Not Einstein, he never was a mathematician. He got helped most of the time to do the math(as he should)
Who Did the Math for General Relativity First, Einstein or Hilbert?
51–60 of 66 posts
Re: Who Did the Math for General Relativity First, Einstein or Hilbert?
#52Earlier quoted context omitted.
I have gotten the impression that Einstein learned the math that he needed to, when he needed to learn it, and that he had hoped to avoid learning the sort of math that Hilbert was already somewhat comfortable with.
Absolutely. Einstein is a bit famous for punching well above his weight compared to his own mathematical background. Most of his great work involves beautiful arguments that requiring only maths that a good-but-not-genius high school student could understand. The GR paper is a bit disappointing in comparison, because after setting out as much as he can of the physics, he just dives into big equations one after anothe…
Can you please post a link to the paper?
Re: Who Did the Math for General Relativity First, Einstein or Hilbert?
#53Earlier quoted context omitted.
I would love to read a deep dive into the history of (semi) modern science. In particular, one that would avoid pop-science analogies and that is unafraid of technical detail. Ideally one that is more focused on the intricacies and lineage of research than the particulars of researchers' personal lives. I feel that academics often have significant insight into the history of their own fields and personalities therein…
In physics there is a rich literature documenting its history. And as you mentioned, it is scattered around books, periodicals and scientific journals. A very small selection for you and any people interested: From Emilio Segre (Nobel Laureate) there is this 2 book series.Recommended. - From Falling Bodies to Radio Waves [1] - From X-rays to Quarks [2] Then, you have Abraham Pais, all his books are highly recommended…
Thanks for the recommendations! Found a couple of books I'd like to purchase, read the first twenty or so pages at one go, then relegate it to the pile along with the 50 others that have been replaced by new ones.
Re: Who Did the Math for General Relativity First, Einstein or Hilbert?
#54Earlier quoted context omitted.
Esther Lederberg - discovered lambda phage in bacteria but the Nobel Prize for Medicine for the discovery went to her husband. Jocelyn Bell Burnell - discovered pulsars and went on to work with her thesis advisor Antony Hewish and Martin Ryle. They got the Nobel Prize for Physics and she didn't. Ada Lovelace - invented computer programming but the credit went to Charles Babbage because he invented the hardware (one o…
>Rosalind Franklin - discovered the double helix structure of DNA using x-rays. This is a gross mischaracterization. Fraklin certainly took some pictures of DNA using x-ray crystallography, but she absolutely did not figure out the structure.
Yeah - and if you believe Watsons autobiography, she was strongly opposed to the idea that DNA had a helical structure until Watson and Crick basically figured it out and presented her with some very convincing arguments.
Franklins contributions seem pretty overstated compared to how people don't mention all the other people involved that had some critical insight.
Re: Who Did the Math for General Relativity First, Einstein or Hilbert?
#55Earlier quoted context omitted.
Absolutely. Einstein is a bit famous for punching well above his weight compared to his own mathematical background. Most of his great work involves beautiful arguments that requiring only maths that a good-but-not-genius high school student could understand. The GR paper is a bit disappointing in comparison, because after setting out as much as he can of the physics, he just dives into big equations one after anothe…
Can you please post a link to the paper?
See https://einsteinpapers.press.princeton.edu/vol6-trans/
Doc. 21 On the General Theory of Relativity https://einsteinpapers.press.princeton.edu/vol6-trans/110
Doc. 22 On the General Theory of Relativity (Addendum) https://einsteinpapers.press.princeton.edu/vol6-trans/120
Doc. 24 Explanation of the Perihelion Motion of Mercury from the General Theory of Relativity https://einsteinpapers.press.princeton.edu/vol6-trans/124
Doc. 25 The Field Equations of Gravitation https://einsteinpapers.press.princeton.edu/vol6-trans/129
Re: Who Did the Math for General Relativity First, Einstein or Hilbert?
#56It’s clear that it’s not who did the math first that gets recognition, but the person who makes the scientific leap to connect math to new ideas of how the world works. Lorentz and Poincaré both had mathematical formulations that were the same as Einstein’s special relativity, but Einstein was the one who gets credit for connecting them to what we now call special relativity.
This narrative is very unpersuasive, since the actual mechanics that are used to perform calculations in special relativity and the idea that they should apply to all matter were developed by Lorentz and Poincare starting in the 1890s. The moving clock idea was also introduced by them before Einstein in 1900 and 1904. The most persuasive narrative to me for why Einstein is credited is because he moved to the USA at t…
I don't buy that narrative. I think that Einstein's special relativity paper showed how the mathematics followed from first principles. Neither Lorentz nor Poincare did that. They may have had the mathematics that worked, they may have had it first. But Einstein told us why.
Re: Who Did the Math for General Relativity First, Einstein or Hilbert?
#57The history misses several salient steps, like Lorentz and Poincare describing special relativity before 1905. I guess if you want to describe the controversy of general relativity you might not want to get distracted by the controversy over special relativity... but a pattern starts to emerge. Then the history leaves out Nordstrom's contributions to the theory of gravity which are really important if you are going t…
> In fact a student of Lorentz, Fokker, working with Einstein was able to show that Nordstrom's theory was equivalent to an expression involving the ricci scalar and a trace of the stress energy tensor. Unlike Einstein's proposal around this time, it was diffeomorphism invariant.
"I know some of these words."
Re: Who Did the Math for General Relativity First, Einstein or Hilbert?
#58The history misses several salient steps, like Lorentz and Poincare describing special relativity before 1905. I guess if you want to describe the controversy of general relativity you might not want to get distracted by the controversy over special relativity... but a pattern starts to emerge. Then the history leaves out Nordstrom's contributions to the theory of gravity which are really important if you are going t…
> In fact a student of Lorentz, Fokker, working with Einstein was able to show that Nordstrom's theory was equivalent to an expression involving the ricci scalar and a trace of the stress energy tensor. Unlike Einstein's proposal around this time, it was diffeomorphism invariant. "I know some of these words."
Ricci scalar: number assigned to each point of a space describing curvature at that point
Stress-energy tensor (field): multidimensional quantity assigned to each point of a space describing how matter and energy are concentrated and moving at that point.
Trace: coordinate invariant transformation that turns a tensor field into a scalar field.
Diffeomorphism invariant: the object in question has the same description regardless of arbitrary coordinate changes
Re: Who Did the Math for General Relativity First, Einstein or Hilbert?
#59Earlier quoted context omitted.
As a Ph.D. candidate at Radcliffe, Cecilia Payne discovered that, contrary to accepted theory of the time, stars (and the universe) are mostly hydrogen, and not the same mix of stuff here on earth. Established astronomer Henry Norris Russell reviewed her thesis and got her to drop this conclusion; then he published the same result later, and is typically credited with its discovery.
That's a bit misleading. (Not deliberately, I'm sure.) When Russell published the same result later, here's one thing he said: "The most important previous determination of the abundance of the elements by astrophysical means is that by Miss Payne, who determined, by Milne's method of marginal appearances, the relative abundance of eighteen of the most important elements." He shows Payne's figures and remarks on how…
Right, and he did not include her as a co-author of his paper. That's dirty pool in the academic world.
As for who typically gets credit, yes, I think you'd get a different result if you ask astronomers and astro-physicists who are over 50 years old, or anyone who hung around science museums and planetariums in the 1960's or 70's, or check out old popular science books and magazines, or the Journal for the History of Astronomy October 1983, which takes on the prevailing attitude. Perhaps it's changing, but that's only through the efforts of folks like you, who take the effort to set the record straight.
Re: Who Did the Math for General Relativity First, Einstein or Hilbert?
#60Earlier quoted context omitted.
I would love to read a deep dive into the history of (semi) modern science. In particular, one that would avoid pop-science analogies and that is unafraid of technical detail. Ideally one that is more focused on the intricacies and lineage of research than the particulars of researchers' personal lives. I feel that academics often have significant insight into the history of their own fields and personalities therein…
I had a professor briefly that studied the history of mathematics. During lectures while he was developing out proofs he would often describe the historical context in which the proof was first developed. Galois has a particularly interesting (tragic) story. There are a lot of interesting historical figures. Probably most people stick to the figures most familiar to them in their own field. The histories of Dijkstra…
Speaking of Knuth, he is extraordinary in this regard apparently as the rigor of his expositions matches his attention to the historical details. Add to that his meticulousness for properly (and aesthetically) spelling people's names for good measure.