It's pretty obvious why peace is a necessary ingredient, firstly the breadth of invention in peace time is wider.

In peace time people invent things for peace and for war, in war time the focus is all on inventing things for war. Screw everything else.

Later on, after the war is over, it may turn out many of the things that were invented for war may also have uses for peace, this however is perhaps not always the case. I don't think the inventions of the first world war that spring first to my mind had a lot of utility beyond war.

The second obvious reason why peace would be a necessary ingredient is the cause of all that inventiveness around creating things for war, it's because in war you are in danger all the time of being killed, which is why when you are not hiding somewhere trying not to be killed you are trying to make things to kill the other guy because if you kill the other guy they can't kill you. If you get killed however, that will be a big dampener on your ingenuity.

Some people might think differently about this state of war, because of historical blindness and the inefficiencies of the English language. If a country is big and powerful enough it can go to war elsewhere, and never have the war touch it.

This is not really war as it has been known in most of the history of humanity, but we call it war. It is really a time of peace in the homeland, and distributed external war.

And in this time of peace in the homeland, people can work peacefully without fear of being killed, and then people who think that this is war say - hey, check it out, peace is not needed for invention and progress at all!

Primarily because war reduces access to certain goods. Certain ideas that could work, need to be tossed due to the war's needs or effects on goods/services.

But do those outnumber the "Einstein being bored as patent clerk" type situations? How many bright minds people died as children or soldiers in those wars? Does war spur inventions, or does it concentrate forces and effort to put things into production that were invented by minds that had to have some peace, sleep and food, at some point, to come up with the kernels of what the war machinery turns into weapons and supplies?

It's probably a bit of both, IMO. I don't doubt that pressure and threats to survival can also make people snap out of ruts they have been in, and look for something beyond what they already know. But I still would say you can have inventions without war, but you cannot have them when there is nothing but war. And my argument would be that the extreme of that would be someone who gets screamed at and beaten from the moment they were born, and lives in constant state of war. They will not be able to find the rest and perspective to invent things, they may not even survive.

Much of human innovation arises out of leisure interests where no immediate demand or need exists. Mathematics for example initially arised out of people with leisure time who found some hobby to do.

Think about it. Math is a hobby, practically useless. But it benefited humanity with side effects like engineering and computers.

Now to your point. Because math is initially a pretty useless endeavor it can only arise as a leisure hobby. A leisure hobby can only arise in people who have tons of leisure time and have no need to fight for survival. Thats why peace time is important.