What is considered a "mathematician"?

[zoobyshoe]

Agreed. I am only trying to point out that "contributions to your field" is not a judgement that a person can make for himself. It comes from after-the-fact recognition.

But you just agreed you would be Picasso, if you were Picasso, before anyone else was aware of it! Now you're contradicting that and saying a person is not Picasso until his peers say so.

It's clear you're primarily concerned about people labeling themselves independent of their actual ability. You want some kind of proof they deserve a label and are not charlatans. But I don't think the issue of what someone should be called should completely revolve around the fact, be directed at the fact, that people can mislabel themselves. That leads to weird restrictions that don't allow people like Ramanujan or Einstein to call themselves what they were.

On the subject of "significant contributions to the field," I think this is not a good criteria. It would make someone an above-average mathematician, but I don't think it should be required to be above-average to simply be a thing. A mediocre mathematician would still be a mathematician.

I liked Simon's post, which put the concept of a mathematician in proper perspective. It's a label distinct from doctor or engineer. Ramanujan was a mathematician primarily because mathematics was the center of his life, the most important thing in the world to him, a mental universe he lived in. By that criteria, there will be, and have been, many mathematicians no one here will ever be aware of.

 

[David Carroll]

One of the main reasons why I like math better than physics is that it is a much more democratic field of study. In math, a proof is a proof is a proof, whether it was performed by Roger Penrose or a homeless guy from the streets of West Philly. And a submission of a relevant and important proof to a math journal would be accepted irrespective of what bureaucratically academic qualifications you have.

 

[Math10]

Getting a Ph.D in mathematics would help someone of becoming a mathematician but not necessarily. Someone who solves the world's most difficult math problems or invents new theories in mathematics can be called a mathematician, but that person doesn't necessarily need a degree to do this. Many mathematicians are self-taught but they became very famous.

 

[russ_watters]

I know this is old now, but since it came back, one little clarification

But you just agreed you would be Picasso, if you were Picasso, before anyone else was aware of it! Now you're contradicting that and saying a person is not Picasso until his peers say so.

The difference I'm trying to convey is that no matter how good you are, it is improper to self-label. You may be Picasso but you shouldn't say you are Picasso until others recognize you.

 

[zoobyshoe]

I know this is old now, but since it came back, one little clarification
The difference I'm trying to convey is that no matter how good you are, it is improper to self-label. You may be Picasso but you shouldn't say you are Picasso until others recognize you.

OK, but this brings us to the limitation of the particular label you pulled out of the air. No one can label himself Picasso, because that is to claim extraordinary originality, but anyone can label himself an artist, which is simply to claim you produce art works. Calling yourself a mathematician would be the same, implying only some way above average interest in Math, not any greatness.

 

[russ_watters]

...but anyone can label himself an artist, which is simply to claim you produce art works. Calling yourself a mathematician would be the same, implying only some way above average interest in Math, not any greatness.

IMO, such labels imply much more than just "interest". They impliy competencce. Perhaps in the grand scheme of things it doesn't matter for artists or mathematicians, but that's really only because it is tough to kill anyone with poorly executed artwork. That's why for some professions and contexts, such as "engineer" and "doctor", the label can only be legally applied after strict demonstration of competencce.

 

[zoobyshoe]

IMO, such labels imply much more than just "interest".

I didn't say you could call yourself an artist by virtue of interest in art. I said you could call yourself an artist by virtue of producing artworks. Your art could suck bananas, you could be the worst artist in the world, but the label would still be accurate, simply because you produce artworks. This is true of many labels. You can call yourself a handyman, a gardener, a farmer, a shopkeeper, a cook, a mechanic, a salesman, and so on, without that label implying anything about how good you are at it.

For someone to call themselves a mathematician, I would only assume a much above average interest in math on their part, and I would assume they were competent to understand what was interesting them, just because it would be really odd for anyone to sustain interest in something they couldn't even understand. I would not require that person to be a particularly eminent mathematician simply to call himself one.

They impliy competencce. Perhaps in the grand scheme of things it doesn't matter for artists or mathematicians, but that's really only because it is tough to kill anyone with poorly executed artwork. That's why for some professions and contexts, such as "engineer" and "doctor", the label can only be legally applied after strict demonstration of competencce.

Here, too, though, the vetting process is a kind of tentative approval and the person so labeled can go astray. Tesla had a legitimate education in EE, but eventually his sanity slipped and he claimed he'd figured out a death ray, and other whacky stuff. Doctors and nurses get addicted to drugs and start making incompetent decisions. (At least 1 in 14 physicians develops a drug problem: http://www.turner-white.com/pdf/hp_jul03_know.pdf Feynman has that story about the engineers who were running all kinds of tests to figure out why their thing was whistling (he took one look inside and saw they had a sharp edge facing right into the air flow). Couple weeks ago I read about a doctor convicted of sexually abusing his female patients. Legal requirements for calling yourself a doctor or engineer only reduce problems. They don't eliminate them.

 

[Medicol]

I think PhD is only used to certify one's completion of a math program. His thesis narrows his research effort into ONE single area. I would like to get at least 5 PhDs in science and technology but then what do you I think I become ?
If you have interest in maths, then show us what math related stuff you worked and are working on. The effort is worthier to say who you are instead.
I am thinking about categorizing people interested in maths into groups and subgroups of different levels.
post PhD: super mathematician
PhD: level 1
Master: level 2
etc

 

[StatGuy2000]

In my personal opinion on this question, I make a distinction between four categories: "mathematician", "mathematical scientist", "math teacher" and "math enthusiast".

A mathematician, in this sense, is someone who works specifically in the development of the field of mathematics (this definition would tend to be restricted to those in academia or in research labs like Google Labs, Microsoft Research, or Bell Labs).

A mathematical scientist (or a "mathematical worker", for lack of better terms) are those who work in fields that actively and extensively use the knowledge built out of mathematics research but may not contribute directly to the field of mathematics itself. This category could include statisticians, actuaries, operations researchers, many physicists, many economists, some computer scientists (particularly those with a theoretical bent), and some engineers.

A math teacher, as I define it, is someone whose role is primary to teach math at the elementary, secondary, and tertiary level, but may or may not be actively involved in the development of mathematics.

A math enthusiast (or "math lover" again for lack of better terms) are those who primarily have an amateur interest in various areas of mathematics, particularly in recreational mathematics.

Please note that these categories are not mutually exclusive (e.g. a professional mathematician may for example, work as a mathematical scientist when working in consulting projects for industry)

 

[Math10]

I agree with StatGuy2000.