Why did the Israelites build a golden calf while Moses was on the mountain?

According to the Book of Exodus, the Israelites built a golden calf because they feared that Moses, who had left them for forty days and nights to go up Mount Sinai, would never come back, and they demanded that Aaron make them "a god who shall go before us". Aaron had them bring their golden earrings and ornaments, made a calf, and declared it the god who had brought them out of Egypt; the people offered sacrifices, feasted and danced.

When Moses came down and saw the calf, he broke the stone tablets he was carrying in anger, then destroyed the idol completely: he burned it, ground it to powder, scattered the powder on water, and made the Israelites drink it. The tribe of Levi had refused to take part in the worship, and at Moses' command they carried out a mass execution in the camp, killing about three thousand people that day.

The story echoes forward in the Bible. Centuries later, King Jeroboam built two golden calves of his own and set them up at Bethel and Dan, telling the people these were the very gods who had brought them out of Egypt, in language scholars note is almost identical to what Aaron's people had said. Some even see a trace of that connection inside the original story itself: Exodus 32:4 oddly refers to 'gods' in the plural, even though only one calf was built, perhaps echoing the two calves of the later Jeroboam story.

The Quran tells a related but different story. There, the Israelites grow restless after Moses fails to return, and a man named Samiri stirs up doubt and fashions the calf from their gold, while Aaron tries to warn the people against worshipping it rather than building it himself. In the Islamic view, their sin was shirk, worshipping something other than God. Centuries later still, the apostle Paul pointed back to the same episode in his letters, warning early Christians not to become idolaters as the Israelites had been.