We know now that Mohamed Lahouaiej Bouhlel, who killed 84 people and injured many more in Nice, was 31, getting divorced and living in a working-class neighbourhood euphemistically described in the French press as "mixed".
He was an immigrant, as are most of his neighbours. One described him as a blédard, a hick from the old country - in his case Tunisia.
Taciturn, Lahouaiej Bouhlel scared the neighbours and was prone to angry outbursts. He beat his wife and was recently convicted of an assault on a motorist.
He had a record of petty crime and a possible history of depression, but no known links to radical ideologies or networks.
French investigating authorities have various theories about the attack. An inquiry into "terrorist mass murder" has been opened, but prosecutors admit that for the moment there is no evidence of ideological motivation.
Yet there has been a claim of responsibility from Isis (Islamic State) and there is evidence of premeditation. The use of a vehicle, the target, and the fact that the attack took place on the highly symbolic Bastille Day all suggest a jihadi operation.
Lahouaiej Bouhlel certainly matches the classic profile of French violent Islamic extremist in many ways - though he is a relatively recent arrival rather than born in the country of immigrant parents, as is more usually the case.
He was a young, male petty criminal. He was also not devout, all witnesses so far agree. He did not fast during Ramadan, ate pork, drank, and was never seen at any local mosque.
This lack of piety among militants may seem confusing. It is, however, the rule rather than the exception.
It was true of the dozen or so French and Belgian young men involved in bombings and shootings earlier this year, and of Mohammed Merah, who committed the first major attack in France in 2012.
Other examples beyond France include that of Omar Mateen, who killed 49 in a Florida nightclub last month.
This apparent paradox has prompted a keen debate among experts. The argument has major policy implications. In France, it has been bitter.
Olivier Roy, a well-known French scholar currently at the University of Europe in Florence, suggests those drawn into violent activism are already "in nihilist, generational revolt".
This is why so many are criminals, or marginal. Extremist Islam gives them a cause and frames anger and alienation in the way extremist leftwing ideologies did for some in the 1960s and 1970s.
The new militants are thus not victims of "brainwashing" by cynical and fanatical recruiters. This is the Islamisation of radicalism, Roy says, not the radicalisation of Islam.
Many disagree. Some say Roy naively ignores the impact of intolerant and reactionary doctrines on Muslim communities in the West.
Others suggest he underestimates the historical impact of Western colonialism as well as that of more recent Western policies in the Middle East.
The case of Lahouaiej Bouhlel will now be picked over by the academics as intensely as by counter-terrorist experts and detectives. All will be focusing on the range and extent of his contacts with other people. Again perhaps counter-intuitively, the more numerous those associations, the more worrying this attack may be.
There are various possibilities.
1 THE ILL LONER
Lahouaiej Bouhlel may be a genuine loner and suffering serious mental illness. His act may have no ideological element at all. This, however seems unlikely.
2 INSPIRED BY EXTREMISTS
A second possibility is that, already angry and violent, he was inspired, if not directed, to commit his attack by Isis or extremist Islamic militancy more generally.
As in the case of Mateen, this would indicate the continuing power of the group's ideology. In this case it is almost certain he will have some contacts with others involved in hardline Islamic activism in Nice or its surroundings.
Police have now detained five people, including Lahouaiej Bouhlel's ex-wife. This scenario is more alarming, suggesting the possibility of more attacks to come.
3 PART OF ISIS CELL
Finally, Lahouaiej-Bouhlel could have been part of the continuing series of attacks on France run by Isis from Syria since 2014.
All have involved recruits being tasked with strikes by more senior leaders in the organisation.
If true, this would indicate that Isis has continuing capacity for ambitious terrorist operations in Europe despite the pressure the group is under. And that would be a highly concerning prospect.