mass is the amount of matter that makes up an object.
That idea served well for a couple of hundred years, and still does for most practical purposes. But it's actually more complicated. For objects moving at higher and higher relative speeds, it becomes less and less accurate. What you're referring to is nowadays known as 'rest mass' (it might help you to understand if you look that up).
what I have a problem with is how people seem to think that the mass of an object will grow as the object speeds up , and even infinitely as it reaches or achieves the speed of light.
As I'm sure you know, Special Relativity has been around for over 100yrs. It's demonstrated every day in the world’s particle accelerators. It's not just a case of what some people (like Einstein) seem to think.
Maybe this will help:
The famous equation E = mc^2 means that a body's relativistic mass is proportional to its total energy.
It also means m = E/c^2.
Here's a version that includes momentum:
m = (SQRT(E^2-(pc)^2))/c^2
Where
m is mass
E is the total energy of the system
p is the total momentum of the system
c is the speed of light.
Which shows that the mass, m, increases as the momentum, p, increases.
If it's not immediately obvious, maybe you could try typing the right side of that equation into a spreadsheet and using any numbers you like for the variables. You'll find that an increase in p gives an increase in m.
You have doubts. No problem. But base your doubts on sound knowledge. Read all you can about it from recognisably reputable sources. Whatever you do, don't just take the word of forum posters like me.
