A reply to: A Short Formal Proof of Goldbach’s Conjecture

A Short Formal Proof of Goldbach’s Conjecture

In one of his papers on Goldbach’s conjecture, Miles Mathis claims to prove the conjecture in a formalized way. While the lack of definitions and explanations of some terminology used by Miles makes the paper harder to follow, we can still find some inconsistencies and flaws to point out.

Even though the method of the proof is itself flawed, let us jump right at an inconsistency in one of the definitions. Let x be an even number greater than 2. Miles writes

Let y = the number of primes less than x.
Let b = the number of non-prime odds less than x, as a fraction of numbers less than x.
b = [(x/2) – y] /(x – 1)

When calculating b, Miles correctly calculates the number of odd natural numbers less than x as \frac{x}{2}. But when substracting the number of primes less than x from this value, he wrongly assumes that all primes are odd numbers as well. Most of them are, but 2 is not. The formula can of course easily be corrected. However, upon sending him an email about this mistake Miles wrote

I don’t include 2 as a prime. The current definition of prime is muddled, in my opinion. If you include 2, you logically should include 1 and 0 as primes.

mm@milesmathis.com to the author of this blog, Jun 12 2010

While it is perfectly reasonable to make up one’s own definitions, stating them is certainly necessary when giving a proof! Excluding 2 from the prime numbers, the given formula for b is correct – But now we find that the conjecture Miles is about to prove does not hold any longer for the number 4! (Again, this is not a very big problem because conjecture could still be true for all even integers larger than 4 and the problem at hand would just be one of definition. However, the authors felt that it is worthwhile to point out these inconsistencies to the readers.)

But there is a more serious problem with Mathis’ proof. At no point does Mathis use any properties of the prime numbers, except that they are odd. If the proof were valid, replacing the word prime in the proof with any word that signifies a set of odd numbers would again give a valid proof and thus every even integer would be representable as the sum of two such numbers. That is certainly not the case for all sets of odd numbers, showing that Mathis’ proof is not correct.

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A reply to “Bremsstrahlung Radiation a better mechanism”

In his new article on Bremsstrahlung, Mathis applies his model (*) of spins and predicts that in this process, electrons turn into photons.

What we will see is that the mechanism of Bremsstrahlung, though roughly correct, is not completely correct. The electron is not emitting a photon, it is becoming a photon.

Mathis takes offence with current theory’s lack of explanation as to why and especially how electrons can emit – that is create – photons. They are not there before, so how can they be there afterwards? He repeatedly expresses the view that scientific description of nature should be “mechanical”.

But notice how convenient it is for them that quantum mechanics has no mechanics. Although they claim to be physicists, the fact that QM and QED are not mechanical allows them to dodge all physical questions.

We do not profess to know what Mathis means when he uses the term “mechanical”, but picture a model of small colliding spheres, not unlike billard balls. In this picture, interaction and forces are transmitted via collisions. Although it seems intuitive for nature to be “mechanical” in this everyday sense, there is no deeper reason why this should be true. Common sense tells us for example that the earth is flat, which is cleary not the case. It remains to say that contempary “non-mechanical” theories like electrodynamics and quantum mechanics are not only useful but make incredibly precise and well verified predictions and are justified in this pragmatist sense.
Mathis clings to his mechanical view because he cannot imagine the universe to be otherwise. His side blow

I thought we were done with force at a distance

to modern theory is in vain, because since the advent of field theory, building so called “local” theories is not a problem anymore. (There, force is mediated through local fields (e.g. the electromagnetic field), which explains the mysterious action at a distance that troubled Newton.)

On a philosophical side note, science has many heuristics, which “explain” how electrons emit real photons in the bremsstrahlung process (for example a cloud of virtual photons surrounding the electron). But they aren’t to be taken at face value from a philosophical perspective. They only thing science can do is make predictions and verify their consistency with experiments. It is true that scientists tend to have a lot of faith in their models, especially if they are established beyond reasonable doubt like general relativity and the standard model. But in the end they will have to hold up to experiment.

This brings us to the most problematic point in Mathis’ theory: He claims that the electron turns into a photon. This would imply that the electron’s negative charge somehow gets lost in the process, leaving the universe with an overall excess of one positive charge. To the best of our knowledge, so far no processes have been observed that violate charge conservation.

(*) “model” is really too strong a word for Mathis’ thinking. He uses heuristics, rather than clearly defined terms, in order to shed light on the problem. His method however, only enables him to make vague descriptions of what might be the case, but fails to produce predictions comparable to experiments.

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In his paper “ON LAPLACE AND THE 3-BODY PROBLEM” Miles gives an argument for why the distance between Saturn’s and Jupiter’s orbit should be shrinking with time if only gravity was present as a force. He writes:

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2010 in review

The stats helper monkeys at WordPress.com mulled over how this blog did in 2010, and here’s a high level summary of its overall blog health:

Healthy blog!

The Blog-Health-o-Meter™ reads This blog is on fire!.

Crunchy numbers

Featured image

A Boeing 747-400 passenger jet can hold 416 passengers. This blog was viewed about 2,600 times in 2010. That’s about 6 full 747s.

In 2010, there were 11 new posts, not bad for the first year! There were 2 pictures uploaded, taking up a total of 36kb.

The busiest day of the year was November 18th with 135 views. The most popular post that day was A reply to “The Extinction of Pi: The short version”.

Where did they come from?

The top referring sites in 2010 were scientopia.org, forum.objectivismonline.net, thunderbolts.info, shmups.system11.org, and iceinspace.com.au.

Some visitors came searching, mostly for miles mathis, ex falso mathis, miles mathis wikipedia, miles mathis ex falso, and “miles mathis”.

Attractions in 2010

These are the posts and pages that got the most views in 2010.


A reply to “The Extinction of Pi: The short version” November 2010


A reply to: Relativity as a concept June 2010


A reply to “Angular Velocity and Angular Momentum” July 2010


A reply to: Why Non-Euclidean Geometry is a Cheat June 2010


About June 2010

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Not Mathis: Test of general relativity

General relativity has been tested using data accumulated over 13 years from the LAGEOS II satellite. Result: \epsilon_{\omega}=1+(0.28 \pm 2.14)\times 10^{-3} where \epsilon_{\omega} is a parameter that measures deviations from GR. The GR prediction yields \epsilon_{\omega}=1

The online journal Physics has a nice summary of the results which should appeal to a wider audience. There is also a free download of the original paper at Physical Review Letters.

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A reply to “Of Monkeys and Typewriters”

This again is a guest post by Dan who has been very productive the last week.

We’ve all heard that if you had an infinite number of monkeys plugging away on an infinite number of typewriters for an infinite amount of time then eventually those monkeys would produce all the works of Shakespeare. In his “paper” Mathis sets his sights on disproving this statement, and fails miserably. This is fundamentally a problem of statistics, yet nowhere does Mathis ever use a single statistical argument.

Mathis asserts that since it is possible for a monkey to type an infinite string of “S”’s, that there is a non-zero probability that this monkey will not produce a work of Shakespeare. It is true that there is the possibility that no work of Shakespeare will be produced, but there is a greater probability one will be produced. Mathis seems to quibble over the statement of the monkey theorem given in layman’s terms, had he taken the time to see the precise formal statement of the theory he would realize his argument is flawed. There are a few ways this theorem can be stated, I will use a formulation that does not appeal to the notion of infinite monkeys. To make this formulation precise a few simplifying assumptions are made that in no way change the problem and the process is clearly defined.

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Mathis’ pi=4 featured at Good math, bad math

On a quick note, Mathis’ pi=4 “proof” is featured at Good math, bad math.

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