# Vector theory of Gravity

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The theory:  http://iopscience.iop.org/article/10.1088/1402-4896/aa93a8/meta    Submitted 2015, revised 2017.

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1 hour ago, coffeesippin said:

The theory:  http://iopscience.iop.org/article/10.1088/1402-4896/aa93a8/meta    Submitted 2015, revised 2017.

There are many theories of gravity including MOND...The theory as evidenced by GR remains superior in the views of most experts and has been extensively tested time and time again, with its latest prdictions of gravitational radiation confirmed  numerous times.

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Was there some reason for not publishing the abstract?

And perchance a comment?

That would make your OP comply with SF rules.

There are 55 pages in the article, which seems well put together at first glance, but it will take some reading.

But definitely worth discussing.

I was particularly interested in his distinction between 'vector' and 'tensor' (midway down the abstract) so my first task is to find out what he means by this, as tensors are technically vectors but only some vectors are tensors and GR relies on this.

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6 hours ago, coffeesippin said:

The theory:  http://iopscience.iop.org/article/10.1088/1402-4896/aa93a8/meta    Submitted 2015, revised 2017.

The abstract:

Quote

We propose an alternative theory of gravity which assumes that background geometry of the Universe is fixed four dimensional Euclidean space and gravity is a vector field Ak in this space which breaks the Euclidean symmetry. Direction of A k gives the time coordinate, while perpendicular directions are spatial coordinates. Vector gravitational field is coupled to matter universally and minimally through the equivalent metric f ik which is a functional of A k . We show that such assumptions yield a unique theory of gravity, it is free of black holes and, to the best of our knowledge, passes all available tests. For cosmology our theory predicts the same evolution of the Universe as general relativity with cosmological constant and zero spatial curvature. However, the present theory provides explanation of the dark energy as energy of longitudinal gravitational field induced by the Universe expansion and yields, with no free parameters, the value of  which is consistent with the recent Planck result . Such close agreement with cosmological data indicates that gravity has a vector, rather than tensor, origin. We demonstrate that gravitational wave signals measured by LIGO are compatible with vector gravity. They are produced by orbital inspiral of massive neutron stars which can exist in the present theory. We also quantize gravitational field and show that quantum vector gravity is equivalent to QED. Vector gravity can be tested by making more accurate measurement of the time delay of radar signal traveling near the Sun; by improving accuracy of the light deflection experiments; or by measuring propagation direction of gravitational waves relative to laser interferometer arms. Resolving the supermassive object at the center of our Galaxy with VLBA could provide another test of gravity and also shed light on the nature of dark matter.

There is an interesting editorial on the paper. No doubt some will see the reactions of some reviewers as typical of the "closed mind" of scientists. On the other hand, the paper did get published so there is no great conspiracy of silence.

The comments from a reviewer that they include are pretty insightful (ie echo my own thoughts!)

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!

Moderator Note

From rule 2.7 (see the guidelines, in the "browse" tab; emphasis added)

Links, pictures and videos in posts should be relevant to the discussion, and members should be able to participate in the discussion without clicking any links or watching any videos.

So, as studiot has suggested, posting at least the abstract is a must, along with a summary of the relevant material you wish to discuss.

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4 hours ago, Strange said:

The abstract:

There is an interesting editorial on the paper. No doubt some will see the reactions of some reviewers as typical of the "closed mind" of scientists. On the other hand, the paper did get published so there is no great conspiracy of silence.

The comments from a reviewer that they include are pretty insightful (ie echo my own thoughts!)

Nothing in particular I want to discuss .. its beyond me too.  But its an opportunity to see input on it, thanks for yours it was valuable.  I dont think many people see scientists as being closed minded, except when the Consensus becomes their truth instead of what might appear beyond the Consensus .. then they refuse to consider beyond it.

I dont see the review to be objectionable in the least, very positive instead, and that the paper goes beyong GR it seems a huge advance for science that it did get published.   It is indeed surprising that such a fundamentally different theory also passes the available tests of gravity without any free parameters, as is shown by the author with all necessary details. If true, this fact alone would make vector gravity a viable alternative to GR. In addition, vector gravity provides an explanation of the dark energy as the energy of the longitudinal gravitational field induced by the expansion of the Universe, and, with no free parameters, yields a value of the cosmological constant that is consistent with observations. Thus, according to this reviewer, vector gravity essentially resolves the dark energy problem. This is what we expect from a correct theory of gravity. Vector gravity also suggests a mechanism of/for matter generation at the Big Bang without involving additional fields and is free of space–time singularities, which is also remarkable.

4 hours ago, studiot said:

Was there some reason for not publishing the abstract?

And perchance a comment?

That would make your OP comply with SF rules.

There are 55 pages in the article, which seems well put together at first glance, but it will take some reading.

But definitely worth discussing.

I was particularly interested in his distinction between 'vector' and 'tensor' (midway down the abstract) so my first task is to find out what he means by this, as tensors are technically vectors but only some vectors are tensors and GR relies on this.

Im new to the forum, there are so many rules written and seemingly unwritten it seems that it would be impossible to participate for a considerable length of time before learning all the rules, as some of them appear impossible to learn except through experience.  I was going to ask if just posting the links would be acceptable, but Im in such bad standing with a couple of mods that I cant trust their responses .. I regret having to say that, and it came very hard coming to that distrust.

Edited by coffeesippin
Commented on the review

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8 hours ago, Strange said:

The abstract:

There is an interesting editorial on the paper. No doubt some will see the reactions of some reviewers as typical of the "closed mind" of scientists. On the other hand, the paper did get published so there is no great conspiracy of silence.

The comments from a reviewer that they include are pretty insightful (ie echo my own thoughts!)

Thank you for extracting the 'abstract' (various puns come to mind) I was struggling with this.

How did you achieve it?

I ask because I want to extract the postulates and discuss them. they are interesting.

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5 minutes ago, studiot said:

Thank you for extracting the 'abstract' (various puns come to mind) I was struggling with this.

How did you achieve it?

Just copy and paste. I think I did it on my phone as well, which is always a bit fiddly.

8 minutes ago, studiot said:

I ask because I want to extract the postulates and discuss them. they are interesting.

In case you are having problems, here you go:

The present vector theory of gravity is based on four postulates:

1. Background geometry of the Universe is a fixed four dimensional Euclidean space with metric  (1, 1, 1, 1). Such space is completely isotropic and has no preferred directions.

2. In the four dimensional Euclidean space there is a dynamical 4-vector field Ak (the gravitational field) which breaks the symmetry. Namely, direction of Ak is now preferred and this direction becomes the time coordinate. Directions perpendicular to Ak are three spatial coordinates.

3. Vector gravitational field is coupled to matter and all nongravitational fields through the equivalent metric fik which is an algebraic function of Ak and the background Euclidean metric . Gravitational field couples universally and minimally to all the fields of the Standard Model by replacing everywhere the Minkowski metric  with the equivalent metric  and replacing partial derivatives with covariant derivatives formed from fik. In particular, the trajectories of freely falling bodies are geodesics of the equivalent metric . Action for a point particle with mass m moving in the gravitational field reads

where c is the speed of light. Action (7) has the same form as in general relativity, however, the tensor gravitational field gik of general relativity is now replaced with the equivalent metric fik. One should note that the Einstein equivalence principle is a consequence of the action (7).

4. The quantum of the vector field Ak (the graviton) is not an elementary particle, but rather it is a composite particle formed of massless fermion–antifermion pairs. Emission and absorption of a graviton corresponds to creation and annihilation of particle–antiparticle pairs.

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4 hours ago, coffeesippin said:

Nothing in particular I want to discuss .. its beyond me too

Me too...But again, let me reiterate that aLIGO and other scientific orginizations are well aware of it, and it is damn well near certain, that if it was/is as good as its authors and formulators claim, why it hasn't started a revolution and displace GR? Anyone proposing any theory, treats that theory as his baby...much as a Mother would with a new born child. It would be rare for that proposer to completely look at his own workings/ideas in an 100% objective manner.

Quote

If true, this fact alone would make vector gravity a viable alternative to GR.

"IF" true, if it does all that is claimed it does do, "IF"....it would replace GR as our utmost accurate theory of gravity.

Quote

In addition, vector gravity provides an explanation of the dark energy as the energy of the longitudinal gravitational field induced by the expansion of the Universe, and, with no free parameters, yields a value of the cosmological constant that is consistent with observations. Thus, according to this reviewer, vector gravity essentially resolves the dark energy problem. This is what we expect from a correct theory of gravity.

"IF" all the maths is correct, if the assumptions made are valid, if all its other claims are shown to be valid.

Let me finish by saying, that if it does pass muster, and successfully  runs the gauntlet unscathed, then it will certainly be proclaimed as GR's successor, and be a "shoe in" for the Nobel prize for Physics. At present though, I don't see any indication of that.

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34 minutes ago, Strange said:

4. The quantum of the vector field Ak (the graviton) is not an elementary particle, but rather it is a composite particle formed of massless fermion–antifermion pairs. Emission and absorption of a graviton corresponds to creation and annihilation of particle–antiparticle pairs.

That sounds weird to me. Maybe I will have to try and work through more of the paper.

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14 hours ago, beecee said:

There are many theories of gravity including MOND...The theory as evidenced by GR remains superior in the views of most experts and has been extensively tested time and time again, with its latest prdictions of gravitational radiation confirmed  numerous times.

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52 minutes ago, beecee said:

Me too...But again, let me reiterate that aLIGO and other scientific orginizations are well aware of it, and it is damn well near certain, that if it was/is as good as its authors and formulators claim, why it hasn't started a revolution and displace GR? Anyone proposing any theory, treats that theory as his baby...much as a Mother would with a new born child. It would be rare for that proposer to completely look at his own workings/ideas in an 100% objective manner.

Let's be fair.

An well respected, but junior mathematician at the univesity of Kazan wrote Geometriya in 1823.
This was the mathematics that paved the way for GR.

It was blocked by the Progfessor of Applied Mathematics (Ostragradskii) and not publish until 1909.

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3 minutes ago, studiot said:

An well respected, but junior mathematician at the univesity of Kazan wrote Geometriya in 1823.
This was the mathematics that paved the way for GR.

For completeness: https://en.wikipedia.org/wiki/Nikolai_Lobachevsky

The same ideas were also (independently) developed by Gauss and Bolyai. It was in the air at the time, I guess.

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7 minutes ago, studiot said:

Let's be fair.

An well respected, but junior mathematician at the univesity of Kazan wrote Geometriya in 1823.
This was the mathematics that paved the way for GR.

It was blocked by the Progfessor of Applied Mathematics (Ostragradskii) and not publish until 1909.

Noted......Sometimes running the gauntlet can and does take some time....and with something as successful as GR has been, and if this V4 does have anything going for it, it will also probably take some time.

But by the same token, if it is as ground breaking as its proposers say, I'm sure there would be plenty of young up and coming scientists/physicists that would like to show that it is superior to GR and be open to the huge accolades he would benefit from.

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At least the paper has a suggestion for a test using gravitational waves

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26 minutes ago, Strange said:

At least the paper has a suggestion for a test using gravitational waves

Yes that's good, and thank you for the next extraction, but I can't aks for all 55 pages.

I tried copy and paste in to my old Word, but didn't get very far.

Anyway I have some thoughts about the axiom vector field to make.
It is a pity ajb is not here as he was the only one I have ever got to understand this point about vector fields.
Even Modred didn't fully appreciate it.

56 minutes ago, beecee said:

Noted......Sometimes running the gauntlet can and does take some time....and with something as successful as GR has been, and if this V4 does have anything going for it, it will also probably take some time.

Quote

He died in 1856, in poverty, unaware that anyone would ever take notice of his discovery of Non Euclidian Geometry.

Unfortunately those pesky philosophers were right insofar as there has been all to much blocking and obstructionism by some established figures in the past.

Although we like to think we are better today still scientific fraud still occurs (cold fusion  and certain skeletons comes to mind).

So open mindedness coupled with vigilance is the watchword.

Edited by studiot
spelling

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13 minutes ago, studiot said:

So open mindedness coupled with vigilance is the watchword.

Bingo!

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Having joined up back in May 2011, this is my first post here. At the outset I will state that as a layman have no formal education re GR. But do understand the basic principles and will claim to think clearly on such things (mostly anyway)  It so happens I started a thread on Anatoly Svidzinsky's Vector Gravity at another forum back on June 8, 2018.
Regarding a 'future test' of Vector Gravity vs GR via GW data - it's in effect already been done wrt the NS-NS merger event GW170817:
https://arxiv.org/abs/1804.03520
However a slightly more recent (than v2 of above linked article) joint LIGO_Virgo analysis has come down strongly favouring GR tensor GW's over Svidzinsky's Vector GW's:
https://arxiv.org/abs/1811.00364
No reference therein to Svidzinsky et. al.'s earlier findings. Nor any publicly available paper since v1 of https://arxiv.org/abs/1804.03520 (April 6th, 2018) attempting to rebut the findings there. Which is strange as Svidzinsky got a very positive response in that Editorial piece already linked to here. A formal response from LIGO et. al. team members was surely expected as a matter of formality if not courtesy. I suspected pure bias by LIGO_Virgo team, so emailed Svidzinsky with 3 pertinent questions. He kindly replied in some detail. Reproduced below is what I posted on it at the other forum site, with only slight modifications:

A short while ago received a very helpful reply email from Anatoly Svidzinsky, where 3 questions put to him were answered. Because it was a private communication I'll just summarize/paraphrase his answers:

Q 1: A recent joint LIGO-Virgo paper https://arxiv.org/abs/1811.00364 makes no mention of your own reanalysis https://arxiv.org/abs/1804.03520
re findings in an earlier joint LIGP-Virgo article. Have you had any private communication from them trying to justify what looks like an outright snub?

A 1: They were contacted by us and alerted to the problematic issues with their pro GR finding, but evidently they failed to see any issue. A detailed response will appear at arXiv.org this or next week. Title:
Comment on “Tests of general relativity with GW170817”
[I was given the draft version. Basically, they point out that Jackson et. al. criticisms (see Q 2 below)] are valid to the extent that improperly applied noise reduction techniques has corrupted key parts of in particular the LIGO Livingston detector GW170817 event GW detection (a 'glitch' coinciding with detection event). Which then skewed the overall Beysian analysis to favour GR over Vector Gravity. When properly cleaned up, the opposite holds true, in agreement with the direct analyses earlier done by Svidzinsky et. al.]

Q 2: Any credibility to recently resurrected Jackson et. al. criticisms re GW detections?:
https://www.newscientist.com/article/mg24032022-600-exclusive-grave-doubts-over-ligos-discovery-of-gravitational-waves/]Ne

A 2: Jackson et. al.'s criticism is imo valid regarding LIGO_Virgo's handling of noise filtering. However, in particular the NS-NS merger event GW170817 has a long train of continuous data that, apart from corruption of segments of the Livingston data, is very clearly a bona fide GW signal.

Q 3: A recent article by Matt Visser et. al.: https://arxiv.org/abs/1805.03781
"The exponential metric represents a traversable wormhole"
The finding (sect 3.1), of a minimum proper radius throat at a modest R = m, seems to imply inevitability of stellar i.e. post NS density collapse to some indefinitely small final size. Given proper volume grows as r continues to decrease! Which effectively makes the EOS very soft for any in-falling matter/radiation beyond that point. This in turn undercuts your arguments re maximum mass of NS's, and viability of theorized 'multi-Mev Axions' 'SMBH's' e.g. at Sagittarius A*?

A 3: I contacted Visser et. al. shortly after their arXiv article was published, and pointed out that their vacuum solution is unrealistic, and furtheremore the situation R < M does not occur for NS's using our EOS. Hence they are stable objects according to Vector Gravity - which automatically includes any potential 'wormhole' character of exponential metric. See fig's 3 & 4 in http://iopscience.iop.org/article/10.1088/1402-4896/aa93a8/pdf
Similarly, for meV [not MeV as I had written] scale axion 'dark matter' 'SMBH' candidates, presence of matter gives a different character than 'traversable wormhole' solution suggests: See e.g. fig.3 in https://arxiv.org/abs/astro-ph/0607179v2
Visser et. al. have raised nothing really new with their article.

In summary, Svidzinsky has detailed answers to all criticisms so far leveled at his theory. Evidently gravity actually takes on a repulsive nature below hypothetical wormhole throat region R = M - making such a vacuum solution 'traversable wormhole' formally symmetrical in nature. The ultimate fail-safe against GR predicted 'collapse to a point singularity'. No need for quantum gravity to ever enter as rescuer of a non-existent problem - imo.

Edited by Q-reeus
closing ] invalidated an article link

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46 minutes ago, Q-reeus said:

In summary, Svidzinsky has detailed answers to all criticisms so far leveled at his theory. Evidently gravity actually takes on a repulsive nature below hypothetical wormhole throat region R = M - making such a vacuum solution 'traversable wormhole' formally symmetrical in nature. The ultimate fail-safe against GR predicted 'collapse to a point singularity'. No need for quantum gravity to ever enter as rescuer of a non-existent problem - imo.

Nice post and argument. As I have previously suggested though, in time, and if this V4 continues to stand up to scrutiny, it will be made public. There are two many young up and comers and plenty of experienced cosmologists, that would like to be able to improve on or widen the parameters of GR. But it won't be easy and nor should it be. GR has an outstanding track record, but if this new V4 is better and more descriptive  without any problems, then it will be revealed in time. At this time though, that investigation and research continues and that claim [V4 being superior] cannot be made just yet, if at all.

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2 hours ago, Q-reeus said:

Which then skewed the overall Beysian analysis to favour GR over Vector Gravity. When properly cleaned up, the opposite holds true, in agreement with the direct analyses earlier done by Svidzinsky et. al.]

Thank you for deciding to participate in the discussion. +1

Hopefully now you have taken the first bite of the apple you will have aquired the taste of posting here at SF.

Meanwhile I was interested in the line above concerning Bayesian methods, which are semi-empirical.

Can you provide more detail?

It is interesting because my view of GR is that our use is in a similar state to late 19th and early twentieth century Physics in many areas.

If you read texts from that era much was made of more and more accurate experimental determination of many coefficients in a wide variety of physical equations, well ahead of any theoretical interpretation or links (for example the Lennard Jones potential).

I'm not saying this was not very good work, because it was.

Just that the Einstein Field equations conntain quite a few such coefficients, the values of which make enormous differences to the outcome solutions.

So I would be very interested to see how Bayesian guesswork ties into this.

(nor is this a condemnation of Bayesian methods which has some spectacular successes over more traditional methods and also offers a fine example of establishment blocking of significant work and theory)

Edited by studiot

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3 hours ago, beecee said:

Nice post and argument. As I have previously suggested though, in time, and if this V4 continues to stand up to scrutiny, it will be made public. There are two many young up and comers and plenty of experienced cosmologists, that would like to be able to improve on or widen the parameters of GR. But it won't be easy and nor should it be. GR has an outstanding track record, but if this new V4 is better and more descriptive  without any problems, then it will be revealed in time. At this time though, that investigation and research continues and that claim [V4 being superior] cannot be made just yet, if at all.

Of course. See last part of my next post re likely time-frame for more definitive results.

1 hour ago, studiot said:

Quote

Thank you for deciding to participate in the discussion. +1

Hopefully now you have taken the first bite of the apple you will have aquired the taste of posting here at SF.

Meanwhile I was interested in the line above concerning Bayesian methods, which are semi-empirical.

Can you provide more detail?

It is interesting because my view of GR is that our use is in a similar state to late 19th and early twentieth century Physics in many areas.

If you read texts from that era much was made of more and more accurate experimental determination of many coefficients in a wide variety of physical equations, well ahead of any theoretical interpretation or links (for example the Lennard Jones potential).

I'm not saying this was not very good work, because it was.

Just that the Einstein Field equations conntain quite a few such coefficients, the values of which make enormous differences to the outcome solutions.

So I would be very interested to see how Bayesian guesswork ties into this.

(nor is this a condemnation of Bayesian methods which has some spectacular successes over more traditional methods and also offers a fine example of establishment blocking of significant work and theory)

Hi studiot and thanks for welcome. Regarding ref to Bayesian method employed re https://arxiv.org/abs/1811.00364, I have no experience working with it. A word search reveals 3 instances of the word Bayesian.:
p10, Under 'Constraints on Modified Dispersion'
p11, right column, 3rd para
p12, right column, 2nd para
So checking those out may provide all the context you need there. Svidzinsky's critique is as I mentioned currently only in a draft version response, and I don't feel comfortable posting it all here. I will however reproduce the precis and initial reference to Bayesian use in first para:

Quote

In a recent paper “Tests of general relativity with GW170817” (arXiv:1811.00364 [gr-qc]) the
authors found overwhelming evidence in favor of tensor gravitational wave (GW) polarization over vector by analyzing GW signal measured by the LIGO-Virgo network. Here we show that measured LIGO-Livingston signal is substantially reduced at certain frequency intervals which might be attributed to noise filtering. We found that if these blunder regions are excluded from the analysis then data are consistent with vector GW polarization and not with tensor. We also show that signal accumulation from the entire bandwidth erroneously underestimates the LIGO-Livingston signal amplitude which yields consistency of the data with tensor polarization and not with vector.

In a recent preprint [1] the authors reported results of the gravitational wave (GW) polarization test with GW170817 performed using a Bayesian analysis of the signal properties with the three LIGO-Virgo interferometer outputs. The authors found overwhelming evidence in favor of pure tensor polarization over pure vector with an exponentially large Bayes factor. This result is opposite to the conclusion of our analysis based on a direct comparison of the GW signals measured by the three detectors [2]. Namely, we found that the measured signal ratios are inconsistent with the predictions of general relativity, but consistent with the recently proposed vector theory of gravity.....

As mentioned in first post, the article proper is due for publishing at arXiv.org probably within a week from now. Sorry but just be patient...
In that vein, I will further reproduce part of my response to his private correspondence reply (prior to that, also posted in the other forum):

Quote

"Annoyingly we will have to wait till ~ Jan-Feb 2019 for LIGO-Virgo-GEO to begin a new ~ year long run:
https://ligonews.blogspot.com/2018/09/update-on-ligo-detectors-and-start-of-o3.html
Then likely some months more into 2019 before new GW data, particularly accurately locatable NS-NS merger events, will likely confirm what the currently sole NS-NS merger GW event implies.

Similarly, EHT data collation and analysis just keeps dragging on and not until sometime in 2019 before initial verdict re Sagittarius A* 'SMBH' is published:
https://eventhorizontelescope.org/faq
And so GR's lengthy stay as incumbent stretches on a while longer."

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6 hours ago, Q-reeus said:

Of course. See last part of my next post re likely time-frame for more definitive results.

"Annoyingly we will have to wait till ~ Jan-Feb 2019 for LIGO-Virgo-GEO to begin a new ~ year long run:

And so GR's lengthy stay as incumbent stretches on a while longer."

As I said previously, it won't be easy and nor should it be. GR has an outstanding track record. I'm sure you would join with me and hope that no mistakes are made, and just as obviously with the scientific world looking on, I'm pretty sure there will be no skull duggery as we often see science labeled with by questionable so called critics...whether GR remains as incumbent or otherwise.

Edited by beecee

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22 hours ago, studiot said:

Let's be fair.

An well respected, but junior mathematician at the univesity of Kazan wrote Geometriya in 1823.
This was the mathematics that paved the way for GR.

It was blocked by the Progfessor of Applied Mathematics (Ostragradskii) and not publish until 1909.

Wow.   Change takes time eh.   At least the professor didn't publish it under his own name.  His lack of understanding didn't prevent his ethics.

2 minutes ago, beecee said:

As I said previously, it won't be easy and nor should it be. GR has an outstanding track record. I'm sure you would join with me and hope that no mistakes are made, and just as obviously with the scientific world looking on, I'm pretty sure there will be no skull duggery as we often see science labeled with by questionable so called critics...whether GR remains as incumbent or otherwise.

Skull duggery may most often arise from desire for personal gain, especially financial, a Nobel is worth a lot of money.

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42 minutes ago, coffeesippin said:

Skull duggery may most often arise from desire for personal gain, especially financial, a Nobel is worth a lot of money.

Quite a cynical outlook, as opposed to critical...Like I said, the many young up and comers that would dearly love to over throw GR, along with the established experts that would love that chance and the rewards that go with it, make any chances of skull duggery virtually non existant.

Also supporting that is the incredible experiments that are now being undertaken that will either confirm GR to even greater precision, or show some limitation with the model...the SKA now being built....the LISA Pathfinder when completed. And obviously of course the realisation and discussions of V4 and other models of gravity that have been discussed in the past like emergent gravity and LQG.

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1 hour ago, coffeesippin said:

Skull duggery may most often arise from desire for personal gain, especially financial, a Nobel is worth a lot of money.

And yet in in previous threads, the clarion cry has been "institutional cover up" , though I don't want to attribute particular members.

I think in fact it has more often been personal, although influential persons can and have used their position for this.

The equivalent of the Nobel in Mathematics is the Fields Medal, which is not of such a high monetary value, but equal prestige in Maths.

1 hour ago, coffeesippin said:

Wow.   Change takes time eh.   At least the professor didn't publish it under his own name.  His lack of understanding didn't prevent his ethics.

Too often a male senior has done this to a female junior.

But mostly male/male since there have been far more males than females in Science.

I'm more suprised that you didn't want to know the name of the junior mathematician.

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