Exactly what is considered to be a mathematician?

In summary, there are three individuals who are being discussed. The first person has a Ph.D. in mathematics and is currently a professor at MIT. The second person has a Bachelor's degree in mathematics and has published papers on simpler and more efficient methods for solving certain math problems. The third person has proven theorems and conjectures and has received the prestigious Field's Medal. Based on the discussion, it can be inferred that all three individuals can be considered mathematicians, with the third person being a particularly distinguished research mathematician."
  • #36
malawi_glenn said:
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.
 
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  • #37
coquelicot said:
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.
 
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  • #38
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.
 
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  • #39
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.
 
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  • #40
coquelicot said:
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.
 
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  • #41
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.
 
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  • #42
mathwonk said:
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.
 
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  • #43
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.

coquelicot said:
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.
 
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  • #44
russ_watters said:
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.

russ_watters said:
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.
 
  • #45
mathwonk said:
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.
 
  • #46
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?
 
  • #47
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?
 
  • #48
coquelicot said:
Do you believe it is possible that an amateur mathematician will solve, one day, the Riemann conjecture?
I belive that an amateur chef will ;)
 
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  • #49
"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.
 
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  • #50
dextercioby said:
"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.
 
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  • #51
the word amateur can be used as either a perjorative or as a compliment to someone not trained at the level of a professional.

In sports, Jim Thorpe lost his Olympic medals because he was paid to play baseball and that in the eyes of the Olympic committee made him a professional. Many years later, they reversed their decision after it was realized that the Olympic Committee had violated its own statute of limitations and that racism had played a key role in the case.

https://en.wikipedia.org/wiki/Jim_Thorpe

In many cases, when we see great accomplishment and the word amateur we don't think its an insult but a compliment as in the case of Fermat and others who treated math as a hobby but discovered great things.

Amateur astronomers are considered a great resource to the field of astronomy because they continually monitor the sky or look through reams of data from telescopes hoping to discover something that was missed.

To say they are amateurs in that context means simply its not their day job.

I could go on but feel that perhaps its time to close this thread and thank everyone for contributing here.

Jedi
 
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