Battlefield Thaumaturge — ruling 1

Battlefield Thaumaturge's first ability doesn't change that spell's mana cost or mana value. It changes only the amount you actually pay (the “total cost” of the spell).

Battlefield Thaumaturge — ruling 2

To calculate the total cost of an instant or sorcery spell you're casting, start with the mana cost (or alternative cost, if applicable), add all cost increases (including additional costs such as those imposed by strive abilities), then subtract all cost reductions (such as the one created by Battlefield Thaumaturge's first ability).

Battlefield Thaumaturge — ruling 3

The cost reduction created by Battlefield Thaumaturge's first ability can reduce only the generic portion of the spell's total cost. Colored mana requirements aren't affected.

Battlefield Thaumaturge — ruling 4

The cost reduction is {1} per target creature, even if the spell targets a creature more than once.

Battlefield Thaumaturge — ruling 5

Heroic abilities will resolve before the spell that caused them to trigger.

Battlefield Thaumaturge — ruling 6

Heroic abilities will trigger only once per spell, even if that spell targets the creature with the heroic ability multiple times.

Battlefield Thaumaturge — ruling 7

Heroic abilities won't trigger when a copy of a spell is created on the stack or when a spell's targets are changed to include a creature with a heroic ability.

Battlefield Thaumaturge : règles, fonctionnement et interactions (MTG)

Battlefield Thaumaturge is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Each instant and sorcery spell you cast costs less to cast for each creature it targets. Heroic — Whenever you cast a spell that targets this creature, this creature gains hexproof until end of turn.

How it works : Battlefield Thaumaturge

Original English text — Wizards of the Coast / Scryfall

#1April 26, 2014· Wizards of the Coast
Battlefield Thaumaturge's first ability doesn't change that spell's mana cost or mana value. It changes only the amount you actually pay (the “total cost” of the spell).
No other card is named in this ruling.
#2April 26, 2014· Wizards of the Coast
To calculate the total cost of an instant or sorcery spell you're casting, start with the mana cost (or alternative cost, if applicable), add all cost increases (including additional costs such as those imposed by strive abilities), then subtract all cost reductions (such as the one created by Battlefield Thaumaturge's first ability).
No other card is named in this ruling.
#3April 26, 2014· Wizards of the Coast
The cost reduction created by Battlefield Thaumaturge's first ability can reduce only the generic portion of the spell's total cost. Colored mana requirements aren't affected.
No other card is named in this ruling.
#4April 26, 2014· Wizards of the Coast
The cost reduction is per target creature, even if the spell targets a creature more than once.
No other card is named in this ruling.
#5April 26, 2014· Wizards of the Coast
Heroic abilities will resolve before the spell that caused them to trigger.
No other card is named in this ruling.
#6April 26, 2014· Wizards of the Coast
Heroic abilities will trigger only once per spell, even if that spell targets the creature with the heroic ability multiple times.
No other card is named in this ruling.
#7April 26, 2014· Wizards of the Coast
Heroic abilities won't trigger when a copy of a spell is created on the stack or when a spell's targets are changed to include a creature with a heroic ability.
No other card is named in this ruling.