Is mathematics something man-made or man-made?

Updated on : January 21, 2022 by Declan Johnston



Is mathematics something man-made or man-made?

Mathematics is a language, but in some way different from English, French or Portuguese. Mathematics is a more limited language than these natural languages, but much more precise (unambiguous).

We can say today, May alone, that mathematics is based on set theory and logic. Set theory and logic are certainly influenced by human physical and mental experience. Therefore, they are not completely separate from the physical world. They are a fragment of any natural language (Portuguese, English, Spanish, ...) built around a consensus on some primitive notions (what is a set, the concept of a set member,

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Mathematics is a language, but in some way different from English, French or Portuguese. Mathematics is a more limited language than these natural languages, but much more precise (unambiguous).

We can say today, May alone, that mathematics is based on set theory and logic. Set theory and logic are certainly influenced by human physical and mental experience. Therefore, they are not completely separate from the physical world. They are a fragment of any natural language (Portuguese, English, Spanish, ...) built around a consensus on some primitive notions (what is a set, the concept of a set member, etc.) and based on rules used to avoid any ambiguity. This consensus is taken by free will. Nobody is obliged. Its validity is judged by its usefulness. Everyone is encouraged to establish a new framework and a new consensus. You will be judged on the usefulness of the new theory in constructing solutions to important problems.

Having said that, I would also say that it has a lot more of something created by humans than discovered. As a poem or a novel is created, it is not discovered.

PS: And many mathematicians see beauty in a lot of axioms and some proofs of theorems, like in a poem!

Both of them. It is quite common, looking back at the history of mathematics, to see some subject described as "not leading to fruitful results." For example, there used to be a topic, "triangulation geometry," which dealt with increasingly subtle properties of triangles. It was once a vigorous theme, now seen as a mined backwater.

The fact that some topics turn out to be unsuccessful shows that the people who explored those topics had no idea that the research was going nowhere. Also, when they hit a dead end, they didn't have the power to simply create more interesting results in their

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Both of them. It is quite common, looking back at the history of mathematics, to see some subject described as "not leading to fruitful results." For example, there used to be a topic, "triangulation geometry," which dealt with increasingly subtle properties of triangles. It was once a vigorous theme, now seen as a mined backwater.

The fact that some topics turn out to be unsuccessful shows that the people who explored those topics had no idea that the research was going nowhere. Also, when they hit a dead end, they didn't have the power to just create more interesting results on their own. That suggests that, to some extent, mathematics is discovered.

But there is a lot of mathematics created by humans. Our notation system is a good example. We use decimal because we have ten fingers, but in computing binary, octal and hexadecimal are used.

Neither of those options is really good, on its own, to be described as the origin of mathematics.

People did not create mathematics because it arose out of vital and common human needs: counting, measuring, recording, finding patterns, and so on. As a result of these universal human needs, similar mathematical systems developed. Form follows function.

Nor would it be accurate to say that people discovered mathematics. Counting years or measuring distance: a year is still 365 and a few days, and the distance between two places is the same regardless of the unit of measurement. A falling tree in the forest makes a noise

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Neither of those options is really good, on its own, to be described as the origin of mathematics.

People did not create mathematics because it arose out of vital and common human needs: counting, measuring, recording, finding patterns, and so on. As a result of these universal human needs, similar mathematical systems developed. Form follows function.

Nor would it be accurate to say that people discovered mathematics. Counting years or measuring distance: a year is still 365 and a few days, and the distance between two places is the same regardless of the unit of measurement. A falling tree in the forest makes noise, whether or not someone is there to hear it.

Framing a question and offering only two options is only valid if there are no other answers, and those two options are mutually exclusive. Yes / No, or should I turn left or right at this T-junction?

The answer to your question, more generally, certainly includes elements of both options, and other things as well. Things like the structure of the brain and the range of our sense organs.

That is a very good question. I would describe it this way: the principles of mathematics are discovered, they are a kind of “part of the universe”, while their notations and the methods to describe them are invented.

The way you look at it is the simple fact that the Fibonacci "golden ratio" existed in nature long before man, but was not "named" that way. I would recommend 2 good books on the original question: (1) The Golden Ratio, by Mario Livio; (2) The last chapter of Contact, by Carl Sagan.

Mathematics is an attempt to standardize the interrelationship between questions that refer to the movement between zero (0) and one (1) by means of the questions that appear to relate to the movement between one (1) and zero (0). Whether this approach is endemic to higher forms of self-actualization or whether we cannot know with any degree of certainty.

Both of them. Fundamentally, mathematics is a language, a collection of abstract symbols and syntax rules. This feature of mathematics is man-made. However, I believe that mathematics is much more than that. Now we can assemble these abstract symbols in specific ways to describe natural phenomena, and these mathematical equations are discovered.

Thanks for A2A, Rahim Bidkanl,

Original question: - Is mathematics something created by man or discovered by man?

Answer: - Mathematics is neither creation nor discovery. Mathematics consists of observational studies. Repeated observations that result in the same way are tabulated and formulated in rules and laws for the sake of brevity. Therefore, mathematics is simply a branch of knowledge that can be molded into creative art to discover new things in the world.

Mathematics, from beginning to end, is a creation of man.

the numbers are our imaginary creatures, like the characters in a fairy tale.

I would say that it is a combination of the two, mathematicians invented mathematical structures and rules to manipulate them, like the number system, but mathematicians also discovered results about structures.

Mathematical facts are discovered, proofs are the work of humans. It is like digging for gold, the precious metal is there before it is found, what takes work is digging for it.

The math, and its internal logic anyway, is totally man-made. Discovered by man, is that some of this mathematics applies to real situations.

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