What is considered a "mathematician"?

[Hercuflea]

What type of credentials generally qualify one to be called a "mathematician"?

I've added a poll. You can choose more than one response if you like. I'd like to hear the community's opinion.

I'd say someone who has studied graduate level mathematics and uses math in their daily life or work would be considered a mathematician.

 

[dipole]

If you publish in peer reviewed mathematical journals and conduct mathematical research I'd say you're a Mathematician. If not, then you're not. You're an engineer, physisist or some other consumer of mathematical knowledge. The goal of a Mathematician is to produce knowledge.

 

[russ_watters]

Such labels usually refer to one's profession. If I studied math in school, but served drinks for a living, I'd be a bartender, not a mathematician.

 

[BobG]

Such labels usually refer to one's profession. If I studied math in school, but served drinks for a living, I'd be a bartender, not a mathematician.

I find this very disheartening, as I studied strippers in college.

Yes, I agree the label should apply to what you do for a living, regardless of what you studied in school - at least in a formal sense.

It's very common to also identify what one does for a hobby - such as an amateur astronomer or an amateur ham radio operator. Except a lot of amateurs actually contribute enough to the astronomy community or the radio community that I might be tempted to just omit the amateur part.

In other words, I don't think there's some hard and fast line you can't cross (which is why I also included the PhD that publishes math papers), but I'd strongly tend towards what one does for a profession.

 

[russ_watters]

I find this very disheartening, as I studied strippers in college.

Not seeing the problem and I don't want to: Keep it on, Bob!

It's very common to also identify what one does for a hobby - such as an amateur astronomer or an amateur ham radio operator. Except a lot of amateurs actually contribute enough to the astronomy community or the radio community that I might be tempted to just omit the amateur part.

Actually, as a self-labeled amateur astronomer, I use the term to mean that I'm a little more serious than a typical hobbyist, but I don't get paid for it. Even if I ever discover a comet or an exoplanet, I don't think I'd drop the label "amateur" out of respect for the professionals.

 

[zoobyshoe]

Based on the fact Ramanujan is called a mathematician, I don't think any official credentials or academic accomplishments are necessary.

 

[Pythagorean]

If it's hobby, I'm a sailor, if it's BS, I'm a physicist, if it's MS, I'm a neurophysicist, if it's PhD, I'm a theoretical neuroscientist / applied mathematician, if it's published work, I'm a neuro-chaostician, if it's tenured job, I'm nothing. Also, my unsigned band would have be believe I'm a musician.

I probably have made the most money as a commercial fisherman.

Not sure what I am anymore, thanks.

 

[russ_watters]

Based on the fact Ramanujan is called a mathematician, I don't think any official credentials or academic accomplishments are necessary.

I would disagree that he had no academic accomplishments, but he was certainly employed as a mathematician, so it fits my definition.

 

[Evo]

My definition is someone employed as a mathematician. A degree alone means nothing.

 

[symbolipoint]

Nearest to this one, but not exactly:

If you publish in peer reviewed mathematical journals and conduct mathematical research I'd say you're a Mathematician. If not, then you're not. You're an engineer, physisist or some other consumer of mathematical knowledge. The goal of a Mathematician is to produce knowledge.

You would need to be at an advanced level, regardless of official credentials or verifiable transcripts. A few people on occasion, labeled me as a "mathematician", but they are wrong, and I do not identify myself as one. With only undergraduate degree in one of the sciences along with the necessary mathematics course credit, and also with true-in-life employed experience using basic algebra and common geometry, this is not enough to be a genuine mathematician. From many peoples' point of view, I have an advanced knowledge and skill in what I know; but that is only according to their limited viewpoint and experiences. From the understanding of more educated and studied peoples' point of view, such as of the many members here in this forum, I am just one of the many "consumers" of mathematics, certainly not any mathematician.

What is or is not a mathematician does not come from taking an opinion poll.

Mathematician: Person who studies mathematics at an advanced level and performs research in the subject. Alternatively, a person who has studied at an advanced level and performs mathematical applied development work.

 

[Evo]

Agreed symbolipoint.

 

[zoobyshoe]

I would disagree that he had no academic accomplishments, but he was certainly employed as a mathematician, so it fits my definition.

What do you think were his academic accomplishments? It doesn't look like he ever finished college or got a degree.

When Hardy at Cambridge found out about him, Ramanujan was employed as an office clerk. You could stretch his long visit to Cambridge into an "employment" of sorts, though it was more like a grant, but you'd be saying he wasn't a mathematician until his arrival in England. Hardy invited him, however, recognizing he was already a remarkable mathematician.

 

[Pythagorean]

I think several significant publications are sufficient. I would have considered Einstein a physicist even when he was employed as a patent clerk because of his contributions to science, not who signed his paycheck.

 

[Rocket50]

I think a mathematician is anyone who is serious about mathematics and does it beyond the undergraduate level. I don't think degree qualifications matter much in this case.

 

[zoobyshoe]

I think several significant publications are sufficient. I would have considered Einstein a physicist even when he was employed as a patent clerk because of his contributions to science, not who signed his paycheck.

I agree, but consider this: Suppose Einstein remained a patent examiner all his life, never published, and only after his death were his 5 famous papers discovered. Was he still a physicist?

 

[Pythagorean]

I agree, but consider this: Suppose Einstein remained a patent examiner all his life, never published, and only after his death were his 5 famous papers discovered. Was he still a physicist?

That would be a very grey area. We would recognize him as a physicist today, yes, still probably idolize him in some way as an ideal scientist. But in his time he would not have been recognized as such, or perhaps trivialized: a scientist at heart.

 

[russ_watters]

What do you think were his academic accomplishments? It doesn't look like he ever finished college or got a degree.

According to his wiki, he was awarded a degree based on his professional accomplishments.

You could stretch his long visit to Cambridge into an "employment" of sorts, though it was more like a grant...

Yes, a research grant would definitely count as employment as a mathematician.

...but you'd be saying he wasn't a mathematician until his arrival in England. Hardy invited him, however, recognizing he was already a remarkable mathematician.

Professional vs amateur. It can be a fine line but it is an unknown line until a person gets judged: Anyone can write a book, but they aren't an author until they sell it. Until then, it is just words on a page and presumptuous to give yourself the label. Until someone recognized his math had value, he wasn't a mathematician, he was just a guy doing math of unknonw value. A person doesn't get to decide his own standing as a professional -- his potential peers make the decision.

I agree, but consider this: Suppose Einstein remained a patent examiner all his life, never published, and only after his death were his 5 famous papers discovered. Was he still a physicist?

We could call him that, but he could not call himself that. Otherwise:

I'm a poet, mason, artist, physicist, chemist, biologist, chef, accountant and lawyer. Because I get to label myself for everything I've dabbled in, right?

 

[Pythagorean]

Referring to Einstein's five as "dabbling" would be quite an understatement.

 

[russ_watters]

Referring to Einstein's five as "dabbling" would be quite an understatement.

Agreed -- But I was talking about myself, not Einstein. Though since you've never seen my paintings, since I self-label as an "artist", you must assume I'm Picasso, right?

 

[zoobyshoe]

According to his wiki, he was awarded a degree based on his professional accomplishments.

All of which he accomplished without a degree. Being a mathematician preceded the academic credential.

Professional vs amateur. It can be a fine line but it is an unknown line until a person gets judged: Anyone can write a book, but they aren't an author until they sell it. Until then, it is just words on a page and presumptuous to give yourself the label. Until someone recognized his math had value, he wasn't a mathematician, he was just a guy doing math of unknonw value. A person doesn't get to decide his own standing as a professional -- his potential peers make the decision.

Extending my conversation with Pythagorean, by your logic Einstein was an amateur physicist when he wrote all his greatest papers, but suddenly became a professional when those papers were recognized as great.

I don't buy your amateur/professional dichotomy at all. Whether a person is getting paid for their work or not can easily have nothing whatever to do with the quality of the work, and whether or not they should be called "physicist" or "mathematician." Ramanujan was obviously a remarkable mathematician before Hardy ever heard of him, just as Einstein was a remarkable physicist before he became a household word. It would be ridiculous to say Einstein wasn't a physicist when he wrote the five papers.

 

[zoobyshoe]

Agreed -- But I was talking about myself, not Einstein. Though since you've never seen my paintings, since I self-label as an "artist", you must assume I'm Picasso, right?

If you were Picasso you would already be Picasso before anyone else noticed it.

 

[Pythagorean]

Agreed -- But I was talking about myself, not Einstein. Though since you've never seen my paintings, since I self-label as an "artist", you must assume I'm Picasso, right?

My only point was that contributions to your field trump employment. Einstein calling himself a physicist wouldn't have added to or taken away from his status as one.

 

[David Carroll]

Huh. According to the views of many people in this forum, Eratosthenes, Diophantus, Pythagoras, and Archimedes would not qualify as "mathematicians" as peer-reviewed journals, tenured positions, and pieces of paper called "degrees" did not exist in their era.

 

[dipole]

Yes but the question referred to modern mathematicians. Given that no journals existed in their time, my definition still works since they preformed research in and contributed greatly to mathematical knowledge, even if publishing didn't work the same way.

 

[symbolipoint]

Modern or ancient are unimportant to the identification. You can argue about why or why not, but those people listed greatly developed what is studied today, so they can be said to have been mathematicians.

 

[zoki85]

Leading votes so far are for "Has a PhD in another field but has done published research in mathematical problems"
LOL

 

[russ_watters]

If you were Picasso you would already be Picasso before anyone else noticed it.

Agreed. And it is also possible I could be Picasso an no one will ever know. The point is, you have no basis for a conclusion that I am NOT Picasso.

 

[russ_watters]

My only point was that contributions to your field trump employment. Einstein calling himself a physicist wouldn't have added to or taken away from his status as one.

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.

 

[Pythagorean]

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.

I agree, I think. Nowadays we have methods to measure impact factor through citations and I would be ok with someone analyzing their own contributions through their impact factor. Of course, the judgment was still made by peer review process and editors, and the cascade of authors that cited the contributor-in-question, but since it's all recorded and measured today by the journal publishing network, you have a bit of a measuring stick around nowadays that Einstein didn't have.

Leading votes so far are for "Has a PhD in another field but has done published research in mathematical problems"
LOL

Yeah, I think that one should have been "made significant published contributions to the field of mathematics, regardless of education". Because otherwise we're ignoring people that have a degree in Math AND make contributions to the field, emphasis being on contribution.

 

[Simon Bridge]

I don't think "mathematician" is usually a legally reserved word like "doctor" or "engineer" so anyone can call themselves a mathematician if they want to. By doing so, though, they are claiming to be an expert in or a student of mathematics. (Check dictionary.)

Under the dictionary useage of the word, you do not have to be paid to be a mathematician to be considered one.

It is only among academia that you need to be academically recognized - the minimum recognition depends on the academic community.
i.e. being famous for contributions to mathematics would get the community of mathematicians wanting to claim you as one of their own regardless of your formal qualifications or current paid job... but that is not "minimal". Enrolling in college mathematics courses would be minimal.

Usually any student majoring in mathematics would get the title in the less prestigious sense but most profs would append "student" to it. You do tend to need to have published to gain full acceptance - though a PhD can do it too. By the time you are post-doc you may be getting paid, but the job title may be something like "consultant" or "teaching assistant" rather than "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.