Why should we learn proofs?
All mathematicians in the study considered proofs valuable for students because they offer students new methods, important concepts and exercise in logical reasoning needed in problem solving. The study shows that some mathematicians consider proving and problem solving almost as the same kind of activities.
What is proof in mathematics in the modern world?
A proof is a logical argument that establishes the truth of a statement. The argument derives its conclusions from the premises of the statement, other theorems, definitions, and, ultimately, the postulates of the mathematical system in which the claim is based.
What is a proof in math?
A proof is an argument, a justification, a reason that something is true. It’s got to be a particular kind of reasoning – logical – to be called a proof. (There are certainly plenty of other, equally valid forms of reasoning. And some of them are even used in “doing” mathematics.
What is the importance of proofs in real life?
Written proofs are a record of your understanding, and a way to communicate mathematical ideas with others. “Doing” mathematics is all about finding proofs. And real life has a lot to do with “doing” mathematics, even if it doesn’t look that way very often.
What do you think every mathematician should know?
I think every mathematician should know the following (in no particular order): Pythagorean Theorem. Summing ∑ k = 1 n k using Gauss’ triangle trick. Irrationality of 2 by proof without words. Niven’s proof of the irrationality of π. Uncountability of the Reals by Cantor’s Diagonal Argument.
What are some of the most beautiful proofs of algebraic geometry?
The proof of the Fundamental Theorem of Algebra via Liouville’s theorem is short and sweet. I personally believe some of the proofs of Pythagoras’ theorem can be both beautiful and elegant, though it is unfortunate that it is not taught in school (at least as far as I am aware). Take any square with sides of length x + y.