Gottfried Wilhelm Leibniz (1646–1716), Theoria cum praxi.
We begin with some quotations which exemplify the philosophical underpinnings of this work.
Johannes Kepler (1571–1630), Astronomia Nova
It is very difficult to write mathematics books today. If one does not take pains with the fine points of theorems, explanations, proofs and corollaries, then it won’t be a mathematics book; but if one does these things, then the reading of it will be extremely boring.
Marvin Schechter, Operator Methods in Quantum Mechanics 5
The interaction between physics and mathematics has always played an important role. The physicist who does not have the latest mathematical knowledge available to him is at a distinct disadvantage. The mathematician who shies away from physical applications will most likely miss important insights and motivations.
Freeman Dyson (born in 1923), From the Preface to Elliott Lieb’s Selecta 6
In 1967 Lenard and I found a proof of the stability of matter. Our proof was so complicated and so unilluminating that it stimulated Lieb and Thirring to find the first decent proof. Why was our proof so bad and why was theirs so good? The reason is simple. Lenard and I began with mathematical tricks and hacked our way through a forest of inequalities without any physical understanding. Lieb and Thirring began with physical understanding and went on to find the appropriate mathematical language to make their understanding rigorous. Our proof was a dead end. Theirs was a gateway to the new world of ideas collected in this book.
Freeman Dyson (born in 1923), The Art in Quantum Field Theory
All through its history, quantum field theory has had two faces, one looking outward, the other looking inward. The outward face looks at nature and gives us numbers that we can calculate and compare with experiments. The inward face looks at mathematical concepts and searches for a consistent foundation on which to build the theory. The outward face shows us brilliantly successful theory, bringing order to the chaos of particle interactions, predicting experimental results with astonishing precision. The inward face shows us a deep mystery. After seventy years of searching, we have found no consistent mathematical basis for the theory. When we try to impose the rigorous standards of pure mathematics, the theory becomes undefined or inconsistent. From the point of view of a pure mathematician, the theory does not exist. This is the great unsolved paradox of quantum field theory.
To resolve the paradox, during the last twenty years, quantum field theorists have become string-theorists. String theory is a new version of quantum field theory, exploring the mathematical foundations more deeply and entering a new world of multidimensional geometry. String theory also brings gravitation into the picture, and thereby unifies quantum field theory with general relativity. String theory has already led to important advances in pure mathematics. It has not led to any physical predictions that can be tested by experiment. We do not know whether string theory is a true description of nature. All we know is that it is a rich treasure of new mathematics, with an enticing promise of new physics. During the coming century, string theory will be intensively developed, and, if we are lucky, tested by experiment.
Hermann Weyl (1885–1930), The Classical Groups
The stringent precision attainable for mathematical thought has led many authors to a mode of writing which must give the reader an impression of being shut up in a brightly illuminated cell where every detail sticks out with the same dazzling clarity, but without relief. I prefer the open landscape under a clear sky with its depth of perspective, where the wealth of sharply defined nearby details gradually fades away towards the horizon.
Steven Weinberg (born in 1933), On the occasion of a conference on the interrelations
between Mathematics and Physics in 1986
I am not able to learn any mathematics unless I can see some problem I am going to solve with mathematics, and I don’t understand how anyone can teach mathematics without having a battery of problems that the student is going to be inspired to want to solve and then see that he or she can use the tools for solving them.
Cheng Ning Yang (born in 1922), Mathematical Intelligencer
In 1983 I gave a talk on physics in Seoul, South Korea. I joked “There exist only two kinds of modern mathematics books: one which you cannot read beyond the first page and one which you cannot read beyond the first sentence. The Mathematical Intelligencer later reprinted this joke of mine. But I suspect many mathematicians themselves agree with me.
Sir Michael Atiyah (born in 1929), Mathematical Intelligencer
The more I have learned about physics, the more convinced I am that physics provides, in a sense, the deepest applications of mathematics. The mathematical problems that have been solved, or techniques that have arisen out of physics in the past, have been the lifeblood of mathematics. . . The really deep questions are still in the physical sciences. For the health of mathematics at its research level, I think it is very important to maintain that link as much as possible.
Richard Feynman (1918–1988), The Feynman Lectures in Physics
Finally, may I add that the main purpose of my teaching has not been to prepare you for some examination – it was not even to prepare you to serve industry or military. I wanted most to give you some appreciation of the wonderful world and the physicist’s way of looking at it, which, I believe, is a major part of the true culture of modern times.
and etc. It turned out that these notations actually are the Greek alphabets. There are 24 number alphabets in the Greek including: Alpha, Beta, Gamma, Delta, Epsilon, Zeta, Eta, Theta, IOTA, Kappa, Lambda, Mu, Nu, Xi, Omicron, Phi, Rho, Sigma, Tau, Upsilon, Pi, Chi, Psi and Omega. The Greek alphabet has been used to write the Greek language since the end of the 9th BC. This is an oldest written alphabet that still used today. The letters are also used for representing Greek figures (numbers), since the 2nd BC.
