Is matter infinitely divisible or not ?

No, because if you break it up too much, it becomes energy. To my understanding, energy is not considered to be infinitely divisible under our current understanding of physics, but that might be just that we haven't discovered divisions below a certain size. If I had to guess, I would probably say that energy is not infinitely divisible, but I do not know.

Logically speaking its possible 🤯

Is this kind of like saying the increasing number of equal-length sides a geometric figure gains as it "evolves" (starting as a triangle which then becomes a square then a regular pentagon... on and on until, FINALLY, it becomes a circle) is the final outcome of reaching the most minute matter?

I know that what was once thought of as indivisible, like an proton, is now regarded as divisible into quarks.

I find it hard to imagine that subatomic particles, even if they can be broken down further, can be infinitely divisible. In fact, i wonder if quantum uncertainty would play a role: would we ever know for sure that the particle had divided? ( I have only an informal acquaintance with quantum mechanics, so what I just said might be nonsense!)

But if they could be infinitely divided, that would actually be pretty wild!

Then there is another possibility, that a physicist friend likes to remind me of. Namely, all of particle physics might be nothing more than an elegant mathematical model that explains observed phenomena very well, but it might not be literal reality at all. In face, he would say that about physics in general. He is prone to utter things like, "When you ask what 'really' happens, I have no idea what you mean!" Needless to say, he is a theoretical physicist!

(My background: I am Christian, but I don't see the relevance of that to this discussion.)

I think there is a limit. There are elementary particles and discrete quantum states.

No, matter is not infinitely divisible. Molecules and atoms are the smallest units of the substances we are familiar with; quarks are the smallest units that make up the particles of which atoms are composed.

We can detect if particles have smaller subunits by smashing them together and seeing what scatters and how. Electrons behave like perfect point particles; protons don't. But the quark constituents of protons do.

This probably doesn't make sense but I think as they keep on dividing particles into smaller states, the idea of dividing further will be irrelevant; they will cease to be particles or even matter as we know it at all.

Since you aren't really defining matter, I'll assume on the particle level, don't they divide constant? So if they do, doesn't that make them divisible? I guess we get to find out, don't we? We are all particles, how long can they divide?

no, subatomic particles cannot be divided; they only create new particles in subatomic annihilations; and in greater quantities, undergo nuclear transmutation (matter to energy, energy to matter conversion)

I think you can get to a zero poin

Matter has structure, even a quark has structure, and a structure is divisible... we can't at the moment say there is a point where matter can no longer be divisible.

My thought is that even that could change if we discover there is another universe(s).

It cant be created or destroyed right? So its gota go somewhere

Impressive question. BlueVeins and wildbill83 nailed it!