Mathematics as an academic discipline has become nearly incomprehensible to anyone except ultra specialists. This kind of abstraction is useless for practical engineering, which relies on the vector notation. In developing ECE I set out to use the simplest possible geometry compatible with the needs of field unification. Therefore I used standard differential geometry as found in any textbook. This was sufficient to show that the standard model is riddled with errors. The manifold in which the ECE theory is worked out is the Riemannian manifold of physics, and the torsion used in ECE is the Riemannian torsion, erroneously neglected in the Einstein field equation. This theory has been worked out in vector notation and has gone into its industrial phase. The mathematicians are well known to use exotic manifolds such as the Mobius strip manifold, Klein bottle manifold and so on, but there is little or no experimental evidence that these are of any relevance to physics – the philosophy of nature. The simplest possible (ECE) type field unification already poses a formidable computational problem when it comes to integrating the field equations. Recent work by Eckardt, Lindstrom and Lichtenberg has shown this clearly. Furthermore, ECE is based on an array of experimental data, for example www.et3m.net shows that there are devices already in existence and being manufactured and sold, based on spin connection resonance. The inverse Faraday effect led to the B(3) field back in 1992. Exotic manifolds are therefore useless for engineering because they are too abstract, and because there is no evidence that they are the manifolds of physics. The latter is thought to be the Riemannian manifold. I do not think that specialist mathematicians have any more inherent ability than physicists, chemists or engineers. The latter three subjects deal with practical problems, and have to make sure that their mathematics can be coded on a computer. Anyone who has done this knows that one must know one’s mathematics meticulously. It is also known that some academic mathematicians have resorted to fraud, so great caution is advised about any academic pronouncement about ECE. This is simply because the main proofs of ECE are self checking and worked out in meticulous detail.

## Criticisms of Abstruse Mathematics

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