Mathematicians are people who do real work as opposed to academic work. ie they work in industry on real problems.

A Mathematician who has ability to solve all kind of physics could be converted into mathematical equations and give a suitable solutions. Doctorate in mathematics is a honor awarded to mathematician who discovered novelty in his research.

Doctorate is a one-time achievement, "mathematician" refers rather to way of life and personality structure.

A Mathematician is anybody who has a deep love for mathematics. He is one who can leave eating, drinking, etc. for his love.

Even a bachelor's degree holder can be called a mathematician, if he /she possesses such a love for maths.

Can one give list of living Mathematicians?

Please visit the following link:

http://www.boydom.com/2012/11/30/top-10-indian-mathematicians-of-modern-times/.

You will be very inspired to read about some great still alive/dead mathematicians of India.

@ T.J. Moir : "Mathematicians are people who do real work as opposed to academic work. ie they work in industry on real problems."

So by your definition Prof. Andrew Wiles, Euclid, Descartes, Leibniz, Cayley, Hilbert, Galois and thousands more working at Oxford, Cambridge, MIT, Stanford etc are not Mathematicians.

Will all due respect, you only get to solve your 'real problems in industry' when these Mathematicians develop the tools you need. They might develop them working from home, in academia or anywhere else.

I totally agree with Shoaib Sir.

Many great mathematicians didn't get the opportunity to go to industries and apply their theories and knowledge. But today these theories have become so vital that Industries might shut down if they stop applying those theories proposed by them.

I think the original poster was asking what the difference between a mathematician with a Ph.D and one with a degree was (first degree). My answer is that those with the Ph.Ds do the fundamental research (ie academic) work whereas the others work on real problems in industry. Maybe that wasn't clear.

What about scholars who teach math at uni level sometimes in some places without a PhD and are not involved in research. Dont we grace them with the name of mathematicians?

The Scholars you talk of Patrick are normally working towards a Ph.D. If they don't have a Ph.D and don't engage in research then in a lot of countries they wouldn't be allowed to teach at all at University level. But this will depend on the institute and country of course. Another possibility is that they have years of senior experience from industry and that counts just as importantly as a Ph.D.

In my view, a degree is more like a union card than a validation that someone is a mathematician. A mathematician is anyone who has sufficient knowledge of mathematics to use math to provide solutions to problems in useful ways as a profession. Applied mathematicians often work with mathematical models for engineering, industry, and science. Mathematicians who work in pure math tend to work with logic, number or set theory or other issues that concern mathematics itself.

In my opinion, who educate student's different mathematical tools and approaches or uses mathematics for solving real world problems and/or develops/modify the existing mathematical tools and techniques are all mathematicians.

A mathematician is a machine for turning coffee into theorems. You can check in the Wikipedia that "altough widely attributed to Erdős, this actually originates with Alfréd Rényi, according to My Brain Is Open : The Mathematical Journeys of Paul Erdos (1998) by Bruce Schechter, p. 155."

In http://arxiv.org/pdf/math/0702396v1.pdf mathematician Terence Tao gives 21 diferent examples of activity considered to be good Mathematics. So I guess anybody doing one of those things might be considered a mathematician.

I agree with Fernando

A nice article by Tao, finally we can say all mathematics petitioner are mathematicians

Is a mathematician not someone who employs math as a logical and relatively unambiguous language to do their work, evaluate, and solve problems.

A much harder question would be "Who is called an Engineer". In the UK an Engineer is anybody from a plumber to a toilet cleaner besides the usual technical ones.

Yes Tainer, I am agree with f you. But the mathematical symbols and equations are not unambiguous, it is one of the scientific language for communication and expression.

I can hardly do better than to begin with G.H. Hardy’s and Galileo’s excellent descriptions:

“A mathematician, like a painter or poet, is a maker

of patterns. If his patterns are more permanent than

theirs, it is because they are made with ideas.”- G.H. Hardy

"The great book of nature can be read only by those who know the language in which it was written. And that language is mathematics.” -Galileo

It is not necessary that a doctorate in maths can be a mathematician

The passion of a mathematician is not just obtain a degree of doctorate it is much more than this

I think you want to talk about job. Yes; previous comments are true. But when we talk about job then it is become more harder to explain it. At many journal and site we see that mathematician is a good job(for example best job in 2009 by wall street journal) but when you receive a  Phd in math(more for pure) and then try to find a job then you see that it is very hard to find a job(more for academic). This is make me confused just like you. So who is a mathematician with the best job in the world? Maybe they called Bill Gates!!!

Anyone who has a tremendous knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.

Borrowing from Cambridge Dictionary: mathematician is someone who studies, teaches, or is an expert in mathematics.

Next, a PhD in mathematics is neither a necessary nor a sufficient condition for being a mathematician.

I suppose there may be cases where someone gets a doctorate in mathematics, and then switches line of work, never again to see such topic. Perhaps mistreated

during the career.