In mathematics, transformations equivalent to what was later known as Lorentz transformations in various dimensions were discussed in the 19th century in relation to the theory of quadratic forms, hyperbolic geometry, Möbius geometry, and sphere geometry, which is connected to the fact that the group of motions in hyperbolic space, the Möbius group or projective special linear group, and the Laguerre group are isomorphic to the Lorentz group.
Mathematicians were following up on "what happens when you discard one of Eucilids Axioms" and discovering there was an entire world of consistent hyperbolic geometry and more.
Some time later:
In physics, Lorentz transformations became known at the beginning of the 20th century, when it was discovered that they exhibit the symmetry of Maxwell's equations. Subsequently, they became fundamental to all of physics, because they formed the basis of special relativity in which they exhibit the symmetry of Minkowski spacetime, making the speed of light invariant between different inertial frames.
If you read mathematics histories it's a common complaint that it's nigh on impossible to discover something new and esoteric that doesn't soon end up with a military application; the ongoing search for interesting but useless mathematics is akin to the search for the fountain of youth.
It is the case (IIRC) that quaterions arose directly from Hamilton's search for a better way to describe mechanical motions in three dimension spaces - ie created to be useful from the outset.
https://en.wikipedia.org/wiki/History_of_Lorentz_transformat...
Mathematicians were following up on "what happens when you discard one of Eucilids Axioms" and discovering there was an entire world of consistent hyperbolic geometry and more.Some time later:
If you read mathematics histories it's a common complaint that it's nigh on impossible to discover something new and esoteric that doesn't soon end up with a military application; the ongoing search for interesting but useless mathematics is akin to the search for the fountain of youth.It is the case (IIRC) that quaterions arose directly from Hamilton's search for a better way to describe mechanical motions in three dimension spaces - ie created to be useful from the outset.