"Any two points can be connected by a straight line." Euclid
Upon this, the very first of his 5 axioms, Euclid built his entire system of mathematics called geometry.
Make any two points, anywhere in the universe, no matter how far apart, and it is physically possible (though not always technically feasible) to draw a perfectly straight line connecting the two of them.
We might say it differently, "The shortest distance between two points is a straight line." On the surface we conclude that this must be true, as anyone can plainly tell upon first glance. Common sense would say, "It's obvious. What else could it be? It's a proven certainty!"
Euclidean geometry, with its postulates, theorems and proofs is founded upon the above axiom, which though apparently not needing to be proved (cuz common sense says so), is nevertheless still an assumption!
Additionally, the above axiom/assumption was also in back of Newtonian physics. From a simple assumption mathematical systems have been created, sytems which have helped us to "grow up" in our understanding of the universe.
But wait a minute! How can we say we truly know something for certain, when at its foundation is something uncertain and unprovable? Wouldn't such a system of knowledge be false, wishful thinking, even a fairy tale?
Hmmmmm! Well, we've built sky scrapers and sent men to the moon...and done so by trusting that assumption. Certainly the unproven must be trustworthy? I guess you could say that trusting the assumption has worked for us, and that the knowledge gleaned from such trust has confirmed the truth of the assumption. And we could also say that our faith in the unprovable foundations of reality has led us to deeper knowledge of that reality.
The statement, "Prove it to me and I will believe" would not have allowed Euclid to move forward and develop his system of mathematical knowledge we know as geometry. The same could be said of Newtonian physics which tells of objects in motion staying in motion unless acted upon by an outside force...and will travel in a straight line. Newton too assumed Euclid's assumption was trustworthy.
At its most elemental level, mathematics begins with a faith assumption, and not a certainty, a faith which leads to higher knowledge.
By the way, the shortest distance between two points is not a line. Euclid's assumption helped us to "grow up" in our understanding, but there is still a higher knowledge which his simple assumption paved the way towards. It took a guy named Einstein to perceive more deeply, also on faith, that Euclid and Newton weren't exactly correct. Their systems are helpful, but not absolute. Without them, however, we would never have come to know that the shortest distance between two points in fact is not a line, but a geodesic.
It's amazing where faith will lead us, and that such is required in all fields of knowing. Indeed, faith comes before knowledge. But it's shameful and tragic that the stalwarts of certainty keep us from going there!
