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?
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?