Compressing big GeoJSON/Shapefle datasets for viewing on web browser

So I have a shapefile that is 3GB in size and as you can imagine my browser doesn't like it. How can I compress the data I have which is either in lon/lat coordinates or points on an X,Y grid?

I saw a video on Computerphile about Discreet Cosine Transforms for reducing high dimesionality data but being a programmer and not a mathematician I don't know if this is even possible. I have tried to take a point every 10 steps in the file like so: map[0:100000:10] but this had an udesireable and very lossy effect.

I would ideally like to have my data so it would work like Google Earth in which the resolution adjusts to your viewport altitude. So when you zoom in to the map higher freqency data is presented in the viewport, limiting the amount of points but I don't know how they do this and Google return nothing of value.

Last point is that since these are just vectors is there any type of vector compression I could use? I'm not to great at math so as you can imagine when I look into this I just get confused fairly quickly. I uderstand SciPy has some DCT built in and I know it has a whole bunch of other features which I don't understand, perhaps I could use this?

I can answer the "level of detail" part: you can experiment with leaflet (a javascript mapping library). You could then define a "coarse" layer wich is displayed for low zoom levels and "high detail" layers that are only displayed at higher zoom levels. You probably need to capture the map zoomend event and load/unload your layers from there.

One solution to this problem is to use a Web Map Server (WMS) like GeoServer or MapServer that stores your ShapeFile (though a spatial database like PostGIS would be better) on the server and sends a rendered image (often broken down into cacheable tiles) to the browser.