Paul Dirac Quotes

How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.

The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.

The advancement and perfection of mathematics are intimately connected with the prosperity of the State.

Math research is more like a marathon.

On the basis of my historical experience, I fully believe that mathematics of the 25th century will be as different from that of today as the latter is from that of the 16th century.

If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.

People who wish to analyze nature without using mathematics must settle for a reduced understanding.

With an absurd oversimplification, the "invention" of calculus [method in mathematics] is sometimes ascribed to two men, Newton and Leibniz.

With an absurd oversimplification, the 'invention' of the calculus is sometimes ascribed to two men, Newton and Leibniz. In reality, the calculus is the product of a long evolution that was neither initiated nor terminated by Newton and Leibniz, but in which both played a decisive part.

I am persuaded that this method [for calculating the volume of a sphere] will be of no little service to mathematics. For I foresee that once it is understood and established, it will be used to discover other theorems which have not yet occurred to me, by other mathematicians, now living or yet unborn.

I'm inspired by everything, really. I'm inspired by locations and travel, I'm inspired by art and music, I'm inspired by people. When my curiosity peaks and I want to know everything about the subject, I want to know how I can get more deeply involved.

The advance and perfecting of mathematics are closely joined to the prosperity of the nation.

The people I admire most are those who are sensitive and want to create something or discover something, and do not see life in terms of power.

I learned what I could do with my voice on stages and because of the people that I was around. It wasn't me sitting in a room by myself. I didn't know what I was doing. I was figuring it out on the fly.

I thought I pretty much knew Johnny Cash's life. But one of my personal discoveries was how little we know about any of these people.

Some like to believe it's the book that chooses the person.

What I love about music, when you can look at something and be like, "Wow, what's this all about?" You can't really picture what these people look like - is it one guy, or a band making music in a garage?

The originator of a new concept...finds, as a rule, that it is much more difficult to find out why other people do not understand him, than it was to discover the new truth.

That was the wonderful thing about Ramanujan. He discovered so much, and yet he left so much more in his garden for other people to discover.

Wonder is very important, because if we never wondered, we would never get to the point of asking questions. Yet wonder may lead people to write poetry or to paint pictures or to pray, as well as to ask the kinds of questions about the world and themselves that can be answered by science.

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.

I enjoy traveling and recording far-away places and people with my camera. But I also find it wonderfully rewarding to see what I can discover outside my own window. You only need to study the scene with the eyes of a photographer.

And as for Mixed Mathematics, I may only make this prediction, that there cannot fail to be more kinds of them, as nature grows further disclosed.

We still don't understand how the big bang and evolving all the way to the human species and so on. So all of this is going to be a very, very exciting to the new people.

We’re taught to do things the right way. But if you want to discover something that other people haven’t, you need to do things the wrong way. Initiate a failure by doing something that’s very silly, unthinkable, naughty, dangerous. Watching why that fails can take you on a completely different path. It’s exciting, actually. To me, solving problems is a bit like a drug. You’re on it, and you can’t get off.