This paper is about a proposed "New Mathematics" (NM) and its potential in science. The NM is proposed as an amalgamation of mathematics with the "SP System" -- meaning the "SP Theory of Intelligence" and its realisation in the "SP Computer Model" -- both now and as they may be developed in the future. A key part of the structure and workings of the SP System and the proposed NM is the compression of information via the matching and unification of patterns. A preamble includes: brief notes about solipsism in science; an introduction to the SP System with pointers to where fuller information may be found; an outline of how the NM may be developed; and a discussion of several aspects of information compression; In sections that follow: 1) A summary of some of the potential benefits of the NM in science, including: adding an AI dimension to mathematics; facilitating the integration of mathematics, logic, and computing; development of the NM as a "universal framework for the representation and processing of diverse kinds of knowledge" (UFK); a new perspective on statistics; and new concepts of proof, theorem, and so on. 2) A discussion of mathematical and non-mathematical means of representing and processing scientific knowledge. 3) A discussion of how the NM may help overcome the known problems with infinity in physics. 4) how the NM may help in modelling of the quantum mechanics concepts of 'superposition' and 'qubits' via analogies with concepts in stochastic computational linguistics and ordinary mathematics. 5) Likewise, how the NM may prove useful in modelling the quantum mechanics concept of 'nonlocality' and 'entanglement' via an analogy with the phenomenon of discontinuous dependencies in natural languages. 6) How the NM, with the SP System, provides alternative, and arguably more plausible, interpretations of such concepts as the 'Mathematical Universe Hypothesis' and the 'Many Worlds' interpretation of quantum mechanics, as described in Max Tegmark's book "Our Mathematical Universe". Two appendices including: A) a tentative 'tsunami' interpretation of the concept of 'wave-particle duality' in quantum mechanics; and B) A discussion of the possibility of interference fringes with real tsunamis.