Alchemist's Greeting

Cards are discarded in a Magic game only from a player's hand. Effects that put cards into a player's graveyard from anywhere else do not cause those cards to be discarded.

Madness works independently of why you're discarding the card. You could discard it to pay a cost, because a spell or ability tells you to, or because you have too many cards in your hand during your cleanup step. You can't discard a card with madness just because you want to, though.

To determine the total cost of a spell, start with the mana cost or alternative cost (such as a madness cost) you're paying, add any cost increases, then apply any cost reductions. The mana value of the spell is determined by only its mana cost, no matter what the total cost to cast that spell was.

If you discard a card with madness to pay the cost of a spell or activated ability, that card's madness triggered ability (and the spell that card becomes, if you choose to cast it) will resolve before the spell or ability the discard paid for.

If you choose not to cast a card with madness when the madness triggered ability resolves, it's put into your graveyard. Madness doesn't give you another chance to cast it later.