According to many hadiths in Sahih Muslim, it is clearly forbidden, so it is haram. You can see them here.
According to Quran, there is no mention about paint, painting or painters. You can search the word "paint" in the same link I gave with any English Translation. Here is the result, nothing. I also checked in the Turkish Translation of Quran, there is no mention about the word "paint".
Again according to Quran, there are 5 verses about "statue", while in some translations like Sahih International it is not translated as statue, but we can understand from meaning what they are.
As you can see, there is nothing about forbidding painting or making statues in Quran. Also we may deduce from 34/13 that, making statues itself is not haram.
We can logically conclude that making pictures or statues contradicting the principles of Islam such as nude(naked), making sexual intercourse, rendering a sin, with the purpose of worship etc is haram, because of obvious reasons.
As a principle, anything not mentioned in the Quran as haram, is halal. But forbidding painting and statues of living things (especially humans) is also logical when we look at the today's Christians. They mostly put Jesus(puh)'s paintings and statues in churches and asking help from him instead of Allah. They are behaving like him as God and any Muslim in future may fall into the same mistake. But there were people who worshipped to sun, we can't forbid to see sun, because it is illogical. Yet paintings and statues have a far more potential to be worshipped. I think, while there is such treat, it may be forbidden for a time, but not permanently.