Paul Dirac Quotes

I consider that I understand an equation when I can predict the properties of its solutions, without actually solving it.

A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data.

God used beautiful mathematics in creating the world.

I do not see how a man can work on the frontiers of physics and write poetry at the same time. They are in opposition. In science you want to say something that nobody knew before, in words which everyone can understand. In poetry you are bound to say ... something that everyone knows already in words that nobody can understand. Commenting to him about the poetry J. Robert Oppenheimer wrote.

Pick a flower on Earth and you move the farthest star.

It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress.

Living is worthwhile if one can contribute in some small way to this endless chain of progress.

If there is a God, he's a great mathematician.

When [Erwin Schrödinger] went to the Solvay conferences in Brussels, he would walk from the station to the hotel where the delegates stayed, carrying all his luggage in a rucksack and looking so like a tramp that it needed a great deal of argument at the reception desk before he could claim a room.

If we are honest - and scientists have to be - we must admit that religion is a jumble of false assertions, with no basis in reality.

The measure of greatness in a scientific idea is the extent to which it stimulates thought and opens up new lines of research.

It is more important to have beauty in one's equations than to have them fit experiment.

What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating.

One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.

Scientific progress is measured in units of courage, not intelligence.

A physical law must possess mathematical beauty.

I found the best ideas usually came, not when one was actively striving for them, but when one was in a more relaxed state… I used to take long solitary walks on Sundays, during which I tended to review the current situation in a leisurely way. Such occasions often proved fruitful, even though (or perhaps, because) the primary purpose of the walk was relaxation and not research.

The aim of science is to make difficult things understandable in a simpler way; the aim of poetry is to state simple things in an incomprehensible way. The two are incompatible.

Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.

If you are receptive and humble, mathematics will lead you by the hand. Again and again, when I have been at a loss how to proceed, I have just had to wait until I have felt the mathematics led me by the hand. It has led me along an unexpected path, a path where new vistas open up, a path leading to new territory, where one can set up a base of operations, from which one can survey the surroundings and plan future progress.

It was not until some weeks later that I realized there is no need to restrict oneself to 2 by 2 matrices. One could go on to 4 by 4 matrices, and the problem is then easily soluable. In retrospect, it seems strange that one can be so much held up over such an elementary point. The resulting wave equation for the electron turned out to be very successful. It led to correct values for the spin and the magnetic moment. This was quite unexpected. The work all followed from a study of pretty mathematics, without any thought being given to these physical properties of the electron.

The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty. He should take simplicity into consideration in a subordinate way to beauty ... It often happens that the requirements of simplicity and beauty are the same, but where they clash, the latter must take precedence.

The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.

A good deal of my research in physics has consisted in not setting out to solve some particular problem, but simply examining mathematical equations of a kind that physicists use and trying to fit them together in an interesting way, regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later to have an application. Then one has good luck. At age 78.

Hopes are always accompanied by fears, and, in scientific research, the fears are liable to become dominant.

There are always more people who prefer to speak than to listen.

A great deal of my work is just playing with equations and seeing what they give.

A termination of one's life is necessary in the scheme of things to provide a logical reason for unselfishness. . . . The fact that there is an end to one's life compels one to take an interest in things that will continue to live after one is dead.

The only object of theoretical physics is to calculate results that can be compared with experiment... it is quite unnecessary that any satisfactory description of the whole course of the phenomena should be given.

I think it is a peculiarity of myself that I like to play about with equations, just looking for beautiful mathematical relations which maybe don't have any physical meaning at all. Sometimes they do. At age 60.

In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it is the exact opposite.

I should like to suggest to you that the cause of all the economic troubles is that we have an economic system which tries to maintain an equality of value between two things, which it would be better to recognise from the beginning as of unequal value.

There is in my opinion a great similarity between the problems provided by the mysterious behavior of the atom and those provided by the present economic paradoxes confronting the world.

Renormalization is just a stop-gap procedure. There must be some fundamental change in our ideas, probably a change just as fundamental as the passage from Bohr's orbit theory to quantum mechanics. When you get a number turning out to be infinite which ought to be finite, you should admit that there is something wrong with your equations, and not hope that you can get a good theory just by doctoring up that number.

I do not see how a man can work on the frontiers of physics and write poetry at the same time. They are in opposition.

As time goes on, it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen.

The methods of theoretical physics should be applicable to all those branches of thought in which the essential features are expressible with numbers.

I learnt to distrust all physical concepts as the basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting interesting mathematics.

Theoretical physicists accept the need for mathematical beauty as an act of faith... For example, the main reason why the theory of relativity is so universally accepted is its mathematical beauty.

It is more important to have beauty in one's equations than to have them fit experiment... It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory.

Well, in the first place, it leads to great anxiety as to whether it's going to be correct or not ... I expect that's the dominating feeling. It gets to be rather a fever... At age 60, when asked about his feelings on discovering the Dirac equation.

A book on the new physics, if not purely descriptive of experimental work, must essentially be mathematical.

It is quite clear that beauty does depend on one's culture and upbringing for certain kinds of beauty, pictures, literature, poetry and so on...But mathematical beauty is of a rather different kind. I should say perhaps it is of a completely different kind and transcends these personal factors. It is the same in all countries and at all periods of time.

Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future... If someone can hit on the right lines along which to make this development, it may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply them... My own belief is that this is a more likely line of progress than trying to guess at physical pictures.

The physicist, in his study of natural phenomena, has two methods of making progress: (1) the method of experiment and observation, and (2) the method of mathematical reasoning. The former is just the collection of selected data; the latter enables one to infer results about experiments that have not been performed. There is no logical reason why the second method should be possible at all, but one has found in practice that it does work and meets with reasonable success.

Quantum mechanics has explained all of chemistry and most of physics.

I admired Bohr very much. We had long talks together, long talks in which Bohr did practically all the talking.

I think it is the general rule that the originator of a new idea is not the most suitable person to develop it, because his fears of something going wrong are really too strong... At age 69.

No. I had successfully solved the difficulty of finding a description of the electron which was consistent with both relativity and quantum mechanics. Of course, when you solve one difficulty, other new difficulties arise. You then try to sove them. You can never solve all difficulties at once.