Whenever one speaks about removing a structural element (column or beam), the initial hypothesis must always be:
NO! GOD NO! WHAT ARE YOU DOING!
The second hypothesis must always be:
No. No. No. No.
That being said, it can be done. But it is not trivial and requires a serious investigation by a structural engineer. This is a "last resort" issue.
Those columns are transferring a load from the beam which can clearly be seen on the ceiling to the foundation. If you remove the columns, then the beam will have to be able to take that load and transfer it across the room to the columns in the walls. The forces the beam will have to withstand will be multiplied many times (possibly 45 times, according to a simplified model).
So, with all certainty, if you simply remove the columns, the beam will collapse and probably take the rest of your house (this is the basement after all) and you with it.
So, you'd need to effectively redesign the structural layout of your basement. Without columns, you'll need to replace the current beam. That's basically a given. Then you'll have two choices:
- Place a much stronger beam in its place, capable of withstanding the increased forces. This almost certainly implies in an increase in beam height (and therefore reduction of usable height under the beam) since beam strength is proportional to the cube of the height.
- Place a grid of multiple beams (parallel and perpendicular to the current beam) on the ceiling, so that each beam absorbs a very small load and is capable of transferring it across the room. This has the additional issue that you'd need to know where the columns (or structural walls) in your wall are: if you don't have many places to rest your beams, your grid won't be efficient.
There are then a bunch of issues of how to make the beams and the ceiling slab work in tandem to improve the beams' efficiency and to certify that the slab isn't "floating" over the beam, how to tie your new beams to the columns (if the beams are of concrete), limiting deflections and vibrations so that your dinning room doesn't sink or feel like a rock and roll concert when your cat walks over it, how to safely remove the existing columns and beam prior to doing your new layout, etc...
So yes, you can do that. But are you really, really, REALLY, REALLY sure you want to?