The lecturer who was teaching me didn't go into the trouble of explaining what Bravais lattices are and instead jumped right into the types of Bravais Lattices in 2D and 3D. Trouble is, without understanding the concept, I can't move forward with Solid State Physics.

Below, I explain what I understand so far, I would request you to point out anything wrong in there.

Now, I know

Bravais Lattices are a periodic arrangement of lattice points such that they are translationally symmetric. These lattices have even distances between consecutive lattice points and they have the same surroundings.

Question 1: I don't understand why there are only 5 types of Bravais lattices, I mean, why that particular number? I asked this question to ChatGPT and here's what it said:

*Q: now why are there only 5 2d bravais lattices?

A: There are only five 2D Bravais lattices because they are the only unique ways

to arrange points in a 2D plane with translational symmetry.

In general, a Bravais lattice is defined as a mathematical framework that

describes how points in space are arranged with translational symmetry.

In 2D, a Bravais lattice is defined by two primitive lattice vectors

that span the lattice. The shape of the unit cell is determined by the

primitive lattice vectors and the lattice symmetry.

Now, I know better than to take ChatGPT's word for it. So, I need your help to verify it. Is it right in everything it had said so far. Can I know how Bravais discovered these 5 lattices to be the only bravais lattices?