Yesterday's toss-off post, which quoted Daniel Fromson saying "beer’s third-most-important ingredient, after water and barley..." raises the question: which is the most important?
Hops, obviously, are out. Beer was made for millennia before anyone thought to toss hops in. (Along the way, they tossed just about everything else in, too. Everyone who thinks bog myrtle should be in the top five most important, raise your hands.) Beer is so simple to make that the ancient proto-Sumerians were able to shake a few stalks of wild grain into a bowl of water and let stand for a few days. It probably wasn't tasty, and it surely wasn't very alcoholic (though even before civilization dawned, those crafty pre-historical brewers had invented malting), but it was beer. Ish.
So grain and water are in. What about yeast? One could argue, and this one might, that yeast is not an ingredient so much as a helper. A microscopic brewer who finishes the job once all the conditions have been met. This is nevertheless a controversial position. When yeast does its thing, it creates all kinds of chemical compounds that remain in the beer. These become ingredients--and essential ones in many styles--so I guess we have to keep yeast in, too.
To make good beer, tasty beer, though--that's another matter. Water is wholly beside the point. As long as you have it, you have beer. Brewers can adjust water's chemistry to look like classic profiles or to compensate for hardness, pH, etc. Even homebrewers can amend water to meet their needs--its effect on the final product is easily the smallest.
The remaining three ingredients play different roles in different styles of beer. Hops play next to no role in lambics, but they're the whole ball game in IPAs. The same is true of malt and yeast, depending on the style. That is, in fact, the wonder of beer as opposed to, say, wine. Beer is constructed of ingredients. Depending on the recipe, you may emphasize one or another element.
The answer to the question: none. Or all--take your pick.
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