What is the proposed scale for rating mathematical acumen?

[Jagella]

How good or bad are we at math? Mathematical ability obviously varies from one person to another. I propose a scale in which a zero is the inability to add 2 + 2, 5 is the ability to successfully complete college-level math courses, and a 10 describes the ability to come up with mathematical theorems that change the way we look at numbers in a way that Archimedes did.

Why do people vary so much in their math acumen? Is it nature, nurture, or a combination of both?

Finally, how would you rate you own ability at math? I'd rate myself as a 7.

Jagella

 

[homeomorphic]

First of all, math is not just numbers. Probably, most of math only deals with numbers indirectly. Think of geometry class. Is it really about numbers? No, it's about shapes. You could certainly interpret it in terms of numbers and numbers are sort of there in the background, but when you think of geometry, you don't start thinking of explicit numbers like 5, 15, or 186285, you think of circles, squares, lines, etc. So, I always find it a little annoying when non-mathematicians tell me "oh, so you're a numbers person" because that is only part of math (and one of the least interesting parts, to my mind), and most of a mathematician's thinking doesn't explicitly have anything to do with numbers. I find it annoying, not just because it's inaccurate, but because it sounds like they think mathematicians just sit around adding and subtracting really, really big numbers and computing pi to a bazillion decimal places, which is just sort of degrading because it's much more interesting than that (well, SOME of it is, anyway).

Archimedes changed the way we looked at geometry, mainly (maybe numbers, too, but I think that's less important). Also, I'm not sure importance of discoveries is related to their difficulty in any clear-cut way. Some people are just in the right place at the right time when they make an important discovery.

The type of scale you mention would suffer from the same problem as IQ. It assumes that people can be ranked in a linear order, which can become silly if you take it too far. For example, my PDE prof was better at certain kinds of very computational PDE research than I will ever be, but my visual reasoning ability was much greater than his, so we have wildly different levels of ability in tackling different kinds of problems. To some extent, if you're good at one type of math, you tend to be good at other types of math, but that doesn't mean there is no such thing as having different strengths and weaknesses.

Why do people vary so much in their math acumen? Is it nature, nurture, or a combination of both?

No one knows, but obviously it's a combination. Understanding math is something you learn how to do, though. I think my own ability was greatly increased by reading Visual Complex Analysis (I was about 21-22 at the time) and following its example.

I'd rate myself about 8.5, considering I got a PhD in math and proved a few new theorems in topological quantum field theory. People who make really revolutionary discoveries typically are quite a bit above my level, even though I am capable of proving theorems that no one else knows. Maybe you could say 9 is like a typical research mathematician, and 8 is like the typical math PhD. But I wouldn't take this scale seriously, other than your own personal use, if you want.

 

[Jagella]

...was Bo Derek really a 10?

...most of a mathematician's thinking doesn't explicitly have anything to do with numbers

I'd say that a mathematician's thinking involves trying to find solutions to problems involving quantity, shape, size, and order.

Some people are just in the right place at the right time when they make an important discovery.

Yes, and the right place is often an environment that is conducive to mathematical research. We should wonder how many people may have made brilliant mathematical discoveries if only they had the resources they needed.

The type of scale you mention would suffer from the same problem as IQ. It assumes that people can be ranked in a linear order, which can become silly if you take it too far.

My scale would take into consideration strengths and weaknesses and measure overall ability.

Understanding math is something you learn how to do, though. I think my own ability was greatly increased by reading Visual Complex Analysis (I was about 21-22 at the time) and following its example.

I try to use a visual approach to math whenever I can. It's easier to understand images than numerals.

I'd rate myself about 8.5, considering I got a PhD in math and proved a few new theorems in topological quantum field theory.

Your resume is very impressive. If you're an 8.5, then I'd rank myself a 6 rather than a 7.

But let's not take this too seriously. After all, was Bo Derek really a 10?

Jagella

 

[homeomorphic]

My scale would take into consideration strengths and weaknesses and measure overall ability.

My point is that you can't do that in any objective way because you'd have to make arbitrary choices as how to take your average of different strengths and weaknesses. Although, if you stick to integers from 1 to 10, without having too much meaningless precision in between, you get a course enough rating that maybe it makes some sense, but still shouldn't be taken too seriously.

Your resume is very impressive. If you're an 8.5, then I'd rank myself a 6 rather than a 7.

Actually, given that I said the typical math PhD was an 8, I would have to downgrade myself to 8. The point is that there's still quite a range of abilities, even once you get to that point, so you have to leave some more room at the top.

 

[Jagella]

My point is that you can't do that in any objective way because you'd have to make arbitrary choices as how to take your average of different strengths and weaknesses. Although, if you stick to integers from 1 to 10, without having too much meaningless precision in between, you get a course enough rating that maybe it makes some sense, but still shouldn't be taken too seriously.

That's obviously correct; my scale is very subjective and is merely an exercise in gauging mathematical ability in a crude fashion. I think it might superficially satisfy our curiosity about how mathematicians compare to each other. I enjoy making such ordered lists that rank my opinion about various things. For instance, my three favorite albums in descending order of preference are:

1. Black Sabbath Sabotage
2. Nazareth Hair of the Dog
3. Aerosmith Get Your Wings

Other people may prefer the Carpenters and list different albums! ;)

Jagella

 

[homeomorphic]

It's also hard to separate innate ability from experience and so on. If you're looking at some 11-year old, it's impossible to predict at that stage whether they might be capable of getting a PhD or whatever, although an astute teacher might have some sense that they have some talent. But there are stories of people who were pretty math-phobic at that age who ended up becoming mathematicians, and I don't know that anyone would have guessed that they could have done it.

 

[ZombieFeynman]

Such a scale need not be linear. I also would humbly propose that most of us forumgoers (myself especially) are quite ill-suited to even rate ourselves or each other. Landau is said to have such a scale for physicists. It was logarithmic, with 0 being the strongest and higher numbers being weaker.