Exactly what is considered to be a mathematician?

[Math100]

Suppose there are three people.
1) Obtained a Ph.D. in mathematics and is a mathematics professor at MIT.
2) Obtained a Bachelor's degree in mathematics, found/discovered/invented simpler/easier/shortcut ways of doing certain math problems and publishes those math papers.
3) Proved theorems/conjectures and won Field's Medal.
Which one of them is considered to be a mathematician?

 

[fresh_42]

The one who doesn't question AC.

 

[Klystron]

Suppose there are three people.
1) Obtained a Ph.D. in mathematics and is a mathematics professor at MIT.
2) Obtained a Bachelor's degree in mathematics, found/discovered/invented simpler/easier/shortcut ways of doing certain math problems and publishes those math papers.
3) Proved theorems/conjectures and won Field's Medal.
Which one of them is considered to be a mathematician?

The one who doesn't question AC.

Given mathematics as the subject of the discussion, I reckon acronym 'AC' refers to the 'axiom of choice' devised by Ernst Zermelo in proofs of set theory. If this is an accurate reading of AC, then the first sentence of the original post may be rephrased

Suppose there are three mathematicians.

obviating the subsequent query. Well done.

 

[berkeman]

Suppose there are three people.
1) Obtained a Ph.D. in mathematics and is a mathematics professor at MIT.
2) Obtained a Bachelor's degree in mathematics, found/discovered/invented simpler/easier/shortcut ways of doing certain math problems and publishes those math papers.
3) Proved theorems/conjectures and won Field's Medal.
Which one of them is considered to be a mathematician?

Ooo, ooo, I know!

Spoiler

Made you look.

 

[George Jones]

Suppose there are three people.
1) Obtained a Ph.D. in mathematics and is a mathematics professor at MIT.
2) Obtained a Bachelor's degree in mathematics, found/discovered/invented simpler/easier/shortcut ways of doing certain math problems and publishes those math papers.
3) Proved theorems/conjectures and won Field's Medal.
Which one of them is considered to be a mathematician?

How much coffee do these three drink?

Alfred Renyi said "a mathematician is a machine for turning coffee into theorems".

 

[fresh_42]

How much coffee do these three drink?

Alfred Renyi said "a mathematician is a machine for turning coffee into theorems".

Thank you for the correct quote! Esp. for not giving it to Erdös, as it is done so often.

 

[Rive]

Suppose there are three people.
...
Which one of them is considered to be a mathematician?

That three does not seems to be a good fit for this type of question.

Maybe you should try using the 'duck test' instead? That's also based on 'three'

 

[Klystron]

That three does not seems to be a good fit for this type of question.

Maybe you should try using the 'duck test' instead? That's also based on 'three'

Now name three ducks.

Wait, I know that one

Spoiler: Name 3 ducks

Hughie, Dewey and Louie
or
Donald and Daisy Duck. Uncle Scrooge makes three.

 

[DrClaude]

Suppose there are three people.
1) Obtained a Ph.D. in mathematics and is a mathematics professor at MIT.
2) Obtained a Bachelor's degree in mathematics, found/discovered/invented simpler/easier/shortcut ways of doing certain math problems and publishes those math papers.
3) Proved theorems/conjectures and won Field's Medal.
Which one of them is considered to be a mathematician?

What is their respective Erdős number?

 

[Fred Wright]

That three does not seems to be a good fit for this type of question.

Maybe you should try using the 'duck test' instead? That's also based on 'three'

Three mathematicians walk into a bar. You'd think the third one would have ducked.

 

[fresh_42]

What is their respective Erdős number?

Did you just sneak into the community with your 3?

 

[Fred Wright]

Did you just sneak into the community with your 3?

Don't despair, Ramanujan also had a 3.

 

[mathwonk]

Assuming the OP actually was hoping for an answer, I suggest that all three candidates are mathematicians, since they all "do mathematics", in the sense of thinking about math problems and questions, and making original contributions to their solution.

 

[Math100]

Assuming the OP actually was hoping for an answer, I suggest that all three candidates are mathematicians, since they all "do mathematics", in the sense of thinking about math problems and questions, and making original contributions to their solution.

Thank you for your response.

 

[mathwonk]

I might say further that perhaps 1) is a professional, or perhaps academic mathematician; 2) is an amateur mathematician (as was Fermat); 3) is an especially distinguished research mathematician.

 

[mathwonk]

and to connect to other responses, I suppose someone knows who said a comathematician is a device for changing cotheorems into ffee?

 

[Math100]

I might say further that perhaps 1) is a professional, or perhaps academic mathematician; 2) is an amateur mathematician (as was Fermat); 3) is an especially distinguished research mathematician.

Thank you for your genuine response.

 

[Scott Mayers]

Exactly what is considered to be a mathematician?
A specialty logician or practicioner of their efforts whose domain is quantity.

Given these two general kinds of people can combine their study as it applies to other subject domains, this might be a simlified GENERAL description of the class we call, "mathematicians".

 

[S.G. Janssens]

whose domain is quantity

To me, mathematics is much more about structure than about quantity.
Quantity can be used to give a description of structure, but other descriptions can and do occur.

 

[wrobel]

Exactly what is considered to be a mathematician?

obtaining results in math what else

 

[Math100]

Exactly what is considered to be a mathematician?
A specialty logician or practicioner of their efforts whose domain is quantity.

Given these two general kinds of people can combine their study as it applies to other subject domains, this might be a simlified GENERAL description of the class we call, "mathematicians".

I really like your answer. Thank you.

 

[mathwonk]

wrobel's answer raises another question, namely when one ceases to obtain results does one cease to be a mathematician? or only when one ceases trying? or never, after having once succeeded, or tried? i.e. did he mean "having obtained"? Scott Mayers' answer also implies that one is [currently] practicing ones art. So maybe I should say I was once a research mathematician, and am now an amateur or even a student of mathematics. Indeed a closer look at the original categories reveals that only 2) explicitly states current research activity, although past activity at least is implied in 1) and 3).

 

[fresh_42]

My best answer, sorry 2ct, would be the same slogan I once heard about Rock:

Mathematics isn't science, mathematics is a state of mind!

This state of mind was best demonstrated by Spock in the original version. It means that mathematicians first want to know all rules before jumping to conclusions. They always point to hidden assumptions in debates, and it is a special torture for them to listen to e.g. politicians because hidden assumptions are their daily business. There is not really this one truth for mathematicians, only valid and invalid deductions.

 

[Scott Mayers]

To me, mathematics is much more about structure than about quantity.
Quantity can be used to give a description of structure, but other descriptions can and do occur.

This would be a more specific goal that all mathematicians, as a class, cannot be asserted without imposing it on all others. I agree to this sub-goal of particular mathematicians. I personally think that the subject math, as a subset of logic, is best differentiated from other forms of logical inquiry by the nature of focusing on quantity. Originally, the ancient Greeks opted to use geometry to prove mathematical truths . In this way, this is about 'structure' but they had no choice at the time given the lack of acceptance of the use of "0" to represent the structural conception of "nothing". People, including mathematicians, will differ on whether they think that numbers represent something 'real' or not. So while you and I might like to favor the concept of math as including "structure", many inversely think that math is only a relatively artificial construct where "structure" to them is about the measured realities, the literal physical representation of structure.

I've heard another that defines math as the subject of patterns. But to me, this is more generically applicable to logic itself, not to a subset of it. Also, "science" acts as a subset as "the logic of observation", when just considering the general topic without considering the institution of science or "what scientists do". As this might demonstrate, there are more than one way to use the terms, like mathematicians.

What I'm wondering is if you are looking for "what should a 'mathematician' do?" and not what one means by it colloquially?

 

[Drakkith]

How much coffee do these three drink?

Alfred Renyi said "a mathematician is a machine for turning coffee into theorems".

No wonder I never became a mathematician. I don't like coffee.

 

[mathwonk]

ok this discussion has me functioning more like a mathematician. i have been struggling to read a section in Dummit and Foote on discrete valuation rings, in particular the theorem that a local domain is a DVR iff every non zero fractional ideal is invertible. These purely algebraic results make my head spin, but i read it. In one direction they assumed every fractional ideal was invertible, applied it to the maximal ideal and deduced the maximal ideal was principal, hence the ring was a DVR. Then I noticed that the proof actually proved more, namely that in any local domain, every invertible ideal is principal. I.e. the proof did not use that they were arguing about the maximal ideal, just that it was invertible. The idea is that invertible ideals in a ring are apparently sort of an analog of codimension one subvarieties of an algebraic variety, and those are the ones that locally are defined by one equation, i.e. their ideals are (locally) principal. DVR's are one dimensional local rings, but this fact is true in any dimension local ring. The point is that once you stop just mindlessly reading a proof, and start thinking about it and its implications, and analyzing just which facts are used and which ones are not, you get a new statement, and you are behaving like a mathematician. Then tedious, uninspiring reading becomes more enjoyable and more illuminating. thank you!

 

[coquelicot]

I might say further that perhaps 1) is a professional, or perhaps academic mathematician; 2) is an amateur mathematician (as was Fermat); 3) is an especially distinguished research mathematician.

Fermat was not an amateur mathematician. This stupid claim originating from one ignorant modern author and propagated then by everyone has to cease.
Please, read the two books of Tannery "Oeuvres de Fermat", the numerous letters he has written to his contemporaries, and especially the overwhelming number of number theoretic problems studied by Fermat at the end of the second tome (especially the variety of problems is amazing).
Fermat was an extremely intensive researcher, who produced many great discoveries that were published, and corresponded intensively with its contemporaries in mathematics and physics. Lagrange, Euler and Gauss (who understood the Latin very well) all described Fermat as a "grand savant", "great man", "the sagacious Fermat" etc. It is now known that Newton was inspired by the work of Fermat for his discovery of infinitesimal calculus.

The right point: Fermat was the only real professional mathematician (in the modern sense of the term) of his time in France.

 

[malawi_glenn]

Depends on what you mean by amateur. Was Fermat ever paid wage for his work on math?

 

[coquelicot]

Depends on what you mean by amateur. Was Fermat ever paid wage for his work on math?

I don't think this is what is intended when one says "amateur". Do you think Archimedes was an amateur mathematician? and Euclides?

 

[mathwonk]

@coquelicot: This confusion illustrates the universal need for definitions if one wishes to be understood. I certainly meant by "amateur" the meaning its word origin implies: namely one who does the activity out of love, rather than to earn a living by it. Thus to me there is no contradiction in calling a great mathematician also an amateur.

Since you ask, it seems to me that Archimedes earned his keep more by his applied works, such as his construction of defensive military engines in the defense of Syracuse, but his pure mathematical results were apparently done for the love of the research. He was certainly a great mathematician. Of Euclid's life we know very little, but it is generally agreed that he was not a great mathematician, although in my opinion he did write a great text book, whose results seem mostly to be the fruit of other mathematicians' research.

There is no challenge offered here to your opinion that Fermat was a great mathematician, but
it is easy to find fairly knowledgable references to Fermat as an amateur:

https://artofproblemsolving.com/wiki/index.php/Pierre_de_Fermat
"Pierre de Fermat (August 17, 1601 – January 12, 1665) was a French magistrate and government official. He, however, is most famous for being an amateur mathematician."

Perhaps you might grant that Stephen Wolfram is not entirely stupid:
https://scienceworld.wolfram.com/biography/Fermat.html
"French lawyer who pursued mathematics in his spare time. Although he pursued mathematics as an amateur, his work in number theory was of such exceptional quality and erudition that he is generally regarded as one of the greatest mathematicians of all times."

Here also is one source to back up your opinion that greatness should not be called amateurism:
https://simonsingh.net/books/fermats-last-theorem/who-was-fermat/
"He was a truly amateur academic and E.T. Bell called him the Prince of Amateurs. However, when Julian Coolidge wrote Mathematics of Great Amateurs, he excluded Fermat on the grounds that he was ‘so really great that he should count as a professional.’ "

Even this reference however makes clear that Coolidge did consider Fermat as technically an amateur.

But I think you can relax. I.e. even people who call Fermat an amateur do regard him as truly great.
Cheers.

 

[malawi_glenn]

I don't think this is what is intended when one says "amateur".

Yes it is, look up the definition of the word.
You need to read the context.
Same as professional, which means that opposite - and can mean two things as well.

There are many amateur mathematicians on this site too :) Just doing math for the sheer joy of it, but are not payed to do so ;)

 

[coquelicot]

@coquelicot: This confusion illustrates the universal need for definitions if one wishes to be understood. I certainly meant by "amateur" the meaning its word origin implies: namely one who does the activity out of love, rather than to earn a living by it. Thus to me there is no contradiction in calling a great mathematician also an amateur.

Since you ask, it seems to me that Archimedes earned his keep more by his applied works, such as his construction of defensive military engines in the defense of Syracuse, but his pure mathematical results were apparently done for the love of the research. He was certainly a great mathematician. Of Euclid's life we know very little, but it is generally agreed that he was not a great mathematician, although in my opinion he did write a great text book, whose results seem mostly to be the fruit of other mathematicians' research.

There is no challenge offered here to your opinion that Fermat was a great mathematician, but
it is easy to find fairly knowledgable references to Fermat as an amateur:

https://artofproblemsolving.com/wiki/index.php/Pierre_de_Fermat
"Pierre de Fermat (August 17, 1601 – January 12, 1665) was a French magistrate and government official. He, however, is most famous for being an amateur mathematician."

Perhaps you might grant that Stephen Wolfram is not entirely stupid:
https://scienceworld.wolfram.com/biography/Fermat.html
"French lawyer who pursued mathematics in his spare time. Although he pursued mathematics as an amateur, his work in number theory was of such exceptional quality and erudition that he is generally regarded as one of the greatest mathematicians of all times."

Here also is one source to back up your opinion that greatness should not be called amateurism:
https://simonsingh.net/books/fermats-last-theorem/who-was-fermat/
"He was a truly amateur academic and E.T. Bell called him the Prince of Amateurs. However, when Julian Coolidge wrote Mathematics of Great Amateurs, he excluded Fermat on the grounds that he was ‘so really great that he should count as a professional.’ "

Even this reference however makes clear that Coolidge did consider Fermat as technically an amateur.

But I think you can relax. I.e. even people who call Fermat an amateur do regard him as truly great.
Cheers.

So, why I've never seen that Archimedes, Euclides or Appolonius were called "amateur". In french, my mother tongue, amateur don't mean "not paid" but "a person generally of low level in the branch, doing that for his pleasure, but of relatively low level". Admittedly, this word of french origin may have got a different meaning in english. I maintain that calling Fermat an amateur is still absurd, because there were no paid mathematician in France in this time: Descartes, Pascal and Robertval were all amateur? that is non sense in my opinion.

Edit: As can be understood in my answer above, the problem is not really calling Fermat "an amateur", the problem is that it is the only great man of his category who is called "an amateur", even among far less great men like Pascal. Again, this negative term (with respect to the greatness of the man) comes from one person (I don't remember his name) who thought Fermat became famous because of one or two enigmas in number theory he found by luck. Nothing is more wrong. The sole work of Fermat in geometry would suffice to categorize him among great men of the past. Add to to that his work in combinatorics and probabilities, in the theory of elimination (the first method of elimination ever published), in analysis and infinitesimal calculus, and you can categorize him among the greatest men. Add to that his overwhelming number of results and problem he studied in number theory, of which he sent many proofs to Carcavi, Robertval, Mersenne and Pascal (most of them were lost), and you get a Giant. This humiliating term of "amateur" which is addressed only to Fermat (among the greatest men) is really ridiculous.

 

[malawi_glenn]

In french, my mother tongue, amateur don't mean "not paid" but "a person generally of low level in the branch, doing that for his pleasure, but of relatively low level".

Who cares about french?

 

[coquelicot]

Who cares about french?

"Amateur" is just a french word.

 

[malawi_glenn]

"Amateur" is just a french word.

Why is it in an English dictionary then?

 

[coquelicot]

Why is it in an English dictionary then?

According to my checking in several english dictionaries (e.g Vicon, Wikipedia and other), the term in english has exactly the same meaning as in french, including a pejorative meaning, and that of novice, unprofessional. You seem to be gifted to extract from my answers the unimportant things. You do not react to the fact that Fermat is the only great man that is called an "amateur" as I wrote above, but to an unimportant fact that I added regarded the French tongue.

This fact, added to the fact that there were no paid mathematicians in France during this era, demonstrates that the word "amateur", when applied to Fermat, can only be understood in the pejorative meaning.

 

[malawi_glenn]

This fact, added to the fact that there were no paid mathematicians in France during this era, demonstrates that the word "amateur", when applied to Fermat, can only be understood in the pejorative meaning.

I have never understood it that way. So it can be understood in other ways.

 

[mathwonk]

M. coquelicot, it is somewhat courageous for someone to whom English is not native to argue so vigorously about subtleties of English meanings. However, trying to be objective, I have consulted my father's Webster's International dictionary from 1934, and found the word professional to have several meanings, among them one who pursues an activity for pay, or hire.

Perhaps you may be more familiar with this use of the word in reference to athletics. In that field we (at least in America) speak of someone as "turning professional" when they begin to accept money for their performance. Indeed this is the well known meaning of the word in regard to eligibility for the Olympic Games.

Nonetheless your arguments are interesting and cause me to wonder why e.g. people do not call Descartes, a contemporary of Fermat, also an amateur. As to the existence of paid mathematicians in France during that period of time, recall that it was somewhat common for famous mathematicians and scientists to be supported by royalty for their work and tutelage, a form of professional pay for services. Although Fermat was a jurist all his life, Descartes became at least briefly an employee of the queen of Sweden, according to wikipedia, engaged to create a scientific institute, near the end of his life.

It also seems there may be other attributes of professionalism that come into play, and which are also mentioned in my father's dictionary, such as undergoing professional training. Unlike Fermat, or at least more than Fermat, it seems, also from wikipedia, that Descartes undertook university training in mathematics whereas Fermat's training was in law.

Furthermore, Descartes published extensively, both his work in mathematics and in other areas, whereas Fermat seems to have limited himself to circulating his results privately among friends, Descartes among them. Thus again the wikipedia article on Fermat refers to his doing mathematics more as a "hobby", again without any pejorative implication, to me at least.

So your points are interesting, but as far as concluding that, in reference to Fermat, the normal, or only possible, meaning of the word "amateur" is pejorative in English, and that of "professional" is unrelated to pay, I must disagree, albeit amicably.

 

[mathwonk]

For variations on the meaning of "amateur mathematician", it may be of interest to read the preface to the book "The mathematics of great amateurs", by Julian Lowell Coolidge, late mathematics professor of Harvard University. (Note that the title alone implies there is no contradiction between amateur and great, or the book would be vacuous.)

https://archive.org/details/mathematicsofgre005808mbp/page/n9/mode/2up?view=theater

First he gives what he calls the "natural" meaning of the term:
"One would naturally mean by an amateur in mathematics one who did not earn his living in large part by the subject, as a teacher or a physicist, or an astronomer or even an engineer."

Thus he confirms that the meaning malawi glenn and I use is the natural one.

Next, for the purposes of his book, he discards this natural meaning for reasons reminiscent of the opinions of M. coquelicot:
"But under such a definition Euclid and Archimedes would be classed as amateurs, which seemed to me absurd."

Then, since he cannot bear the consequences of using the natural definition, he substitutes his own definition (which by the way has to him a gender component):
"In general I have taken men who were principally known for some other activity, yet whose success in the field of mathematics enabled them to make contributions of permanent value."

So now he takes only those who not only earned their living otherwise, but were principally known for the other activity.

Then he also makes one exception from his targets solely on the grounds that he is too great.
"I have not included Fermat, whom Bell has called the Prince of Amateurs, who was [professionally] a 'Maitre des requetes ', because he was so really great that he should count as a professional....."

However, note that he does include Pascal, Bolzano, and Leonardo da Vinci, and that he does not intend the use of the word "amateur" as pejorative in regard to any of his subjects.

So perhaps we can agree to disagree on when it is appropriate to use these terms in English, even though the "natural" meaning seems clearly confirmed by some famous scholars.

 

[TeethWhitener]

According to my checking in several english dictionaries (e.g Vicon, Wikipedia and other), the term in english has exactly the same meaning as in french, including a pejorative meaning, and that of novice, unprofessional.

https://en.wiktionary.org/wiki/amateur#English
https://en.wikipedia.org/wiki/List_of_amateur_mathematicians

Also, checking actual dictionaries (not wikipedia), including Merriam Webster, Oxford, Cambridge, and even Encyclopedia Brittanica gives the primary definition as "non-professional." Merriam Webster offers up the tidbit that its original meaning was acquired from French as early as 1757 to be "lover," as in an art amateur is a lover of art. OED confirms this and adds that by end of the 18th century, it had taken on the meaning "non-professional practitioner." The pejorative use comes much later. Also, I checked French dictionaries. Amateur as a pejorative is not the primary definition in general:
https://www.larousse.fr/dictionnaires/francais/amateur/2695
https://www.le-dictionnaire.com/definition/amateur
https://dictionnaire.lerobert.com/definition/amateur

It's clear that "amateur," as used when referring to Fermat as an amateur mathematician, is meant in either the "lover" or the "non-professional" sense.

As for Descartes (and many other mathematicians at the time), he lived off investments his whole life, so his avocation was also his primary vocation.

 

[russ_watters]

I really don't see the big deal here. If nobody was paying mathematicians hundreds of years ago then by the simple definition there were no professionals and everyone was an amateur. So what? Yes, professionals in modern times by recognition tend to be more serious/accomplished (because who has the time to spend on the pursuit otherwise?), but so what? I still fail to see an insult.

Now, calling someone an amateur when they are not - obviously that would be an insult.

I feel that often people bring the negative connotations of words with them.

 

[Vanadium 50]

courageous

Excellent word.

From the point of view of a bystander, it's hard to reconcile two things: we have someone who feels Physicists Are Doing It All Wrong because of a perveived lack of mathematical rigor, but at the same time being all loosey-goosey with definitions of "amateur" and "professional". Either is fine - it's just the juxtaposition that is hard to reconcile.

 

[Klystron]

No doubt subject matter and area of concentration weigh heavily on these descriptions of Fermat including E. T. Bell's.

Rene Descartes became a darling of certain philosophers for reasons abstracted from his direct contributions to mathematics. The same philosophers mildly disparage Pascal for his early publications and letters motivated by solving gambling problems, ignoring or possibly not understanding binomial theory. IOW gambling solutions appear tainted and ungentle to certain authors who practically deify Descartes.

The sole work of Fermat in geometry would suffice to categorize him among great men of the past. Add to to that his work in combinatorics and probabilities,...

No argument here, but doubtful that many writers, historians and philosophers over the intervening centuries truly understand nor attach as much importance to combinatorics as they might to simpler pictures of, say, x, y, z axes drawn on graph paper. Despite ubiquitous application, probability theory's origins in gambling on dice and cards soils the subject among the fainthearted.

Analogously, certain writers disparage Robert Oppenheimer, greatly respected by his peers (with the possible exception of Edward Teller), as merely an organizer of other's work. Likewise, Albert Einstein, once a darling of the press and public, had his reputation sullied when his theories led to unpopular applications near the end of his life.

 

[coquelicot]

I really don't see the big deal here. If nobody was paying mathematicians hundreds of years ago then by the simple definition there were no professionals and everyone was an amateur. So what? Yes, professionals in modern times by recognition tend to be more serious/accomplished (because who has the time to spend on the pursuit otherwise?), but so what? I still fail to see an insult.

You would be right if all great men of this time were called "amateur". But it appears that only Fermat is, at almost all possible occasion. Nobody, above, has been able to explain this fact, except one or two persons that have tried very hard to demonstrate that, in some (acrobatic) sense, Descartes was a professional mathematician while Fermat was not. What about Pascal, Robertval, Frénicle (well, I would actually call him an amateur), Leonardo da Vinci, Vietes, Euclides, Appolonius, Archimedes, and many, many other?
My original post was not a critic of Mathwonk which I estimate otherwise: he was just repeating what I see everywhere "Fermat an amateur". My critic is that this stupid opinion has to cease to be propagated by intelligent people.

Now, calling someone an amateur when they are not - obviously that would be an insult.

I feel that often people bring the negative connotations of words with them.

I'm a doctor in mathematics, and I'm not earning any money in this domain. Yes, I would be vexed if you call me "an amateur" mathematician. Maybe the negative connotations of words I bring with me.

 

[coquelicot]

M. coquelicot, it is somewhat courageous for someone to whom English is not native to argue so vigorously about subtleties of English meanings. However, trying to be objective, I have consulted my father's Webster's International dictionary from 1934, and found the word professional to have several meanings, among them one who pursues an activity for pay, or hire.

I was not dealing with subtleties of English meanings. Actually, you begun with that and the other took the train on that. The meaning of "amateur" in English is exactly what I thought. It is not necessarily negative nor in French, nor in English, and may be even positive, depending on the context. I knew that very well from the beginning. What was boiling down, from the beginning, and that was not clear in my first post, but that I explained in the next reply, is the contrast between Fermat and pretty all genius of his time who are never called "amateur", while I see almost everywhere Fermat is (in the recent era). I would never have reacted to your post if it was your own opinion, I mean, an original one or a not too common one, even if I had thought it is negative. I reacted to your post because the application of this term to Fermat is propagating almost everywhere in forums and books, in English and in French articles as well. I maintain that with respect to the context, it does imply something not very serious about Fermat and that this was intentionally done by the author who qualified Fermat so.

I feel that my post has caused you to reflect about that, and I'm happy for that.

 

[malawi_glenn]

One of my favorite tv shows is masterchef sweden. There, the participants are called "amateur chefs", by the judges, by the tv-stations, and the participants also call themselves that.

If amateur means "bad", why would anyone watch that show?

 

[coquelicot]

Because that's amusing to see the mediocre guys trying to do something good :-)

More seriously, I have never said that amateur means "bad", but that no one expect from an amateur to do something really good, like a professional. Do you believe it is possible that an amateur mathematician will solve, one day, the Riemann conjecture?

 

[malawi_glenn]

Do you believe it is possible that an amateur mathematician will solve, one day, the Riemann conjecture?

I belive that an amateur chef will ;)

 

[dextercioby]

"Amateur" understood today in modern English means non-professional, i.e. being not paid (as employee) to work in a particular field. So putting the common acceptance of this word to a person from 400 years ago earning his living by offering legal advice (jurist, legal counsellor), or arguing in court (attorney or lawyer) who happened to have great accomplishments in mathematics should not feel belittling, not at all. OTOH, it is unfair to call just Fermat that way, if any of his other contemporaries did not make a living from studying or teaching mathematics.

In modern times, strictly related to academic studies/careers, a person earning a PhD in mathematics, but making a living from investments in the stock exchange or as an accountan should be called until death a mathematician. He cannot "earn" the adjective "amateur" next to his "mathematician", if all of a sudden decided spending less time with family and more with mathematics research as an unpaid/unprofessional activity.

I have a degree in physics as hundreds of thiusands of people on the planet, but did not go to PhD, therefore I cannot call myself a physicist, for I am not expert in any area of physics. If someone called me "amateur physicist", I would still reply: "hold your horses, I am not even that. I am however "an amateur of physics" (otherwise I would not be here writing this stuff). Intriciacies of language, but no negative connotation anywhere.

PS. I am an amateur linguist and an amateur of liguistics, I am an amateur of meteorology and climatology.

 

[coquelicot]

"Amateur" understood today in modern English means non-professional, i.e. being not paid (as employee) to work in a particular field. So putting the common acceptance of this word to a person from 400 years ago earning his living by offering legal advice (jurist, legal counsellor), or arguing in court (attorney or lawyer) who happened to have great accomplishments in mathematics should not feel belittling, not at all. OTOH, it is unfair to call just Fermat that way, if any of his other contemporaries did not make a living from studying or teaching mathematics.

In modern times, strictly related to academic studies/careers, a person earning a PhD in mathematics, but making a living from investments in the stock exchange or as an accountan should be called until death a mathematician. He cannot "earn" the adjective "amateur" next to his "mathematician", if all of a sudden decided spending less time with family and more with mathematics research as an unpaid/unprofessional activity.

I have a degree in physics as hundreds of thiusands of people on the planet, but did not go to PhD, therefore I cannot call myself a physicist, for I am not expert in any area of physics. If someone called me "amateur physicist", I would still reply: "hold your horses, I am not even that. I am however "an amateur of physics" (otherwise I would not be here writing this stuff). Intriciacies of language, but no negative connotation anywhere.

PS. I am an amateur linguist and an amateur of liguistics, I am an amateur of meteorology and climatology.

I am an amateur of physics and linguistics too. I don't feel belittled about that because this is the suitable term with respect to my knowledge and my achievements in these domains. I don't know if I would insist in being called a "professional mathematician", but I definitely don't think I am an amateur in this domain, unless it is dully precised that this is in the sense of "aimer", to love the mathematics. Anyway, you say that a doctor cannot be called "amateur", and this proves that this term is not interchangeable with "not paid", as many asserted above. One has to be careful when using the definitions from a dictionary; the semantic field of the words is much more involved than it may seem.