Mathematical Framework Quotes

I accept no principles of physics which are not also accepted in mathematics.

One of the strangest features of string theory is that it requires more than the three spatial dimensions that we see directly in the world around us. That sounds like science fiction, but it is an indisputable outcome of the mathematics of string theory.

Well, gauge theory is very fundamental to our understanding of physical forces these days. But they are also dependent on a mathematical idea, which has been around for longer than gauge theory has.

In every department of physical science there is only so much science, properly so-called, as there is mathematics.

I assert that, in any particular natural science, one encounters genuine scientific substance only to the extent that mathematics is present.

The introduction of numbers as coordinates by reference to the particular division scheme of the open one-dimensional continuum is an act of violence whose only practical vindication is the special calculatory manageability of the ordinary number continuum with its four basic operations.

It is however pretty evident, on general principles, that in devising for mathematical truths a new form in which to record and throw themselves out for actual use, views are likely to be induced, which should again react on the more theoretical phase of the subject.

For hundreds of pages the closely-reasoned arguments unroll, axioms and theorems interlock. And what remains with us in the end? A general sense that the world can be expressed in closely-reasoned arguments, in interlocking axioms and theorems.

The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena.

The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms.

The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.

The basic theory in twistor theory is not to add extra dimensions.

We have elected to put our money and faith in a mathematical framework that is free of politics and human error.

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

The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena. The verbal interpretation, on the other hand - i.e., the metaphysics of quantum theory - is on far less solid ground. In fact, in more than forty years physicists have not been able to provide a clear metaphysical model.

Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.

In this metaphor we actually have a picture of the computational universe, a metaphor which I hope to make scientifically precise as part of a research program.