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In an interview for the Yorkshire Television program Take the World from Another Point of View (1972), Richard Feynman said:

You see, I have had in my life a number of pleasant experiences. One of the earliest ones was when I was a kid I invented a problem for myself, the sum of the powers of the integers, and in trying to get the formula for it I developed a certain set of numbers, the formula for which I couldn’t get, and I discovered later that those were known as the Bernoulli numbers and discovered in 1739. So I was up to 1739 when I was about 14 you see. And then a little later I discovered something that I’d find out I just may have invented a thing which we now call operator calculus. That was invented in 1890-something. Gradually I was inventing things that came later and later.

But the moment when I began to realize that I was now working on something new was when I read about quantum electrodynamics at the time and I read a book, and I learned about it. For example, I read Dirac’s book, and he had these problems that nobody knew how to solve that were described there. I couldn’t understand the book very well because I really wasn’t up to it. But there in the last paragraph at the end of the book it said, “Some new ideas are here needed.” And so there I was. Some new ideas were needed? OK! So I started to think of new ideas.

What book does Richard Feynman refer to exactly?

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Dirac’s The Principles of Quantum Mechanics (1930) ends with the paragraph:

The present theory is very symmetrical between the electrons and protons. The symmetry is not mathematically perfect, as may easily be verified, when one takes interaction between the electrons into account. This cause, however, hardly appears to be sufficient, according to present ideas, to account for the very considerable observed differences between electrons and protons, in particular their different masses. Possibly the solution of this difficulty will be found in a better understanding of the nature of interaction.

Feynman’s “Some new ideas are here needed” seems like a reasonable paraphrase of the last sentence.

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    It's worth noting that this book is, to quote Wikipedia, a landmark in the history of science. It's still used today as one of the main textbooks on quantum mechanics, and was written by one of the creators of the field. So when Feynman said "Dirac's book", it's already quite likely that this was the one he meant.
    – Rand al'Thor ♦
    Oct 27, 2018 at 21:15
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    @Rand al'Thor: what is still used is the 4th edition, which is significantly changed from the 1st edition (as quantum mechanics has been developed quite a bit further), and very probably doesn't have the same last paragraph.
    – Peter Shor
    Nov 9, 2018 at 19:40
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    @PeterShor Indeed, the quote above is now in the penultimate chapter as "...The theory could be developed consistently with the hypothesis that all the laws of physics are symmetrical between positive and negative electric charge." However, the final paragraph now exists in the chapter on Quantum Electrodynamics: "It is to be hoped that with increasing knowledge a way will eventually be found for adapting the high-energy theories into a scheme based on equations of motion, and so unifying them with those of low-energy physics."
    – Polydynamical
    Sep 3 at 1:09

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