As a mathematician, I have the opinion that working in the field of mathematics in most of the cases is harder than working in the field of physics. The reason is that in the first case, you do not have any lab that can be used to prove your theory, and the level of abstraction is higher, while in the second, you can use the lab more often.

In addition, you do not need any physical theory to develop a new mathematical theory or model while in the field of physics you need, in most of the cases, a mathematical model to explain any new conclusion or development.

However, both disciplines are extremely important for the development of science.

Dear Esakki,

Your question is interesting.

There is no the general consensus on whether physics or math is a more respectable and which is "harder" intellectual field (''which one is tough job'').

As a mathematician, I know both can be very hard.

Roughly speaking, we can say in mathematics we have developed very difficult rigorous theory, but in physics we have prediction  and hypothesis   which are difficult to be understood

(Einstein's theory, gravitational wave, etc ...)  and perhaps important  for  understanding reality and applications..

I don't think one can draw conclusions about that in general.

There is a joke which says: 'Chemists think they're physicians; physicians think they're mathematicians; mathematicians think they're gods.'

We list some known mathematicians/physicists

1. Einstein 2. Gauss 3. Newton 4. Euler 5. Archimedes, Riemann,Galois, Hawking, Feynman, ...

See also  RG: Miodrag Mateljević asked a question in Human Activities:

Which mathematical results have important application?

As a mathematician, I have the opinion that working in the field of mathematics in most of the cases is harder than working in the field of physics. The reason is that in the first case, you do not have any lab that can be used to prove your theory, and the level of abstraction is higher, while in the second, you can use the lab more often.

In addition, you do not need any physical theory to develop a new mathematical theory or model while in the field of physics you need, in most of the cases, a mathematical model to explain any new conclusion or development.

However, both disciplines are extremely important for the development of science.

As a mathematician in the field of applied mathematics (Fluid Dynamics research), that is, my work is mix between mathematics and physics, I can say that:

We have two branches of mathematics: pure mathematics and applied mathematics, pure mathematics research can run away from the sense of applications, it's full theoretical work, but in applied mathematics you use mathematics as an accurate and powerful tool to find solutions for many difficult application problems in many fields.

In pure mathematics it's needn't to know physical meanings, but in applied mathematics some problems can't be solved away of physical meanings, because real problems are most complicated, so we frequently try to solve these complicated problems in graduated manner, beginning with  simple assumptions till we reach the general solution. Our research is also can be full theoretic away from  any labs. and we may resolve the same problem several times to reach to the acceptable solution that agrees with physical phenomena  and has acceptable real explanation. 

Best Regards

There is no the general consensus on  who are  greatest-mathematicians.

For example  we will  mention  M. R. Sexton    and  Gunther lists:

A1.  See http://listverse.com/2010/12/07/top-10-greatest-mathematicians/

Top 10 Greatest Mathematicians

according M. R. Sexton December 7, 2010, are

1. Euler 2. Gauss 3. Riemann 4. Euclid 5. Descartes 6. Turing 7. Bigollo 8. Newton and Leibniz 9. Wiels 10 Pythagoras

A2.According  Shea Gunther

May 22, 2013,

MNN.com > Tech > Research & Innovations,

5 brilliant mathematicians and their impact on the modern world

''We owe a great debt to scores of mathematicians who helped lay the foundation for our modern society with their discoveries. Here are some of the most important.''

According Shea Gunther   5 brilliant mathematicians   are 

Newton, Gauss,Neumann,Turing,  and   Mandelbrot.

A3.  We can  also mention some  mathematicians and   physicists  that come in my mind:

1. Einstein 2. Gauss 3. Newton 4. Euler 5. Archimedes, Riemann,Galois, Hawking, Feynman, Witten, Pythagoras, Nash,Euclid, Neumann, Cantor, Thales, Descartes,Turing,Leibniz,Perelman, Mandelbrot,Max Planck, Michael Faraday,James Clerk Maxwell, Erwin Schrodinger, etc ...

There were quite a few named mentioned and hard to disagree. For the tough job the list will be longer and I think the job of a physicist is tougher for many reasons.

If a mathematician proves something it  generally remains proven. In physics it is trial and error. People are fighting who is right or who was the first.

Additionally the wicked nature does not always follows equations....

Or brilliant mathematical ideas may get imperfect mapping to reality causing paradoxes. So we have some examples how tough this job can be:

Ludwig Boltzmann

Allegedly  depressed by the violent attacks made on his ideas by Ostwald

and Mach ended his life by hanging

Julius von Mayer

the first who postulated conservation of energy has been overwhelmed by contemporary celebrities and is little known. He was ridiculed for his idea for quite some time. He ended his life jumping out of the window

Stefan Marinov

Bulgarian physicist pursuing anti relativity ideas of the absolute reference frame

Killed himself, on July 15, 1997, jumping from the University of Graz Bibliotheque building in peculiar circumstances

Tough job indeed to be a physicist.

Dear colleagues,

Our discussion may  also be   related to the  question:

How important is mathematical proof in physics? (

see  Physics Stack Exchange).There is also   an interesting article published in 1960 by the physicist Eugene Wigner with the title

"The Unreasonable Effectiveness of Mathematics in the Natural Sciences". In the paper, Wigner observed that the mathematical structure of a physical theory often points the way to further advances in that theory and even to empirical predictions.

Wigner begins his paper with the belief, common among those familiar with mathematics, that mathematical concepts have applicability far beyond the context in which they were originally developed. Based on his experience, he says "it is important to point out that the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena." He then invokes the fundamental law of gravitation as an example. Originally used to model freely falling bodies on the surface of the earth, this law was extended on the basis of what Wigner terms "very scanty observations" to describe the motion of the planets, where it "has proved accurate beyond all reasonable expectations."

Another oft-cited example is Maxwell's equations, derived to model the elementary electrical and magnetic phenomena known as of the mid 19th century. These equations also describe radio waves, discovered by David Edward Hughes in 1879, around the time of James Clerk Maxwell's death.

We add that scientists with the LIGO collaboration claim they have once again detected gravitational waves — the ripples in space-time produced by objects moving throughout the Universe. Up until recently, gravitational waves were the last piece of Einstein’s theory that still hadn’t been proven. That’s because detecting these ripples is a super precise science.

Wigner sums up his argument by saying that "the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it.

" He concludes his paper with the same question with which he began:

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

Wigner's original paper has provoked and inspired many responses across a wide range of disciplines.

If a mathematical proof disagrees with experiment    it says that the physics is not well modeled by that math.

Experiments are extremely important for natural sciences, but not for mathematics.

We can not  verify the Euclid's parallel postulate  by experiments.

Lobachevsky showed that  the hyperbolic geometry has  a sound axiom system that fulfilled all Euclid's postulates but NOT the parallel one.

General Relativity is based on non-Euclidean, generally curved geometry, and there is non-Euclidean geometrical interpretations of gauge theories.

my students said physics