ultimately solving a problem comes easier the more problems you have solved. If a geometry problem obscurely relies on some trick involving a right triangle then someone who knows more about triangles will solve it faster.

There's also a caustic societal problem involved. People will declare themselves bad at math and stop trying. There is no bad or good at math. There is only persistence.

I agree. I recently read the book, "A Mind for Numbers" which also agrees with you. Math is abstract and people struggle with that (often giving up), but I don't believe it is inherently more difficult than other complex things we train our brains to do. It's a matter of creating new neural pathways through study and time.

>I realized in my math undergraduate studies that mathematicians have merely "sat" with the material longer.

Even if true, this just moves the issue to the ability to make yourself "sit" with the material. The variability here is at least as high, most people hate doing mathematics, some love it.

In any case this only concerns "mathematicians", not "people considered math geniuses". There are plenty of mediocre mathematicians.

EDIT: And it is of course not true that it's just a matter of spending time. Some people learn maths 100 times faster than others.

The statements in the article, even if true, in no way motivate the claim in the title (and the text).

"In other words, all my experience in mathematics tells me I do not have an absolute ability limit. Nor, I am sure, do you. Mathematical proficiency is indeed a spectrum."

Of course it's a spectrum, and sure practice helps anyone. But that in no way implies that there is no such thing as a "math gift". In fact, the spectrum presupposes that some people are on the most advanced part of it. They are the ones with the gift. The ones on the other end don't have the gift. They may have other gifts, and they may be productive members of society nonetheless, but they don't have the math gift.

Yeah, I mean, it's self-evident that people with exceptionally high general intelligence are ~100% of people who advance mathematics. I don't understand why people want to think otherwise, fooling themselves isn't going to raise their IQ.

Edit: I neglected to mention conscientiousness, which would be the other half of the puzzle. there are plenty of geniuses who will nonetheless never put themselves to work.

If some form of anxiety and the ability to cope with it are major factors in affecting one's potential ability to do math, then in theory anyone could benefit from learning to cope with anxiety and to persist in mathematical study. The idea certainly rings true with my experience.

> it's self-evident that people with exceptionally high general intelligence are ~100% of people who advance mathematics.

Counterargument: anyone who advances mathematics will be considered of exceptionally high intelligence. Mathematicians like Gödel were known for being very eccentric and many might not consider them of exceptionally high _general_ intelligence. Whether that is an accurate assessment, I doubt you or I could say with any authority.

EDIT (post-replies): Replies to this have descended into technical terminology from cognitive science, so I must remove myself from this discussion as I lack the required education [clearance?] to participate at the expected level. Nevertheless, without some objective way of measuring the psychometric "g-factor" of mathematicians throughout history up to now, I don't see this as particularly useful in addressing the issue of aptitude of the "~100% of people who advance mathematics". If you could point to any data sets on psychometric g-factors among practicing mathematicians (particularly, alongside values from the general population), that would lend some credence to what you say. The idea is very provocative.

I neglected to mention conscientiousness, which would be the other half of the puzzle. There are plenty of geniuses who will nonetheless never put themselves to work. Intelligence can't make you productive all alone. Which is why I said it the way I did, because otherwise I would imply that they are mathematicians because they are intelligent, where I was trying to say that in order to advance mathematics, you essentially have to be very intelligent.

That said...

> Counterargument: anyone who advances mathematics will be considered of exceptionally high intelligence.

I'm referring to the psychometric g factor type of intelligence. Not the "I know a real smart gal" type. g is shockingly consistent, measurable, and clearly an important part of many human behaviours.

Intelligence is a very specific thing, people can be exceptionally good at things without being exceptionally intelligent, but people can not be exceptionally intelligent merely by being exceptional at something.

General intelligence is not _that_ general. You can be extremely eccentric without lowering your g factor.

Yes this self deception is strange, both because it's so obviously wrong, but mostly because math genius doesn't have a lot of correlation with success in life. Why not just accept that some people have a much easier time learning some subjects but that anyone can learn a bit of it and definitely enough to live a happy and fulfilling life.

We don't all have to be born with the potential to reach the top in all areas. The idea is ludicrous.

I think the author's point is that movement on the spectrum isn't constrained by some abstract concept of "gift." That is, the people on the lower end of the spectrum aren't constrained against moving to the other end by some intrinsic (in)ability.

(I'm not taking a position for or against that premise.)

That's a slightly more subtle interpretation than I made, and you are probably right that this was the message. I still wouldn't agree with it, I know by experience that there are vast differences in how fast and more importantly how far you can improve your understanding of complex mathematics. Just like in sports. Anyone can improve, but some improve much faster and can reach much further.

Ah, but that brings us to what I took as the main give-away the post: the fundamental mistake is talking about mathematical aptitude in terms of a gift that one either has or has not, because it hurts the motivation of everyone who is not immediately recognizable as ranking on the most rightmost tail end of the spectrum when they start their formal schooling. And that group still includes many people who would benefit from further improvement of their mathematical skill.

Consider the famous story about Gauss, baffling his teacher by coming up with a formula for 1+2+...+n [1]. Or Kolmogorov who reportedly started his own 'journal' at age of 5. Or Terence Tao, who already had his M.Sc. at the age of 16 and was a professor by 24 [2]. Sure, such people exist and they can be spotted early. But the humanity needs also regular engineers and statisticians and other math-capable people, especially in non-obvious fields such as journalism.

[1] http://www.americanscientist.org/issues/pub/gausss-day-of-re...

[2] https://en.wikipedia.org/wiki/Terence_Tao#Childhood

If people actually think the math gift is binary I can agree that would be harmful, just as in any other discipline. I also think that most people can be pushed much further than what is done currently in western countries. Just look at Russian children, I don't believe there are fundamental genetic reasons why they are often years ahead of for example Swedish pupils.

I don't think it's helpful to downplay the role of genius. Top athletes inspire millions of children to work hard on their skills in football, basket, hockey etc, even though almost all of them obviously lack the genetics to reach the top.

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