Euclid
In your own mathematical education, did you learn to regard math as a set of rules to follow (algorithms) or as a body of knowledge that needed to be proved? When you apply math in your career as, say, an accountant, will you be using algorithms or proofs?
And why were the ancient Greeks so obsessed with the need to prove everything? Maybe they took us up a 2000-year blind alley?
Learning math through the educational system was obviously a set of tools you acquire throughout the years that allow you to solve complex problems. Just like a mechanic fixing a car, you need to use the right tools to fix a particular problem. Proofs are really the essence of math because the focus is not on the final answer but on understanding and logically demonstrating why this exact answer is indeed correct. In the modern business job market it is not required to know proofs but if you want to pursue a career in math it is a necessity. Understanding a proof only reinforces the basic set of rules acquired in secondary school.
There is something special about a mathematical proof. Physical laws are based on repeated observations, and are adjusted to accommodate new discoveries. But if you prove a theorem today, it will be just as valid 1000 years from now.
As a child and even now as an adult i have always been tought to regard mathematics as a set of rules to follow. In accounting we are given set of rules and simply must understand how to apply those rules to different situations. I think the ancient greeks awere so obsessed with proving everything becuase before them no one had really gone far into the world of mathematics and therefore they really didn’t have not much to stand on whereas something like accounting has alreaddy been proved and we thereofre dont have to prove anything we can simply follow a set of rules. In accounting we may add rules as we see fit as long as they have reasons behind them, but they do not necessarily have to be proven as math ideas constantly are.
Even if you don’t need proofs to USE an algorithm, someone had to PROVE that the algorithm works (that it always does what it purports to do).
Yes that is true, I also think that the use of technology has significantly simplified perhaps how people may actually prove an algorithm.
In my own mathematical education I learned math as a set of rules to follow. When it comes to math you are either right or wrong. When it comes to math I have to make sure that I know all the formulas, all the rules and algorithms needed so I can solve a problem. I dont see math as information that needs to be provided. Only when it comes to basic math like adding and subtracting. As math advances it becomes less of an necessity. I believe that the ancient Greek were obssessed with proving everything because they had to make sure what they were saying was right. They couldn’t just say that 4+4=8 without showing that its true because anybody can come up with their own assumptions as to what 4+4 is equal to.
I have learned math as a set of rules. For example the area of a circle is pi*r^2. I only had to learn, perhaps memorize what people had already proof. As an accountant I don’t think I will be dealing with proofs, since the algorithms provided had already been proof. I think, I only need to understand when or how to apply a specific rule. Furthermore, I don’t think the Greeks were obsessed by proofs. I think they grow up in a culture where people were curious about what they observed, also based on general Greek history most philosophers or mathematicians loved to argue and debate ideas. I think they pass this cultural idea of proving what they observe, to the different generations.
Math has always been a set of rules to follow in my opinion. Today, formulas are simply built into softwares like Quickbooks and Microsoft Excel, where answers are generated for you and you don’t have to know how they came about. We can do this because these algorithms have been around for a long time and it is simply accepted as fact rather than theory now. I think mathematicians in the past were eager to prove everything because at the time, these algorithms were not universally accepted yet. People have a tendency to question topics before they can fully believe it. Thus, these mathematicians had to come up with rules that were both convincing and easy to understand. Without these proofs, we may never have had all these softwares that run our daily lives.
Before the advancement of technology, math was a body of knowledge that needed to be proved because the ancient Greeks and mathematicians didn’t have the resources that we have now to prove anything. They had to use what natures has to prove some subjects of mathematical education. But now math is seen as a set of rules to follow because it became much more simpler with resources and technology. For example, let’s take the calculator for example, most people if not everybody use a calculator to help them get the right result doing a calculation; we barely use “tally” to help us count. Nowadays, people are not as passionate as the Ancient Greeks were about mathematics. We just know that we can use l’Hopital’s rule for example to evaluate limits with indeterminate forms, we just know the rule but do we ever try to prove it? I doubt it. Since math has became so much simpler over the years, it is now a simple set of rules to follow to get a result.
The Ancient Greeks were so obsessed with the need to prove everything to get a proven result. They were also passionate about the subject. Also, they could even name some formulas after themselves.
My mathematical education showed that math is both set of rules (algorithms) and the body of knowledge that need to be proved. In my opinion, the ancient Greeks obsessed with the need to prove everything because they did not have enough solutions for existing problems. They paid much more attention on algebra and geometry. Even today, some mathematicians find absolutely new proofs for mathematical tasks. Mathematicians critic each other, agree or disagree with each other. Anyway, they are all addicted to prove their divisions.
Nowadays people (accountants, financiers, managers, etc.) do not prove everything, they just simply use the algorithms (set of rules). They might do not want to spend so much time on proofs, that s why basically rely on existing solutions and proofs.
My education has shown math to be a set of rules that are to be followed, much the same way as music or color theory. Follow the basic format and we are rewarded for doing the right thing. Greece was apt to be obsessed about their beliefs. They are considered the foundational culture of Western civilization. It was interesting to see how in Plimpton 322 that The ancient Greeks actually gathered information in what is now Iraq.
In a field like accounting , you would use algorithm not proofs to solve your problems. However , it is due to these proofs that formulas and functions are generated through which a set of rules or aglorithm is made possible to use .
The Greeks loved to argue, debate, and hence therefore may have always been involved in figuring out how to prove everything they observed.They were more inclined towards pure math.All surviving records of pre-Greek mathematics show the use of inductive reasoning, that is, repeated observations used to establish rules of thumb. Greek mathematicians, by contrast, used deductive reasoning. The Greeks used logic to derive conclusions from definitions and axioms, and used mathematical rigor to prove them.
I believe we are taught algorithms and we apply in terms of them. We dont use proofs in application of our work because it was already proven so there isnt a need to prove it and just apply it. We may apply and work on that algorithms on what proofs have proven so we can do our work. Greeks were probably obsessed with being able to make sure such calculations are allowed and corrcet with proofs so it cant be wrong.