## Paul Dirac on mathematics and progress in physics

The steady progress of physics requires for its theoretical formulation a mathematics that gets continually more advanced. This is only natural and to be expected. What, however, was not expected by the scientific workers of the last century was the particular form that the line of advancement of the mathematics would take, namely, it was expected that the mathematics would get more and more complicated, but would rest on a permanent basis of axioms and definitions, while actually the modem physical developments have required a mathematics that continually shifts its foundations and gets more abstract. Non-euclidean geometry and non-commutative algebra, which were at one time considered to be purely fictions of the mind and pastimes for logical thinkers, have now been found to be very necessary for the description of general facts of the physical world. It seems likely that this process of increasing abstraction will continue in the future and that advance in physics is to be associated with a continual modification and generalisation of the axioms at the base of the mathematics rather than with a logical development of any one mathematical scheme on a fixed foundation.

dirac diracing it up

"Quantised Singularities in the Electromagnetic Field", Dirac 1931, proceedings of the royal society A

I do believe Dirac was making a valid point here.

**Addendum, September 10, 2014**

I feel compelled to make an additional comment/clarification here. The statement “dirac diracing it up” is not mine nor do I agree with it, either in content or tone. It seems to me in some sense derogatory. But when reblogging posts I rarely remove comments others have appended, not without very good reason (which to me is not simply because I disagree with a remark.)

Let it be known by all that Paul Dirac was one of the great theoretical physicists of the 20th century. He made significant contributions to the early development of both quantum mechanics and quantum electrodynamics and shared the Nobel Prize in Physics for 1933 with Erwin Schrödinger “for the discovery of new productive forms of atomic theory”. He did work that forms the basis of modern attempts to reconcile general relativity with quantum mechanics. He was also a gifted mathematician who was the Lucasian Professor of Mathematics at the University of Cambridge.

I have good reason to suspect that the individual who actually made the remark noted above has come nowhere close to any of these achievements. I personally find the remark disrespectful to the memory of one who was an important contributor to the development of both modern mathematics and physics.

**Antonino Zichichi** (born 1929), an Italian physicist who has worked in the field of nuclear physics [in ETTORE MAJORANA: GENIUS AND MYSTERY, p.24 found online at www.ccsem.infn.it/em/EM_genius_and_mystery.pdf] This is a fascinating, if somewhat technical, account of the history of the development of a number of pivotal ideas in early quantum mechanics.