https://www.youtube.com/watch?v=xf9cDKqw...
As for the United States - there is a clue in the Declaration of Independence which speaks of "life, liberty and the pursuit of happiness." Where did that bit about the 'pursuit of happiness', come from? Socrates, who created an entire philosophy wherein anyone can have a life of happiness.
http://www.pursuit-of-happiness.org/hist...
Now for the science - the Greeks had the world's very first working computer - we think created by Archimedes.
https://www.youtube.com/watch?v=Ubjfcikv...
But that's not all - the Greeks invented 'printing' some 4000 years ago, but for reasons not explained they abandoned it. Probably had more pressing issues to deal with.
https://uk.news.yahoo.com/mystery-of-4-000-year-old--cd-rom--is-solved-140139939.html#DdSGMmL
We have a Hell of a lot of catching up to do.
London UK
Greek society inspired achievements that shaped the foundation of Western civilization. The Greeks were intelligent, daring, energetic and sensible, accomplishing great feats in the arts, philosophy, architecture and more. The Greeks introduced our cherished concepts of citizens' rights, democracy, and freedoms of speech and religion. They excelled in mathematics, physics and astronomy. The Greeks had a highly developed spiritual life, imparting human traits to their many gods and goddesses.
Early physicists were mostly concerned with the workings of the heavenly bodies. Greeks in the fifth century B.C. came up with theories about the planets and their movements, but they did not subject them to tests and experiments. Their elegant statements about the universe turned out to be mostly wrong. In all fairness, Aristotle, a Greek philosopher-scientist who lived in the fourth century B.C., laid the foundation of empirical science, but the more reliable Scientific Method was still more than 1,000 years away [source: Experiment-Resources]. He may be justifiably famous for writing the first books on physics; yet his speculations, which were widely adopted by scientists for a long time afterward, were often based only on observation and were generally incorrect.
Eratosthenes, who lived in the third century B.C., used principles of math and physics to arrive at a rough but pretty accurate measurement of the Earth's circumference [source: PBS]. Around the same time, Archimedes discovered that submerging a solid object will displace an amount of liquid that matches the object's weight. And if you think the Greeks don't still play a role in modern science and math, just check out the symbols often used in physics and higher math equations; many of them are derived from the Greek alphabet.
The architectural influence is certainly the obvious one. It can be seen on many Federal and private buildings all over USA.
However, the main influence is the idea of Democracy, that originated in old Athens and is practiced in all levels of government in USA.
It's been a while but I believe something of the U.S.'s government is based off of Greece (may have been Rome actually now that I think about it...) But one thing that is certain is architecture. All those fancy pillar structures you see on/in government buildings? Greek. (In origin)