I would first try to chip them off with a thumbnail, then rub/polish the area with some cheesecloth and mineral spirits.
A harsher solvent would take off the latex faster, but also the finish on the mahogany which would probably be difficult to spot repair.

What finish is on the mahogany?

try Goof Off (first on some part of the finish that is hidden). I've had success with it on a pretty wide variety of solvent-based finishes and it takes the latex off without any risk of scratching the finish below. (Made the mistake of letting my daughter paint her room unsupervised, got to remove latex paint from lots of different surfaces!) If the finish on the mahogany comes off or gets sticky in the test spot then try a different route.

Goof Off is overpriced xylene in tiny containers.

Fresh latex may come off with just rubbing alcohol (use the 90% stuff) from the drug store.

You really should try to determine what the finish on the item is first.

Latex on varnish is not that hard to remove (varnish is pretty solvent resistant).

Latex on shellac is likely to result in a new coat of shellac to repair the finish after removing the latex (the water in latex damages the shellac under the paint spot, and shellac is easily damaged by solvents)

they do sell latex paint remover in home depot that comes in a spray bottle.

"Goof Off is overpriced xylene in tiny containers."

Actually it's mostly acetone according to the MSDS (acetone + xylene + ethylbenzene). At around $25/gallon it's not that much more expensive than xylene paint thinner or hardware store acetone (about $18-20/gal these days at the Borg) and the mixture of solvents seems to work better in my hands. Pretty much any solvent in tiny cans is going to be expensive, but if you don't use much the cost of properly disposing of the leftover amount from a big can can be much more than the purchase price.

They must have added the acetone lately.

it used to be almost straight xylene from an old MSDS sheet I have.

Acetone will do a LOT of damage to many other finishes.

It is far worse than xylene.

Unless the OP wants to figure out what the finish is, they can just keep shooting in the dark and see what damage occurs.

Gof Off 2 looks very differet.
3. Composition/Information on Ingredients
Hazardous Components (Chemical Name)
Ethanol, 2-Butoxy- (Ethylene glycol n-butyl
ether, (a glycol ether))
111-76-2
CAS #
3.0 -7.0 %
Concentration
1.
2. Benzenemethanol (Benzyl alcohol) 100-51-6 5.0 -10.0 %
Diethylene glycol monobutyl ether
(2-(2-Butoxyethoxy)ethanol ((a glycol ether))
3. 112-34-5 1.0 -5.0 %
4. Propylene glycol phenyl ether ((not 313)) 770-35-4 1.0 -5.0 %

Here is a link that might be useful: Gof Off 2 (GO2)

This post was edited by brickeyee on Tue, Apr 2, 13 at 14:27

It's certainly helpful to know what the finish is, I can't disagree. However, I most often figure that out by asking which solvents soften or dissolve the finish by testing them in as hidden a spot as I can find. This works pretty well for shellac (dissolves in alcohol), lacquer (lacquer thinner), and water-based finishes (xylene), but beyond that in the world of urethanes, catalyzed lacquers and epoxies it gets tough. But then it's pretty easy to get latex paint spots off those tough finishes without damage with xylene, toluene, or probably any number of other solvents.