The question of whether mathematical truths are discovered or invented is a philosophical debate, with some arguing that they are discovered as inherent features of the universe and others arguing that they are invented by humans as tools for understanding the world.
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The question of whether mathematical truths are discovered or invented is a long-standing philosophical debate. Those who argue in favor of the discovery view believe that mathematical truths are inherent features of the universe that exist independently of human minds. On the other hand, those who believe in the invention view argue that mathematical concepts and principles are created by humans as tools for understanding the world around us.
One of the leading proponents of the discovery view is the physicist and mathematician Eugene Wigner, who famously wrote, “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.”
While there is no consensus on the issue, there are some interesting facts and arguments that contribute to the debate. For example, some mathematicians and philosophers argue that mathematical truths exist beyond the physical world, and that we discover them through our own observations and reasoning. Others argue that mathematics is a human invention that reflects our cultural and historical context.
One way to summarize the arguments on both sides of the debate is to create a table:
|Discovery view||Invention view|
|Mathematical truths exist independently of humans.||Mathematics is a human invention.|
|Mathematics reflects the inherent structure of the universe.||Mathematics is culturally and historically contingent.|
|Mathematical truths are discovered through observation and reasoning.||Mathematical concepts and principles are created as tools for understanding the world.|
|Mathematics is a universal language that transcends human culture and history.||Mathematics reflects the biases and assumptions of human society.|
In conclusion, the question of whether mathematical truths are discovered or invented is a complex and ongoing philosophical debate that continues to fascinate mathematicians, scientists, and philosophers alike.
This video discusses the debate between those who believe that mathematics is discovered, and those who believe that it is invented. The video provides examples of how mathematics has been used to solve problems in the real world.
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Mathematicians invent math all the time, formalizing observations they make about the mathematical world into rules. To understand what that might be like, take for example the famous paradox of infinite sums first proposed by the Greek philosopher Zeno.
The nature of mathematics is a subject of debate. Some argue that mathematical truths are discovered through the intuition of the mathematician and then being established by proof, while others argue that mathematical truths are invented or emerging as the by-products of inventions. However, mathematical truths are universal, objective and certain, and are made true or false by the objects with which they are concerned and these objects’ perfectly objective properties, similar to statements about electrons and planets.
The absolute nature of mathematics is universal, objective and certain, with mathematical truths being discovered through the intuition of the mathematician and then being established by proof while the fallible nature of mathematics is an incomplete and everlasting work-in-progress, and is corrigible, revisable, changing, with new mathematical truths, being invented, or emerging as the by-products of inventions, rather than…
And just as statements about electrons and planets are made true or false by the objects with which they are concerned and these objects’ perfectly objective properties, so are statements about numbers and sets. Mathematical truths are therefore discovered, not invented.
I am far from an expert on this subject, but it might be illuminating to consider what happens when a dog catches a ball. Neglecting air resistance and other secondary effects, the ball follows a predictable trajectory that is shaped by gravity, and math allows us to predict where it will land. Astonishingly, a dog can _also_ predict where the ball will land almost immediately after the throw, and some dogs can even run and leap to catch the ball before it touches the ground. When you consider that the dog has far less visual acuity than we do and that it is estimating the three-dimensional geometry of the world and position of the ball in real time from imperfect two-dimensional signals bouncing on its retinas as it runs, you might be tempted to award the dog a degree in Applied Mathematics!
So does the dog that successfully locks the ball in its jaws in mid-air invent math, discover it, or neither?
One perspective would be that the dog discovers math: through life experience, it ob…
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Is mathematics is invented or discovered?
Answer to this: 2) Math is a human construct.
If the universe disappeared, there would be no mathematics in the same way that there would be no football, tennis, chess or any other set of rules with relational structures that we contrived. Mathematics is not discovered, it is invented.
Is mathematics an absolute truth or created?
As an answer to this: Absolute truth in mathematics
Some believe that pure mathematics proves the existence of absolute truth. As evidence of this, they point to mathematical structures such as Maxwell’s equations as a type of absolute truth. Introduced in the 19th century, the equations describe the fundamentals of electromagnetism.
Are theorems discovered or invented?
As a response to this: Theorems are discovered. The goal is to prove this conjecture, or to refute it. Below, some arguments in support of the conjecture are presented. The physical world has always provided inspiration for mathematicians.
Why math is discovered and invented?
The answer is: Throughout history, different cultures have discovered the maths needed for tasks like understanding groups and relationships, sharing food, looking at astronomical and seasonal patterns, and more. There are probably forms of mathematics that were understood by people we don’t even know existed.
Is mathematics invented or discovered?
Some mathematics, I think, is definitely invented, not discovered. That tends to be trivial mathematics — papers that fill in much-needed gaps because somebody has to publish. So you take some problem, you change the wording of the mathematical problem a little bit, then you solve it, and then you write a paper.
Are mathematical truths out there?
Some scholars feel very strongly that mathematical truths are “out there,” waiting to be discovered—a position known as Platonism.
Does mathematics exist within us?
Answer will be: Some believe that mathematics exists within us, and that the objects of mathematics were therefore our creation. Other philosophers thought that mathematics exist independent of our thoughts, outside of us. However, does the truth lie somewhere between the stark choice of being invented or discovered?
Why do some people oppose the idea that math was discovered?
Answer: Some people oppose the idea that math was discovered. They belong to the anti-Platonic school of thought, which believes that mathematics was invented. They consider math to be a human invention designed in a way that suitably describes the physical world. To suit our needs, the human mind continually makes up new mathematical concepts.
Is mathematics invented or discovered?
Response: Some mathematics, I think, is definitely invented, not discovered. That tends to be trivial mathematics — papers that fill in much-needed gaps because somebody has to publish. So you take some problem, you change the wording of the mathematical problem a little bit, then you solve it, and then you write a paper.
What are the truth values of mathematics?
As an answer to this: Their truth values are based on rules that humans created. Mathematics is thus an invented logic exercise, with no existence outside mankind’s conscious thought, a language of abstract relationships based on patterns discerned by brains, built to use those patterns to invent useful but artificial order from chaos.
Is mathematics just a creation of the human mind?
Answer: "Intuitionists" believe that mathematics is just a creation of the human mind. In that sense you can argue that mathematics is invented by humans. Any mathematical object exists only in our mind and doesn’t as such have an existence.
Are mathematicians justified in taking (s) as literal truths?
When a mathematician accepts a mathematical statement \\ (S\\), the content of this attitude is in general the literal meaning of \\ (S\\). From these three claims it follows that mathematical experts are justified in taking the theorems of mathematics to be literal truths.