At which time in history did most of the nations of the middle ages reach the levels of knowledge and skill that the Romans had at their peak.
I have heard it said, but have no idea if it is true, that it was not until Victorian times.
It depends what you mean by “reach the levels of knowledge and skill”. There was some stuff, like how to make concrete, that didn’t get rediscovered until the 1500s-1600s. But there were other technologies where the Medieval world surpassed the ancient Romans. The Romans never knew about fractional distillation, for instance. That wasn’t developed until the 13th century.
Some agricultural innovations, such as the horse collar and heavy plow, were created in the early middle ages (6th to 8th Cen) and were a definite improvement over old Roman techniques and technology. Other techniques, like some types of fruit tree grafting, were lost after Roman times and not rediscovered for centuries.
To paint it with a broad brush, I would say the Renaissance.
I’ve always been intrigued by some lines fromA History of the English-Speaking People. I’ve no idea if they’re valid, or the great P.M. was just “smoking something.” 
[QUOTE=Winston Churchill]
[under Roman rule] well-to-do persons in Britain lived better than they ever did until late Victorian times. From the year 400 till the year 1900 no one had central heating and very few had hot baths. A wealthy British-Roman citizen building a country house regarded the hypocaust which warmed it as indispensable. For fifteen hundred years his descendants lived in the cold of unheated dwellings, mitigated by occasional roastings at gigantic wasteful fires. Even now a smaller proportion of the whole population dwells in centrally heated houses than in those ancient days. As for baths, they were completely lost till the middle of the nineteenth century. In all this long, bleak intervening gap cold and dirt clung to the most fortunate and highest in the land.
[/QUOTE]
How about crop yield per acre/hectar? I’d think as knowledge was lost in the middle ages they would get much less crop yield. Or is that incorrect?
It is correct for the early middle ages, where crop yields do seem to have dropped. This was probably less due to technological decline, than political and social disruption that led to the dissolution of the old Roman agricultural system which was characterized by huge landowners and exploitation of mass slave labor.
However by the high middle ages new technology ( as noted by Hypno-Toad above ) allowed European agricultural yields to surpass earlier Roman yields. So you had a dip in the post-Roman era, but a recovery and advance beyond Roman capacity long before the Renaissance rolled around.
In 1586, Domenico Fontana moved a 327 ton Roman obelisk in St. Peter’s Square in the Vatican. He used 900 men, 75 horses, and lots of rope, pulleys, and scaffolding. According to a history of science that I once read, this was considered to be the greatest engineering achievement since Roman times and a huge confidence booster for European civilization. Before that, it was claimed, they were in awe of the Roman achievements and did not think they could do anything comparable.
Sorry for veering completely off-topic, but at 280 tonnes (310 tons?) Le Grand menhir brisé in Brittany was nearly as massive as the Vatican Obelisk, was moved 12 kilometers from its quarry almost 7000 years ago and is thought to have remained upright for seven centuries.
Likewise, I’ve heard that finding the general solution to cubic equations (in the 1500s) was seen as a startling advance beyond the math of the classical era.
Yes, that is amazing.
I can’t comment on the technical merits of those neolithic engineers relative to Fontana. He had the benefit of better public relations (not to mention a mandate from the Pope). He wrote a book about it, paintings were made, and it became known as one of Italy’s greatest engineering achievements.
And there was at least one area where the Europeans surpassed Roman technology early on: the stirrup, which some argue completely changed the value of cavalry in battle.
For more information on the stirrup than you would have thought possible, see the wiki articles on the stirrup, particularly the Great Stirrup Controversy:
So to sum up, just a bit:
As several people have pointed out, one should be wary of casing the Roman period as an age of technological marvels. You can find individual technologies that were lost, some of which were indeed quite impactful. But in general the rhetoric of the “Dark Ages” in historiography has resulted in these losses being a little overemphasized in the popular imagination.
It was not a matter of most everything being lost in a cataclysmic fashion, only to be discovered centuries later. In many fields - like for example mining technology, agriculture and metallurgy - medieval Europeans technology continued to develop ( or adopt/adapt from elsewhere ) and eventually outpaced their classical forerunners.
Medieval Europe vastly outpaced Roman finance. Medieval Europe had public finance, a credit economy, and sophisticated legal institutions to support overseas commerce.
Maybe in the Renaissance, not the Middle Ages per se. Roadmaking is another technology that was lost after Rome and not rediscovered until recently.
I’m not sure if you were replying to me, but if so, that’s false. The commercial changes in the Middle Ages were certainly more revolutionary than in the Renaissance. Even basic modern commercial concepts are medieval or origin. The word mortgage itself is medieval. Le gage mort was a credit agreement, with or without security, that could be paid off over time. In other words, the agreement died (hence mort) when the loan was repaid. The medieval gage vif, or living loan, was a revolving credit agreement.
The Romans never had anything like the Champagne fairs nor the institution of the law merchant. Some of this sophistication actually disappeared in the Renaissance when states became more viable economic actors with the paper to enforce long-distance transactions. Medieval merchants were able to do it without third parties thanks to their incredibly sophisticated institutions.
Medicine was problemactic.
Roman Military surgeons cleaned their tools with fire, & used wine (alcohol) to wash woulds. Used cleaned bandages, too.
I cite Legionary: The Roman Soldier’s (Unofficial) Manual by Philip Matyszak PhD.
What have the Romans ever done for us?
They went home.