Another thing I learned: Most engineers can build something that works. It is much, much harder to build something that optimizes for cost.

“Anybody can build a bridge that stands - it takes an engineer to build a bridge that barely stands.”

This brings to mind my amusement when friends would bash Ikea cabinets as too flimsy. I was struck that they were just strong enough to do what they claimed. No more.

Everyone loves to shit on value engineering but the reality is that it's a lot harder and takes a lot more craftiness than designing things under less price pressure. When you start talking about revisions to complex things where you have to both work fast and avoid revising too much of the thing (to keep costs down) it gets really crazy.

And it takes an architect to build a bridge that rarely stands...cf. the millennium bridge in london. Designed by architects, fixed by engineers.

You do know that the architects hand off their work to structural engineers on anything more complex than a single pavement building before it gets built, do you?

To be fair to the architects of the Millennium Bridge, the structural engineers used a vehicle bridge model, not one for pedestrians.

Multiple comments seem to imply the Millenium Bridge has some really egregious design flaw. So I'm curious: what is it?

It has a resonance mode at 2Hz, now successfully damped. Bridge designers know to look out for resonances at those frequencies, because pedestrians tend to identify and accentuate them by walking, especially in large numbers immediately after opening. The resonance mode wasn't identified during design because unusually it is in the horizontal plane - most bridge designs have very slow resonances in that plane (sway) but the millennium bridge is a side mounted suspension bridge, with the pylons alongside the roadway.

This video explains the problem - it is worth watching the entire video. If you are pressed for time jump to 15:00 mark https://www.youtube.com/watch?v=t-_VPRCtiUg

In 99% of cases yes, but the millennium bridge was a special case.

Or a tower that has trouble standing... the millennium tower in San Francisco.

Designing to fit requirements is easy.

Making it scale economically is where all the math gets involved.