According to MathSciNet, Professor Terence Tao, a Fields Medalist (2006), publishes 289 papers in 21 years (1996 - 2017), i.e., nearly 14 papers per year. And Paul Erdős, a Wolf Prize winner (1983/84), published over 1,500 mathematical papers in his lifetime, i.e., average 24 papers per year. 

On the other hand, Professor Jesse Douglas, the first Fields Medalist (1936), published 43 papers (1921-1961) about one paper per year. Another Fields Medalist (1970), Professor Heisuke Hironaka published 52 papers (1957-2005), also about one paper per year.

Personally, I do not believe there is a good answer to your question: A good mathematician, how many articles could publish in a year?

I believe that the answer of your question shall depend on each individual. Maybe we can just say that a good mathematician is a mathematician who makes his/her best effort, with at least one good paper per year.

An interesting question! Waiting to see the expert's answers curiously..

According to MathSciNet, Professor Terence Tao, a Fields Medalist (2006), publishes 289 papers in 21 years (1996 - 2017), i.e., nearly 14 papers per year. And Paul Erdős, a Wolf Prize winner (1983/84), published over 1,500 mathematical papers in his lifetime, i.e., average 24 papers per year. 

On the other hand, Professor Jesse Douglas, the first Fields Medalist (1936), published 43 papers (1921-1961) about one paper per year. Another Fields Medalist (1970), Professor Heisuke Hironaka published 52 papers (1957-2005), also about one paper per year.

Personally, I do not believe there is a good answer to your question: A good mathematician, how many articles could publish in a year?

I believe that the answer of your question shall depend on each individual. Maybe we can just say that a good mathematician is a mathematician who makes his/her best effort, with at least one good paper per year.

In my opinion being a good mathematician does not depond on the number of published article in a year. A good mathematician reads, search and determine the important problem and gives the solution. Maybe someone publishes only one paper in a year, but he gives the solution of an important conjecture. I think it is more important than published more article. As I remember the Turkish academician Cahit Art published only 19 papers in his life But he made good jobs. 

In my own perspective, a good mathematician rank is not attained only based on the number of  publications but mainly based on the impacts and the contributions the researcher's works(research articles) have in the direct advancement of science and technology and in solving existing problems. 

The reason of my question is criticising the academical systems in the world. Mathematicians are compared with empirical sciences, like engineering, and there some pressures on them for writing more articles. From this point quality of paper is down and quantity of papers is up... Some scientists publish lots of redundant research (?) for only take academical title. Nobody read their papers. As Dr. Balkan told a mathematician do contributions to math and related areas. Much time I do not see this aim. I think to be a mathematician is not a "job", it is an "interest", "exploration", "adventure"...

On the other hand there are some different types of ranks for measure the academic performance like h-index, impact factor and etc. But I think for mathematician, especially theoretical mathematician, these ranks are not suitable. Because for refering a paper you may be read decades papers and it could take one or more years.   One my friend told me that, may be there will be references to my papers after years and years or after I died!

Finally I want to add other questions:

       How much time writing a good article get?

       What are the properties of quality articles?

Thank you very much.

Dear Inan:

For your first question: How much time writing a good article get? The answer again depends very much on each individual.

For instance, Leonhard Euler was one of the most eminent mathematicians of the 18th century, and is held to be one of the greatest in history. Euler had made many very important contributions in Mathematics, Sciences, Astronomy, Engineering as well as in Music. He is said to have produced on average one mathematical paper every week. Even his blindness later in life did not slow his prodigious output. Euler's complete works fill about 90 volumes. 

On the other hand, one of my teachers, Professor Tominosuke Otsuki, told me in 1980 while I was in Japan that he spent 10 years to solve a second order differential equation (now well-known as Otsuki equation, see e.g. [Utz, W. R.: A second order differential equation of T. Otsuki.  Proc. Amer. Math. Soc. 64 (1977), no. 2, 238–240]).

Sincerely,

B.-Y. Chen

Dear Prof.Chen thank you very much for your explanatory responses. Your opinions is very important for me and young geometers. We follow you with admiration... 

Best regards. 

Dear Dr Unal

This question is not measurable and it differs from one to another and depends on the area of research.

Dear Dr Unal

This question is not measurable and it differs from one to another and depends on the area of research.

Very thanks to Prof Chen for his inspirable answer and information.

I would like to add three comments:

First, Gauss' motto was Pauca sed matura.  Don't publish before a paper is ripe to publish.  He also stated that Dirichlet did not write many papers, but "jewels are not weighed on a grocery scale".

Second, Prof. Chen is a very productive writer himself with about 500 papers and more than 10 books, with many original and deep contributions to geometry.

Third, I find the article of William Thurston On Proof and Progress very inspiring. 

Dear Prof. Gielis thank you for your good answer.  I will read William Thurston's article, it looks like very useful for a mathematician. 

It focuses also on individual talent. 

One or two publications for a pure mathematician and up to 10 for applied types. I have played both games. My answer comes from personal experience.

I think it varies. Some good pure Mathematicians are prolific, and others are not. Think of the impact of John Nash's (relatively) few papers for instance! Detlef Gromoll is another such example: think about the impact of his "soul theorem" which is now taught in elementary Differential Geometry books. This is just to name a few. I agree with Dr. Bang-Yen Chen's answer, but wanted to add a few other concrete examples.

Regardless of the obvious differences from area to area, it would be interesting to see a distribution of publication rates(for years active) in pure and/or applied math. It would be nice if some some minimum standard of a "quality" peer-reviewed journal were used. Does anyone know of any such report?