Making bread without sugar is nothing strange - I do so several times a week!
The wheat flour (or whatever you're using) contains enzymes which, when you blend it with water, breaks down starch to sugars which fermenting agents such as yeast or lactobacilli can feed off.
The Wikipedia page on sourdough has more info.
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I assume, by sugar you mean sucrose .
However, yeast actually prefers glucose and maltose, see nutritional requirements of Saccharomyces cerevisiae and also proofing .
Luckily, we get glucose and maltose "for free" from the flour, see this article on bread chemistry :
Flour naturally contains both α- and
β-amylases, which between them break down some of the starch in the dough to the fermentable sugars, maltose and glucose The short answer is thus, bread does not need additional sucrose, as the maltose and glucose we get out of the flour is already sufficient for the job.
On a sidenote, as other answers mention, basic bread dough does not call for sugar in the recipe.
Technically, by adding sugar you get an enriched dough (a dough with additional sugar, syrup, butter, oil, eggs, milk, or cream, etc. is called an enriched dough).
In this case, the sugar is added for achieving a specific effect, most typically making the dough sweeter or also more tender see
What is the purpose of sugar in baking plain bread?
and this article and also this paper .
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You do not need sugar to make bread.
The majority of traditional, rustic breads use just 4 ingredients - water, yeast, flour, and salt.
Consequently, rising times are slower (usually resulting in better flavour) and the bread goes stale quicker (hence, for example, the French practice of buying fresh bread every day).
Sugar softens bread by slowing gluten development - contrast a soft white sandwich loaf with a rough French baguette - and at a certain level acts as a preservative, but is by no means essential.
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Sugared bread is something mostly specific to the US.
There might be a little sugar in European bread, but not much.
From a personal opinion as a Belgian, I have to say that the few time I ate sugared bread (Harry's American bread), I found that it completely ruined the taste of the condiment on my bread, as well as make the bread less suitable to be used in a toaster.
And I'm not alone, because I've heard a number of immigrants from EU to US say that they didn't like the bread in the US and had to go to specialty bakers to get sugarfree bread.
So not all modern bread recipes contain sugar.
And as others said, we had non-sugar sweeteners in older days.
Raisin bread, honey bread and milk bread used to be common and are still eaten in a number of European countries during certain periods.
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I would assume the sugar is added for more "optimized" and foolproof bread making (industrialized)
It is not necessary at all.
Also in the "old time", people had access to other types of sugar ( honey,fruits, ... ) and as far as I known, big fluffy bread is quite recent in the history of time.
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Yeast can start faster given simpler carbohydrates (not just plain sugar but also milk sugar and dextrose).
However, it breaks down starch into such simpler sugars with some of its enzymes anyway.
Since most of the leavening is supposed to happen after the loaves have been properly worked and formed, fast fermentation is not all that desirable anyway for achieving consistent leavening without holes or boils.
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They used malted barley (diastatic) flour--just a little goes a long way--and is usually present in "bread flour".
It makes bread rise as the yeast feed upon it.
Also, you can use a starter (called a polish or biga in Italian (though they are slightly different from each other), an active yeast culture maintained separately from a bread recipe but that is used for making bread.
Similar to sourdough starter, but a biga only takes a few hours, while sourdough takes days.
Biga is not sour, though it is fermented a bit, which causes a better rise.
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Modern recipes (as far as I know) for bread includes sugar.  Sugar gives the yeast a food source, which supports it growth and allows yeast to give bread many of its qualities.  It hit me the other day that sugar (produced from sugar cane) is a relatively new commodity.  People did not have this kind of sugar 1000 years ago in Europe, the middle east, etc.  How did they manage to make bread without it?
How did people make bread before sugar was 'discovered'
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<bread><sugar><yeast>
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Sugar is not necessary to make bread, although it does slow down gluten development and act as a preservative. Many European breads use little or no sugar, and may have a starter, sweet ingredients like honey, milk and raisins or malted barley flour. Sugar is not essential to bread making. Traditional recipes do not contain sugar, except in the US. In the past dried fruit, honey and malt flour were used to enrich the dough or a biga [starter] was used to cause the rising.
Sugar is not needed to make bread and not all modern recipes contain sugar. European bread has little or no sugar. Sugar in bread is mainly an Amrican tradition. Alternatives to sugar in bread-making include honey, dried fruit, malted barley and biga or Italin starter.