I do not think that it is scientifically sound & reasonable to generalize the results of a certain single research on every place & on every time. We have to take into account other factors that play role in reaching top positions in a society such as politics, affiliations, connections, opportunities, attitudes, and -sometimes- color, belonging to certain family or particular region, and membership of a "secretive" lodge.

According to research conducted by scientists from the American Vanderbilt University top mathematicians are quite successful in life - have excellent career I a sense of personal satisfaction. The study, that was continuation of the studies conducted in 1970s, encompassed a sample of 1037 young men and women 613 and period of 13 years, indicates that these mathematical geniuses obtained high positions in society and statistically succeeded beyond all expectations .

No, I am not agree with this thesis. You have to make difference between society, in general, and academic society

Plants are shaped by cultivation and men by education. .. We are born weak, we need strength; we are born totally unprovided, we need aid; we are born stupid, we need judgment. Everything we do not have at our birth and which we need when we are grown is given us by education.

(Jean Jacques Rousseau, Emile, On Philosophy of Education)

Dear Darko,

Lots of Mathematicians have problems to interact with society. They are able to study concepts that noone will know what it can be good for. Mathematics is a language and usually people tend to exclude others that would not speak like them, like adolescents do.

Though Success cannot be attributed only to Mathematics, but surely it is essential

With the advent of computing devices, complex problems get easily solved. Naturally it is unnecessary for everyone to understand all the computing, which can take place in microseconds without our noticing. But it means that anyone who refuses to acknowledge the role of mathematics will see the changing technosphere as something strange and in the worst case as something irrational or even frightening. A very good way to understand and come to terms with an important aspect of modern life our ever-growing dependence on interpreting digital data is to have a basic knowledge of mathematics. 

http://ercim-news.ercim.eu/en73/special/introduction-to-the-special-theme-maths-for-everyday-life

No, the good results in mathematics are not only essential in reaching higher positions in society/academics/other place.

Reaching to a higher positions requires a combination of skills along with competence in maths.

Along with this, behavioural and interpersonal skills are also essential.

I do not think that it is scientifically sound & reasonable to generalize the results of a certain single research on every place & on every time. We have to take into account other factors that play role in reaching top positions in a society such as politics, affiliations, connections, opportunities, attitudes, and -sometimes- color, belonging to certain family or particular region, and membership of a "secretive" lodge.

The results of that survey may be valid in the U.S.A., a rich society highly rewarding performance...but this may not happen in other developing (and corrupted) societies, which do not promote genuine values...besides that, I agree with dr. Magalhaes that lots of Mathematicians are reluctant or have problems to interact with society and they may have a brilliant academic and scientific life and achievements, but an almost inexistent private and social life...

Dear Darko,

As a rule, the great mathematicians are closed people who often become antisocial. Look at the Perelman as an example: 

https://ru.wikipedia.org/wiki/%D0%9F%D0%B5%D1%80%D0%B5%D0%BB%D1%8C%D0%BC%D0%B0%D0%BD,_%D0%93%D1%80%D0%B8%D0%B3%D0%BE%D1%80%D0%B8%D0%B9_%D0%AF%D0%BA%D0%BE%D0%B2%D0%BB%D0%B5%D0%B2%D0%B8%D1%87

Very good elaboration dear @Eraldo! Mathematical intelligence is necessary but not sufficient condition for success! Someone once said that for the great success, the synergy of this three things is needed, namely fate, luck and coincidence!

Dear @Darko, please share a link for the research of Vanderbilt University that You have mentioned earlier. Thanks!

I agree with dr. Eraldo that mathematical (logical) intelligence could be a good precondition (basis) for further career success... and that an autonomous approach to mathematics is crucial in the early childhood years.

David Lubinski, professor of psychology and human development at Peabody, led the study, which tracked 300 gifted children from age 13 until age 38, logging their accomplishments in academia, business, culture, health care, science and technology. The link to the publication can be found at:

https://my.vanderbilt.edu/smpy/files/2013/02/Kell-Lubinski-Benbow-20132.pdf

Dear Darko,

I think the question of mathematics is related more to those professions that require this profile. I agree that the analytical thought and being organized can help, but is not enough.

I think que anyone of any area, struggling and smart and know to communicate, has great chances to occupy good positions.

(but it's just my opinion without scientific basis).

Best wishes,

Vanessa

Yes I do agree with the statnent under certain conditions. With justice and avoid connection most people who are good mathematics are good to grasb position successfully. 

Thanks @Darko for the paper. Actually, it is about longitudinal research on Who Rises to the Top? Early Indicators." Although it would be difficult to quantify participants’ collective accomplishments in a single number, by any standard, it appears that many individuals identifiable by age 13 as having profound mathematical and verbal reasoning ability develop into truly outstanding contributors in their respective fields." So, it is not just a mathematics!

“I had a feeling once about Mathematics - that I saw it all. Depth beyond depth was revealed to me - the Byss and Abyss. I saw - as one might see the transit of Venus or even the Lord Mayor's Show - a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go.”

Winston S. Churchill, My Early Life, 1874-1904

Dear: All

Basicly, I think that the one who succeed in mathematics has an expert in a quantitative  ............... ;)

"... In Sarsi I seem to discern the firm belief that in philosophizing one must support oneself upon the opinion of some celebrated author, as if our minds ought to remain completely sterile and barren unless wedded to the reasoning of some other person. Possibly he thinks that philosophy is a book of fiction by some writer, like the Iliad or Orlando Furioso, productions in which the least important thing is whether what is written there is true. Well, Sarsi, that is not how matters stand. Philosophy is written in this grand book, the universe, which stands continually open to our [p.238] gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth..."

GALILEO GALILEI

https://www.princeton.edu/~hos/h291/assayer.htm

Not necessary at all dear Darko.

Roger Bacon  wrote in 1267 that "mathematics is the gate (door) and key to the sciences".

"Each progress in mathematics is based on the discovery of stronger tools and easier methods, which at the time makes it easier to understand earlier methods.By making these stronger tools and easier methods his own, it is possible for the individual researcher to orientate himself in the different branches of mathematics.The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena."

David Hilbert (1900)

Neglect of mathematics works injury to all knowledge, since one who is ignorant of it cannot know the other sciences of the things of this world. And what is worst, those who are thus ignorant are unable to perceive their own ignorance and so do not seek a remedy. Roger Bacon

Dear: All

I think all your suggestion is true. I endorese that......

It is depend on how competency that they have.... The more competence they have...the more opportunity they get........... 

Have a nice week end guys......... ;)

Dear Arar Ivica,

No doubt, mathematics is the key to the sciences. What about other fields?

Dear Eraldo Banovac,

Everything turns into mathematics, because one is using other skills/competences also.

Dear Hengky S H,

Yes, multiple competencies.

Dear Darko Pavlović,

Yes, successive developments in mathematics -- makes it more easier.

--- Can't we have inclusive set of competencies to reach higher? Should be!

If I were again beginning my studies, I would follow the advice of Plato and start with mathematics.

Galileo Galilei

Life is good for only two things, discovering mathematics and teaching mathematics

 Siméon Poisson

Dear Darko Pavlović, Yes, evryone in one way or other discovers mathematics. But every one can't teach mathematics.

Those use other skills with mathematics are suitable cases to reach to higher positions.

A mathematician is a blind man in a dark room looking for a black cat which isn't there

Charles R. Darwin

Mathematics has its importance... 

Quite a good insight into Mathematical applications into various disciplines and usage.

- Mathematics and Human Daily activities

- Mathematics and Personality Development

- Mathematics and Reasoning

- Mathematics as a tool for other subjects

- Mathematics as a universal language.

http://pelagiaresearchlibrary.com/advances-in-applied-science/vol2-iss5/AASR-2011-2-5-449-456.pdf

In my school, the brightest boys did math and physics, the less bright did physics and chemistry, and the least bright did biology. I wanted to do math and physics, but my father made me do chemistry because he thought there would be no jobs for mathematicians.

Stephen Hawking

Dear All

I see what you’re discussing,. I was thinking of it this way.that success sometimes it's depend on luck as well..!

In a lot of scientists, the ratio of wonder to skepticism declines in time. That may be connected with the fact that in some fields—mathematics, physics, some others—the great discoveries are almost entirely made by youngsters.

Carl Sagan

Getting higher positions requires a balanced personality, not a unique one. Unique may create wonders in its own field, not in public higher positions.

What about Khan Academy? They shall be willing to help with your projecta too.

I am agree with Dear @Subhash, the balance of personality is essential, and I add with the effort that would help on getting the success.

Gradually, at various points in our childhoods, we discover different forms of conviction. There’s the rock-hard certainty of personal experience (“I put my finger in the fire and it hurt,”), which is probably the earliest kind we learn. Then there’s the logically convincing, which we probably come to first through maths, in the context of Pythagoras’s theorem or something similar, and which, if we first encounter it at exactly the right moment, bursts on our minds like sunrise with the whole universe playing a great chord of C Major.

Philip Pullman

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. “Immortality” may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

G. H. Hardy

I do agree dear @Eraldo. Finding order in chaos is fine reading with good examples about. ""Does nature obey rules, and is it in any sense predictable?" This question is, in a sense, the motivation behind all of science, which can loosely be described as the search for pattern in the universe. So, does nature have any pattern and order beneath it? Despite the evidence of children (I have two!) the answer is essentially: "Yes". We will now have a look at the reasons for believing this, before we tackle the thorny issue of predicting the future...Chaotic motion really does exist both in nature and in mathematics. Why should this concern us? " Must read!

https://plus.maths.org/content/finding-order-chaos

"I've dealt with numbers all my life, of course, and after a while you begin to feel that each number has a personality of its own.  A twelve is very different from a thirteen, for example.  Twelve is upright, conscientious, intelligent, whereas thirteen is a loner, a shady character who won't think twice about breaking the law to get what he wants.  Eleven is tough, an outdoorsman who likes tramping through woods and scaling mountains; ten is rather simpleminded, a bland figure who always does what he's told; nine is deep and mystical, a Buddha of contemplation....  "

Paul Auster, The Music of Chance

"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."

John Louis von Neumann

"Twice two makes four seems to me simply a piece of insolence.  Twice two makes four is a pert coxcomb who stands with arms akimbo barring your path and spitting.  I admit that twice two makes four is an excellent thing, but if we are to give everything its due, twice two makes five is sometimes a very charming thing too." 

Fyodor M. Dostoevsky

Are best mathematicians think so about themselves?

Personally I think so. A philosopher is an equal foot with the mathematician. It suffice rigor in thought and whatever the domain

I think, the fate of a  philosopher may be the same as the mathematician -- for reaching higher positions in society.

Can a philosopher! 

"When in the 18th century Euler discovered those formulas which today still delight the mathematical phantasy, he seriously stated that his pencil was more clever than himself. This impression that mathematical structures can include a kind of self-determination concerns me at this time. ... Mathematics and Philosophy attack the world's problems in different ways. Only by their complementary action do they give the right direction."

 E. Kaehler

Mathematics, science, standing, full, unaltered, and have absolutely not true

But also socio-historical-cultural phenomenon seen, Mathematics A

Quasi-experimental science that is based on the needs of the life forms.

The mathematical proof are based on assumptions made by humans

Conditions are fallible and therefore mathematical certainty, the absolute sense, is negated.

In fact, what is the reason and how the concepts of mathematical knowledge, can appeal.

Mathematics is a human performance, a social phenomenon and a part of human culture

The IS. Mathematical objects like money, cards and invitations. . ., And mathematical sentences like

Law, and religion. . . , As contained in our social consciousness and therefore

Without humans, there is no mathematical

Existence of mathematical objects rather than the nature of the outer reef or spirit

Nor the intrinsic nature of such intellectual ideas. In fact, as

Reuben Hersh, mathematical philosopher argues that the rejection of the nature of the debate

Allocated to common mathematical ontology, a third type

You can select the most discussed sciences such as anthropology and community

Shnasyand. He says we are on a train or habit, the world of

Myangarym matter and mind. But these categories are inadequate, just as the four elements

Ancient Greek soil, water, fire and air is insufficient for new physics.

Hirsch believes that mathematical objects, social beings and existence

As a social phenomenon of the third kind.

Such as science, mathematics can be considered a fault and

Correction of errors caused by these advances. Mathematics

Science is not a hundred percent true, but unlike many areas of knowledge

Human knowledge is free from contradiction. We do not find any mathematical theory

Another theory is that the infringer. Euclidean geometry is still on going

(Albeit in a limited area of land), while the physics of Aristotle long ago

Is gone. Is this the result of a mathematical certainty and reality uncritically

Or just trying to justify those who have tried the knowledge free of inconsistencies

Shape?

Mathematics is not absolute reality and of course that is imposed on us. Vice versa,

We're the mathematical structures are in fact trying to adapt the world

To improve various aspects of the physical and social world in terms of the patterns of justification

Them. But how do the math so much, functionality and pure cases

Mathematics that were created long ago, in explaining the phenomena around us today to work

They come from? Hirsch says.

"Mathematics is a part of human history and culture of a physiological nature

We and our physical and biological environments originated. Math projects

In general, the reason the world is that we adapt our lungs atmosphere atmosphere

The matches. "

Mathematics in interactions within a community, and cultural and

Join the community. The community can gather you and me duo or community

Is a great man. According to research, archeology, linguistics, genetics and

Ethnology, counting both act as Ghazynhhay human thought and conversation

Have. Mathematics as a language is a cultural product. When human

Social life, the need to communicate with human beings, language conventions

Created and mathematics within the nascent human communities and the

Associated with the need to overcome the surroundings were formed. Purely mathematical rules

Social contracts within the community, and find a meaning to the words of Wittgenstein,

Question of the truth or falsity of a mathematical theorem where the problem arises, the

Review. Account numbers are usually normal rules of society, not the sellers.

Humanistic Mathematics, strives to comply with the terms of its structural rules

Physical, biological and cultural place. The Humanistic Mathematics, the pattern

Structural numbers, always 2 + 2 does not equal 4. Sometimes, this pattern

Structure may be a cup of milk when added to a cup of popcorn

We used to work in the other case, 1 + 1 does not equal 2, because Zrtha,

Two glasses of milk is absorbed and not sure it's less than two glasses.

This pattern may biology (breeding animals) to be applied,

There is probably more like 2 + 2 to 4 and 6. The typical calculations can

Knowing the price of a barrel of oil cost a trillion billion barrels account

Because the pattern of reserve accumulation are used which are declining

And the price is proportional to the demand goes up and never fixed.

In general,good result in their thesis alone won't help much. Reaching higher position depends upon individual's ability in other aspects of life apart from lab work. 

For example, even in interviews, the questions are mainly to know about the person and his attitude and not their research alone. 

"One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers."

Heinrich Hertz

Mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the actual world, but every possible world, must conform. Bertrand Russell

I think that those who have good results in mathematics have a certain sens of logical thinking, ordering, organization and mapping, with fast reasoning, so they could achieve their tasks more efficiently and more quickly. But to reach high positions added skills are needed from communication, social relation, scheduling, team work, etc...in societies managed throughout merit and proved expertise. In societies differently managed,  skills in mathematics or else are not needed to reach positions, may be more money, good relationships with influencing people, or hazard are more efficient means.

"The magical mathematics of music" -  Jeffrey Rosenthal

The astronomer Galileo Galilei observed in 1623 that the entire universe "is written in the language of mathematics"

https://plus.maths.org/content/os/issue35/features/rosenthal/index

Recent Happening on Maths

A maths problem that first appeared in a test for Singapore’s elite high school students has baffled Internet users around the world after it went viral, prompting a rush of attempts to solve it.

http://www.thehindu.com/todays-paper/tp-national/singapore-maths-problem-leaves-netizens-puzzled/article7103111.ece

“I see some parallels between the shifts of fashion in mathematics and in music. In music, the popular new styles of jazz and rock became fashionable a little earlier than the new mathematical styles of chaos and complexity theory. Jazz and rock were long despised by classical musicians, but have emerged as art-forms more accessible than classical music to a wide section of the public. Jazz and rock are no longer to be despised as passing fads. Neither are chaos and complexity theory. But still, classical music and classical mathematics are not dead. Mozart lives, and so does Euler. When the wheel of fashion turns once more, quantum mechanics and hard analysis will once again be in style.”

Freeman Dyson (Mathematician and Physicist)

“The uniform character of mathematics is the essence of science, for mathematics is the foundation of all exact scientific knowledge.” 

David Hilbert

"What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else. Roughly speaking, people know that it deals with numbers, figures, with relations, operations, and that its formal procedures involving axioms, proofs, lemmas, theorems have not changed since the time of Archimedes.”

Stan Ulam

“Find the number such that if the whole of it is added to one-seventh of it, the result will be nineteen.” 

The Ahmes Papyrus (Ancient Egyptian mathematics problem from c. 2200 BC)

Dear @Eraldo, my dear friend @James has nice thread on beauty of patterns in mathematics!

https://www.researchgate.net/post/Is_the_beauty_of_patterns_or_are_the_structures_in_patterns_the_most_important_source_of_mathematics

"The invention of logarithms came to the world as a bolt from the blue. No previous work had led up to it… It stands isolated, breaking in upon human thought abruptly, without borrowing from the work of other intellects or following known lines of mathematical thought.” 

John Moulton

David Hilbert was one of the mathematical greats of the 19th and 20th centuries.

“I didn’t work especially hard at mathematics at school, because I knew that’s what I’d be doing later.”

Today, mathematics and physics are still powerfully influenced by his work and his vision

"Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry."

David Hilbert

"Simple laws can very well describe complex structures. The miracle is not the complexity of our world, but the simplicity of the equations describing that complexity.”

Sander Bais

Regarding simplicity and beauty, I have found nice book about! "We usually associate a sense of elegance with art or fashion design, poetry or dance, but the idea of elegance is surprisingly important in science as well. The use of the term is most apparent in the "elegant proofs" of mathematics--which Bertrand Russell once described as "capable of a stern perfection such as only the greatest art can show"--but as Ian Glynn reveals in this fascinating new book, the idea of elegance is essential to scientists working in all fields. "

http://www.amazon.com/Elegance-Science-The-beauty-simplicity/dp/0199668817

Is mathematics an effective way to describe the world?

Mathematics has been called the language of the universe...

http://phys.org/news/2013-09-mathematics-effective-world.html

The 12 Mathematicians Who Unlocked The Modern World

Mathematics is an increasingly central part of our world and an immensely fascinating realm of thought...

http://www.businessinsider.com/12-classic-mathematicians

What exactly is mathematics ?

How Mathematicians Think

http://www.ams.org/notices/200711/tx071101496p.pdf

After so many fine contributions and quotes, how this one, the Einstein quote reflect to this thread ?

http://www.todayinsci.com/E/Einstein_Albert/EinsteinAlbert-Quotations.htm

Bertrand Russell argued that although mathematical truths were not analytic, they were nevertheless ‘logical’ truths. His argument depended on technical developments in logic and in mathematics.

http://documents.routledge-interactive.s3.amazonaws.com/9781138793934/AS/ReasonandExperience/Empiricism-on-the-limits-of-knowledge.pdf

Yes, Krishnan,

Mathematical truths are what these exactly are!

But, ----- may have logic!

Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them."

Jean Baptiste Joseph Fourier

 "Mathematics is the queen of science, and arithmetic the queen of mathematics."

Carl Friedrich Gauss

Level up your mathematics skills and become King of Maths!

Leonhard Euler King of Mathematics!

https://itunes.apple.com/gb/app/king-of-maths/id473904402?mt=8

http://francoisproject.weebly.com/

"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."

John von Neumann

Mathematics is used universally as an essential tool in many fields ---- including natural science, engineering, medicine, finance, the social sciences, --- may be many more.

 "Where there is matter, there is geometry."

Johannes Kepler

"Since the mathematicians have invaded the theory of relativity, I do not understand it myself any more."

Albert Einstein