"Where is the math?" is a cliché trotted out with monotonous regularity, the implication being that mathematics is of primary importance. It is not, as history clearly shows. Just think Epicycles, where the mathematical model could make accurate predictions up to a point, yet failed to reflect the underlying reality. Heavier-than-air flight was also considered impossible a little over one hundred years ago and they had the math to prove it. Making science subservient to mathematics is putting the cart before the horse, let alone hubristic.

The importance of mathematics is not denied. The point is that math should follow the science rather than building the science on idealised mathematical models and selectively interpreting data to fit. In other words, the role of mathematics should be ancillary, not dominant.

"...the underlying assumptions of cosmologists today are developed with the most sophisticated mathematical methods and it is only the plasma itself which does not understand how beautiful the theories are and absolutely refuses to obey them."
Hannes Alfvén

Moreover, the father of Plasma Physics and Plasma Cosmology, Hannes Alfvén, was always quick to point out that plasmas have a tendency to ignore the elegant laws of mathematics. Likewise, it certainly seems that many cosmologists prefer to look the other way when it comes to space plasmas and their contemptuous behaviour. After all, space was supposed to be a near perfect vacuum, and dominated by gravity ... not unpredictable plasmas and electromagnetism.

There are many who display something akin to a religious devotion for math based theories, and prefer to side-step the philosophical issues, very often by ignoring or dismissing them. However, there are more presssing issues at hand, and these are not so easily ignored.

There is a new mathematician on the scene. He packs a punch to match his credentials, and he has a very low tolerance threshold for handwaving and equivocation. Thus far he has made light-work of apologists for mathematical cosmology. The problems he has highlighted are mathematical, not philosophical. In short, there is no longer any hiding place for the true-believers.

"I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce."
Freeman Dyson

Stephen J. Crothers is a gifted mathematician from Tasmania. Inevitably, some have nicknamed him the Tasmanian Devil. He is not one to pull his punches:

"Hawking was a pop scientist who ipso facto contributed nothing of value to science. Einstein was the first pop scientist; promoted at some time or another by that other entertainer, Charlie Chaplin. Hawking and the Einstein cult have ruined physics and astronomy, turning them into circus freak shows. Science cannot just wait until they all disappear. Whilst they are active they are ruining young minds entering science, to be caught up in the same rat race, producing more pop scientists. The cycle must be broken."
Stephen J. Crothers

Below are a few links to some of his work exposing fatal flaws in math-based cosmology.

The General Theory of Relativity is notorious for complicated mathematics. This is an impediment to many seeking to understand the likes of black hole and big bang theories, but perhaps convenient to those who might have something to hide.

Crothers explains the salient facts in simple terms without recourse to confusing math. It becomes easy to understand why black hole theory and big bang cosmology are mutually exclusive ...and ultimately, therefore, why General Relativity is itself inconsistent.

"Propositions arrived at by purely logical means are completely empty as regards reality." Albert Einstein

Black Holes, Unicorns, and All That Jazz

"There has been a deliberate suppression of important scientific papers by the community of physicists and astronomers concerning the black hole, beginning with the original paper by Karl Schwarzschild of 1916, evidently for vainglory, money and self-aggrandisement. I bring you free access to those papers, and others of relevance, in the hope that this fraud can be exposed and physics restored to a rational search for knowledge. The black hole has no foundation in theory whatsoever. Neither Newton's theory nor Einstein's theory predict it. In fact, both theories preclude it, contrary to what the orthodox relativists claim."
Stephen J. Crothers

Stephen Crothers, pictured right, has the following to say in respect of the claimed Black Hole pictures taken in March 2019:

"It is not a discovery at all!

"This is how astronomers and cosmologists do science: fraud by means of mass-media induced mass-hysteria. It beggars belief. Think about it: according to the astronomers and cosmologists the finite mass of their black hole is concentrated in a 'physical singularity' of zero volume, infinite density, and infinite gravity. But no finite mass has zero volume, infinite density, and infinite gravity, anywhere!

"Similarly, the astronomers and cosmologists assign to their black hole two different escape speeds (v_esc = 0 metres per second and v_esc = c = 300,000,000 metres per second, and in the same equation) and no capacity for an escape speed (since nothing can even leave), simultaneously, at the same place (at the 'event horizon'). But nothing can have two different escape speeds and no capacity for an escape speed, simultaneously, at the same place! (See [1]). Furthermore, the astronomers and cosmologists assert that the escape speed at the event horizon is the speed of light, yet light cannot either leave or escape; indeed, nothing, they say, can even leave the event horizon. But since light travels at the speed of light, which is the escape speed at the event horizon, light must both leave it and escape! And, moreover, anything else can leave.

"On the mathematical level, the black hole is conjured by violations of geometry. Geometrically speaking, the theory of black holes moves a sphere originally centred at the origin of a coordinate system to some other place in that same coordinate system but leaves its centre behind. By this means the two 'singularities' of the black hole are produced, the centre of the moved sphere, now thought to be an event horizon, and the left behind centre at the origin of coordinates, thought to be the 'physical singularity'. (See [2]). Analytically speaking, the violation of geometry manifests in black hole theory as the requirement that the absolute value of a real number must take on negative values which is also impossible. (See [3]).

"The laws of thermodynamics require that temperature must always be an intensive thermodynamic property. To argue otherwise is a violation of both the 0th and 2nd laws of thermodynamics. The Hawking temperature of a black hole is however non-intensive, in violation of the laws of thermodynamics. So black hole thermodynamics is entirely nonsense. (See [4])

"So their black hole does not exist; proven with common sense and high-school science. Yet they have managed to image that which does not exist. Of course they did - they have to justify their lucrative jobs and their vast grants of unaccountable public money."

For a comprehensive coverage of the frauds see [5], [6], and [7].

[1] Crothers, S.J., Black Hole Escape Velocity, Sky Scholar, 2018, https://www.youtube.com/watch?v=dZbDLd42Uws

[2] Crothers, S.J., Black Hole Geometry Analyzed, Sky Scholar, 2018, https://www.youtube.com/watch?v=0-xCMZLUc2A&t=5s

[3] Crothers, S.J., On Corda's 'Clarification' of Schwarzschild's Solution, Hadronic Journal, Vol. 39, 2016, http://vixra.org/pdf/1602.0221v4.pdf

[4] Robitaille, P.-M., Gravitational Thermodynamics - Is it Science?https://www.youtube.com/watch?v=mZ2F2Kw5-nQ

[5] Crothers, S.J., A Critical Analysis of LIGO's Recent Detection of Gravitational Waves Caused by Merging Black Holes, Hadronic Journal, n.3, Vol. 39, 2016, pp.271-302, http://vixra.org/pdf/1603.0127v5.pdf

[6] Crothers, S.J., LIGO Its Claims for Black Holes and Gravitational Waves | EU2017, https://www.youtube.com/watch?v=ev10ywLFq6E&t=496s

[7] Crothers, S.J., Gravitational Waves: Propagation Speed is Co-ordinate Dependent, Poster Presentation, 2018 April APS Meeting, Columbus, Ohio, presented on 14th April 2018. http://vixra.org/pdf/1804.0399v1.pdf

An excellent talk with Crothers, where the issues are explained in clear language. While it might be lengthy at almost three hours, an index is provided below the video so you can click straight to any particular topic.