Greek mathematicians, for example
Euclid, were the first to use the concept of proof. They figured out that in
order to show that a statement was true they must use logical arguments. Before
Euclid, mathematicians such as the Egyptians and Babylonions “proved” statements
from repeated observations and inductive reasoning. However, the Greek
mathematicians realized that they needed to have logical explanations to prove
that statements were true. These proofs needed to clearly show why the
statement was true in a way that would last over time. In order for Euclid to
use this new system, he had to create definitions and axioms that would be
accepted by everyone. These were written and shared with others in “The Elements”.
Some of the definitions in this book include point, line, and surface. “The
Elements” also contain Euclid’s five postulates which he assumed to be true. Euclid
used these definitions, axioms, and postulates to prove statements. When the
statements had been proven, the statement became an accepted theorem. Most of
Euclid’s proofs involved geometry, but ever since Euclid, all types of mathematics
use his logical argument concept and create accepted definitions to prove
statements.
Euclid’s
idea of proofs changed mathematics. He found a way to prove statements in a
consistent way that is still accepted today. Euclid created the foundation for
how mathematicians would solve proofs. Mathematicians start with a statement
they would like to prove. In order to do this, they use the definitions and
axioms to create a logical argument showing the statement is true. Once they
have done this they have found a new theorem. Euclid changed the way
mathematicians proved statements from a system of trial and error to forming
logical explanations.
No
one has been able to disprove what Euclid found. He was a founder for Euclidean
Geometry. However, after him, Non-Euclidean Geometry was discovered when you
change one of Euclid’s main axioms or assumptions about parallel lines.
Citations
Abby, I really like how you explained how the concept of proof was different to the Greeks in that they used logic and reason (deductive reasoning) to show that ideas were indeed always true instead of repeated observations like the 'proofs' of their predecessors. One way I think think that you could make this blog post better is to elaborate more on Euclid's methods. What were his axioms? (Or what even the heck is an axiom?) Or, you could give some examples of some of the ideas he proved to show how his proofs have lasted over time.
ReplyDelete-Holli. Apparently it didn't post under my name even though it made me enter it... hmmmmm
DeleteTo us as students I think that it is second nature to just assume that we need a proof to show that it is true. But it is interesting that it wasn't always that way. Knowing that Euclid did this isn't a surprise he was a genius.
ReplyDeleteContent: weirdly, Euclid's first 9 'definitions' are now considered to be undefined objects; that includes point and line. Definition 10 is what is a right angle and perpendicular. The last statement is pretty broad, too. I'd like to hear you argue that! (Goes towards better consolidation, too.)
ReplyDeleteComplete: expand a little bit. Here's a good reference for some more ideas/facts. Or follow up on the first commenter's ideas.
clear, coherent +
Oops: https://plus.maths.org/content/origins-proof
Delete