You should not choose to do mathematics if you want to make money; your salary as a mathematician will never correspond to the amount of time and energy invested in your work.

… mathematicians are much more concerned for example with the structure behind something or with the whole edifice. Mathematicians are not really puzzlers. Those who really solve mathematical puzzles are the physicists. If you like to solve mathematical puzzles, you should not study mathematics but physics!

A mathematician starts with a problem and creates a solution; a consultant starts by offering a solution and creates a problem.

A mathematician starts with a problem and creates a solution; a consultant starts by offering a “solution” and creates a problem.

... Eventually, I became a tenure-track professor at , which had a combined math department with .
And then I made a big change. I quit my job and went to work as a quant for , a leading hedge fund. In leaving academia for finance, I carried mathematics from abstract theory into practice. The operations we performed on numbers translated into trillions of dollars sloshing from one account to another. At first I was excited and amazed by working in this new laboratory, the global economy. But in the autumn of 2008, after I'd been there for a bit more than a year, it came crashing down
The crash made it all too clear that mathematics, once my refuge, was not only deeply entangled in the also fueling many of them. The housing crisis, the collapse of major financial institutions, the rise of unemployment—all had been aided and abetted by mathematicians wielding magic formulas.

Comparatively few engineers are good mathematicians; and... it is fortunate that such is the case; for nature rarely combines high mathematical talent, with that practical tact, and observation of outward things, so essential to a successful engineer.
There have been... brilliant exceptions; but they are very rare. But few even of those who have been tolerable mathematicians when young, can, as they advance in years, and become engaged in business, spare the time necessary for retaining such accomplishments.

Mathematicians are extremely lucky, they are paid for doing what they would by nature have to do anyway. One should not have a non-teaching fellowship too long, there comes a time when one must make a contribution to society. Great mathematics is achieved by solving difficult problems not by fabricating elaborate theories in search of a problem.

Mathematicians are there to find the constraints and to eliminate those things that aren't constraints... I know this will surprise many of you, but they are useful!

Our future rates of gain will fall far short of those achieved in the past. Berkshire's capital base is now simply too large to allow us to earn truly outsized returns. If you believe otherwise, you should consider a career in sales but avoid one in mathematics (bearing in mind that there are really only three kinds of people in the world: those who can count and those who can't).

A mathematician is not a man who can readily manipulate figures; often he cannot. He is not even a man who can readily perform the transformation of equations by the use of calculus. He is primarily an individual who is skilled in the use of symbolic logic on a high plane, and especially he is a man of intuitive judgment in the choice of the manipulative processes he employs.

I believe that this danger of the mathematician making mistakes is an unavoidable corollary of his power of sometimes hitting upon an entirely new method. This seems to be confirmed by the well known fact that the most reliable people will not usually hit upon really new methods.

Would you like to know, for instance, to what extent higher mathematics is used in our two great industries? Well, it is never used at all. Having found this to be the case in my own experience, after quite a long career, I wondered whether I was not an exception; so I made enquiries, and I found that it was a general rule that neither engineers nor managers used higher mathematics in carrying out their duties. We must, of course, learn mathematics that goes without saying but the question is how much must we learn? Up to the present this point has nearly always been decided simply by professors, but it seems to me to be a question in which professors do not count very much, and in which they count less as they become more learned and more devoted to their work. They would like to pass on all their scientific knowledge and they find that their pupils always leave them too soon.

A mathematician is bound to be horrified by my mathematical comments, since he has always been trained to avoid indulging in thoughts and doubts of the kind I develop. He has learned to regard them as something contemptible and […] he has acquired a revulsion from them as infantile. That is to say, I trot out all the problems that a child learning arithmetic, etc., finds difficult, the problems that education represses without solving. I say to those repressed doubts: you are quite correct, go on asking, demand clarification!

Trying to solve real-world problems, researchers often discover that the tools they need were developed years, decades or even centuries earlier by mathematicians with no prospect of, or care for, applicability.