WI: Karl Friedrich Gauss had published all his results?

Historian of mathematics Eric Temple Bell remarked that if Gauss had published all his results, he'd have advanced mathematics by 50 years. What if he did publish all his results? How would mathematics, and of course, physics and other branches of applied mathematics, look like then?

IMO, the biggest change would be that we might have had general and special relativity sooner. Non-Euclidean geometry is used to explain relativistic effects. Non-Euclidean geometry were discovered by Bolyai and Lobachevsky. On seeing Bolyai's results, Gauss had said that to praise those would be tantamount to praising himself and that he'd had the same idea for 50 years. However, he never published anything in non-Euclidean geometry. Assuming he did publish his results much earlier, we could have expected a lot of mathematicians working out the ramifications and applications of non-Euclidean geometry — Gauss' stature in the mathematical world would have ensured that, no matter how 'heretical' the concept might have sounded. Probably, Lorentz transformations, and other mathematical underpinnings of relativity would have been discovered sooner. And we could expect mathematicians and physicists hit upon relativity, which flows logically from these mathematical underpinnings, a lot sooner than 1905 — which is the year in which Einstein published his discoveries.

Is the above scenario plausible? And what else might have happened?
 
Historian of mathematics Eric Temple Bell remarked that if Gauss had published all his results, he'd have advanced mathematics by 50 years. What if he did publish all his results? How would mathematics, and of course, physics and other branches of applied mathematics, look like then?

IMO, the biggest change would be that we might have had general and special relativity sooner. Non-Euclidean geometry is used to explain relativistic effects. Non-Euclidean geometry were discovered by Bolyai and Lobachevsky. On seeing Bolyai's results, Gauss had said that to praise those would be tantamount to praising himself and that he'd had the same idea for 50 years. However, he never published anything in non-Euclidean geometry. Assuming he did publish his results much earlier, we could have expected a lot of mathematicians working out the ramifications and applications of non-Euclidean geometry — Gauss' stature in the mathematical world would have ensured that, no matter how 'heretical' the concept might have sounded. Probably, Lorentz transformations, and other mathematical underpinnings of relativity would have been discovered sooner. And we could expect mathematicians and physicists hit upon relativity, which flows logically from these mathematical underpinnings, a lot sooner than 1905 — which is the year in which Einstein published his discoveries.

Is the above scenario plausible? And what else might have happened?

Hmmm... Indeed. One of Gauss's problems was that he HATED publishing anything unless it was highly polished. If he was prepared to publish more preliminary work, there would have been huge advances. Of course, someone might have to devote an entire publishing house just to his work:) [Springer Verlag a century earlier?]

OT3H, if he had published all that, his name would be a household name like Newton, not most ignored like today.
 
[Springer Verlag a century earlier?]

OT3H, if he had published all that, his name would be a household name like Newton, not most ignored like today.

Scientific publishing becomes a viable branch of publishing, thanks to Herr Gauss. That's a good one. Thanks Dathi.

Here's one: In OTL, Gauss, along with Wilhelm Weber, came up with the first working telegraph in 1833. This was a side-project, Gauss was more interested in setting up a series of magnetic observatories. In ATL, Gauss, along with Weber, presides over the development of telegraphy. He gets support from the Hanoverian government — Göttingen, his institution, was in Hanover at that time — as well as the British Empire, which was in a personal union with the Kingdom of Hanover at that time. Sir William Fothergill Cooke, who in OTL, co-invented the Cooke-Wheatstone telegraph, worked with Gauss and Weber on the development of the technology. This kickstarts a communications revolution.
 
Scientific publishing becomes a viable branch of publishing, thanks to Herr Gauss. That's a good one. Thanks Dathi.

Here's one: In OTL, Gauss, along with Wilhelm Weber, came up with the first working telegraph in 1833. This was a side-project, Gauss was more interested in setting up a series of magnetic observatories. In ATL, Gauss, along with Weber, presides over the development of telegraphy. He gets support from the Hanoverian government — Göttingen, his institution, was in Hanover at that time — as well as the British Empire, which was in a personal union with the Kingdom of Hanover at that time. Sir William Fothergill Cooke, who in OTL, co-invented the Cooke-Wheatstone telegraph, worked with Gauss and Weber on the development of the technology. This kickstarts a communications revolution.

I don't get how that follows; it the OTL, the first public telegraph in Britain was in 1839; surely6 years is nothing?
 
I don't get how that follows; it the OTL, the first public telegraph in Britain was in 1839; surely6 years is nothing?

Yes, six years is nothing. But England had the head-start in OTL in telegraphy — and a monopoly: Samuel Morse invented the telegraph independently only in 1839, Alexander Bain invented the 'recording telegraph' in 1843, and Giovanni Caselli invented the Pantelegraph in 1855.

In ATL, with Gauss, Weber, and Cooke having joined forces, the developments were much faster, and managed to spread to the European mainland more quickly than in OTL. In OTL, the International Telegraph Company started laying submarine cables to the Netherlands and Belgium only in the 1850s.

In ATL, the International Telegraph Company could come into being much earlier. Also, the union of Hanover with Great Britain was dissolved in 1837. In ATL, this might mean the German branch of the International Telegraph Company would work independently. Which might mean direct competition with the British branch, and therefore, a much quicker establishment of pan-European telegraphy.
 
Mathematics are connected to everything, but its not that simple, there is a lot of stuff that has to happen before stuff becomes possible. I'm trying to say, long term that would likely cause a 20-30 years advance of science over OTL at most.

We might see WWI fought with WWII weapons and ended with nukes, completely butterflying rest of 20th century history. Rest of divergences in 19th century would likely be small enough to pass unnoticed.
 
Maybe, but you have to remember that Einstein is going to be butterflied away by this, he was only 20 something in 1905. With the more advanced mathematics we probably would get Special Relativity faster, but without Einstien General Relativity and Quantum Mechanics are going to be set by years or decades.
 
Answers to problems...

Both theories of relativity were answers to experiments differing from predictions. When were the observations that prompted a need for a new theory done? And would they be done earlier if mathematics was more advanced?
 
Both theories of relativity were answers to experiments differing from predictions. When were the observations that prompted a need for a new theory done? And would they be done earlier if mathematics was more advanced?

Einstein came up with GR because SR didn't jive with Newton's gravity. The first technology that needs to be engineered with GR is GPS IIRC.
 
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