4 ms·

Totally disagree. Mathematics is not a science at all because there is no any possible experiments in the Math fields. And remember what David Hilbert has told

Totally disagree. Mathematics is not a science at all because there is no any possible experiments in the Math fields. And remember what David Hilbert has told about one of his students who decided to go into arts instead of keep learning Math with him. He told "he did not have enough imagination to become a mathematician".

yesenadam 4y ago
> there is no any possible experiments in the Math fields. https://en.wikipedia.org/wiki/Experimental_mathematics https://en.wikipedia.org/wiki/Experimental_mathematics Worth googling too, a wide range of things come up: https://www.google.com/search?q=experimental+mathematics https://www.google.com/search?q=experimental+mathematics
- eimrine 4y ago
  Experimental mathematics is not a field of mathematics, but an approach. In the link you have given I found two approaches called experimental mathematics: proofing theorems by computer contrary to proofing with a pensil, and searching new problems contrary to solving some existing ones.
  - yesenadam 4y ago
    I was responding to your apparent claim that experimentation is not possible in mathematics. Maybe I misunderstood what you meant. From Halmos' quote from the wiki page: "Mathematics is not a deductive science—that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork. You want to find out what the facts are, and what you do is in that respect similar to what a laboratory technician does" - it sure sounds like he thinks experiment/experimentation a key part of maths.
  - Burner7799 4y ago
    What evidence would convince you that mathematics is empirical? If your argument was a tautology then what’s the point? Would you consider interactive theorem proving to be empirical or not? The sort of experiment you perform is you try to see if the computer accepts your proof or not.
    - sudosysgen 4y ago
      Interactive theorem proving is not an experiment on nature because the theorem priver is itself a mathematical construct.
      - ukj 4y ago
        It sure seems like the goal posts are being moved. Every experiment is an experiment of nature. Humans are part of nature. Human constructs are part of nature. Every interaction that results in the testing or falsification of some hypothesis is a valid experiment. Irrespective of the object being experimented/interacted with. I am experimenting with (testing/falsifying hypotheses against) your linguistic constructs right now.
        sudosysgen 4y ago
        I think you're missing the point. Mathematics isn't a natural science, and that's what I was trying to point out. There is a term for doing science on human constructs - it's called social science. Is your thesis that mathematics is a social science? > Humans are part of nature. Human constructs are part of nature. Humans physically are part of nature, sure. Human constructs are not considered to be as far as classification in the social and natural sciences.
        ukj 4y ago
        I am not sure why you are using the phrase "natural science", is there any other kind? Lets revisit with the wikipedia definition: Science (from Latin scientia 'knowledge') is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. That seems pretty general and all-inclusive to me. Any knowledge about humans; or societies; or the stuff human societies invent is knowledge about the universe. Because we are part of the universe. Now, you seem to be trying to differentiate the different sciences from one another - tell us why. What's the purpose of drawing a distinction between science and (what you call) "natural science"?
spacemanmatt 4y ago
Math is abstract, so I would expect experiments in math to have abstract results. I don't think that makes it less of a science.
- eimrine 4y ago
  Any experiment has an abstract result. For example: If throwing a rock from the tower of Pisa gave us result that acceleration of gravity on Earth is 9.8 m/s^2 then that number will be exactly same for throwing any other materials from any other tower on the Earth.
  - spacemanmatt 4y ago
    The result of 9.8m/s^2 is descriptive of a concrete result, isn't it?
deleted 4y ago
[deleted]
ukj 4y ago
In the pyramid of human knowledge physics (a science, according to you) rests on top of mathematics (not a science, according to you). We had mathematics long before we had physics. So it is pretty obvious that physic is founded upon a liberal art - mathematics.
- eimrine 4y ago
  > We had mathematics long before we had physics. I disagree. People haven't had a Mathematics before Pythagoras. All Mathematics people had at that moment was that 1 golden coin + 1 golden coin = 2 golden coins or one copper knife. But trading is not mathematics if not talking about modern things like HFT with broad using of probability theory (and we obviously are talking about ancient times). Physics is understandable even with way more simple (and way more ancient) species then humans. For example, an ape can take a stick and use more heavy end to make a more powerful hit. Birds seems to understand physics quite well - starting from setting wings while flying and ending to general intelligence of crows. And BTW why are you concerned that in the pyramid of knowledge (Biology is a science > Chemistry is a science > Physics is a science > Mathematics is a language) there are three sciences and one a non-science?
  - ukj 4y ago
    Mathematics is a language, but then why are you saying there was no Mathematics before Pythagoras? Obviously Pythagoras didn’t invent language! Long before Pythagoras people had been using language for doing and expressing computation. Pāṇini did it. The Babylonians did it. It then took us a few thousand years to mechanize that knowledge and invent computers as we know them. As for physics being “understandable” - I think you are conflating the ability to exploit nature with the ability to understand it. Physics isn’t something “out there”. Available to birds and apes. It it is the body of knowledge (texts, ideas, concepts, formulas, narratives) instrumental to humans navigating nature. There would be no physics without humans inventing it just like there would be no language without humans inventing it. I am not at all concerned about the contents; or the structure of the pyramid. I am simply expressing a fact about the pyramid. That which people call science is not founded upon science. It is founded upon the liberal arts, humanities and social constructs (logic, philosophy, mathematics, computation, language) - the pyramid is founded upon human invention.

yesenadam 4y ago

> there is no any possible experiments in the Math fields. https://en.wikipedia.org/wiki/Experimental_mathematics https://en.wikipedia.org/wiki/Experimental_mathematics Worth googling too, a wide range of things come up: https://www.google.com/search?q=experimental+mathematics https://www.google.com/search?q=experimental+mathematics

eimrine 4y ago
Experimental mathematics is not a field of mathematics, but an approach. In the link you have given I found two approaches called experimental mathematics: proofing theorems by computer contrary to proofing with a pensil, and searching new problems contrary to solving some existing ones.
- yesenadam 4y ago
  I was responding to your apparent claim that experimentation is not possible in mathematics. Maybe I misunderstood what you meant. From Halmos' quote from the wiki page: "Mathematics is not a deductive science—that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork. You want to find out what the facts are, and what you do is in that respect similar to what a laboratory technician does" - it sure sounds like he thinks experiment/experimentation a key part of maths.
- Burner7799 4y ago
  What evidence would convince you that mathematics is empirical? If your argument was a tautology then what’s the point? Would you consider interactive theorem proving to be empirical or not? The sort of experiment you perform is you try to see if the computer accepts your proof or not.
  - sudosysgen 4y ago
    Interactive theorem proving is not an experiment on nature because the theorem priver is itself a mathematical construct.
    - ukj 4y ago
      It sure seems like the goal posts are being moved. Every experiment is an experiment of nature. Humans are part of nature. Human constructs are part of nature. Every interaction that results in the testing or falsification of some hypothesis is a valid experiment. Irrespective of the object being experimented/interacted with. I am experimenting with (testing/falsifying hypotheses against) your linguistic constructs right now.
      - sudosysgen 4y ago
        I think you're missing the point. Mathematics isn't a natural science, and that's what I was trying to point out. There is a term for doing science on human constructs - it's called social science. Is your thesis that mathematics is a social science? > Humans are part of nature. Human constructs are part of nature. Humans physically are part of nature, sure. Human constructs are not considered to be as far as classification in the social and natural sciences.
        ukj 4y ago
        I am not sure why you are using the phrase "natural science", is there any other kind? Lets revisit with the wikipedia definition: Science (from Latin scientia 'knowledge') is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. That seems pretty general and all-inclusive to me. Any knowledge about humans; or societies; or the stuff human societies invent is knowledge about the universe. Because we are part of the universe. Now, you seem to be trying to differentiate the different sciences from one another - tell us why. What's the purpose of drawing a distinction between science and (what you call) "natural science"?

spacemanmatt 4y ago

Math is abstract, so I would expect experiments in math to have abstract results. I don't think that makes it less of a science.

eimrine 4y ago
Any experiment has an abstract result. For example: If throwing a rock from the tower of Pisa gave us result that acceleration of gravity on Earth is 9.8 m/s^2 then that number will be exactly same for throwing any other materials from any other tower on the Earth.
- spacemanmatt 4y ago
  The result of 9.8m/s^2 is descriptive of a concrete result, isn't it?

deleted 4y ago

[deleted]

ukj 4y ago

In the pyramid of human knowledge physics (a science, according to you) rests on top of mathematics (not a science, according to you). We had mathematics long before we had physics. So it is pretty obvious that physic is founded upon a liberal art - mathematics.

eimrine 4y ago
> We had mathematics long before we had physics. I disagree. People haven't had a Mathematics before Pythagoras. All Mathematics people had at that moment was that 1 golden coin + 1 golden coin = 2 golden coins or one copper knife. But trading is not mathematics if not talking about modern things like HFT with broad using of probability theory (and we obviously are talking about ancient times). Physics is understandable even with way more simple (and way more ancient) species then humans. For example, an ape can take a stick and use more heavy end to make a more powerful hit. Birds seems to understand physics quite well - starting from setting wings while flying and ending to general intelligence of crows. And BTW why are you concerned that in the pyramid of knowledge (Biology is a science > Chemistry is a science > Physics is a science > Mathematics is a language) there are three sciences and one a non-science?
- ukj 4y ago
  Mathematics is a language, but then why are you saying there was no Mathematics before Pythagoras? Obviously Pythagoras didn’t invent language! Long before Pythagoras people had been using language for doing and expressing computation. Pāṇini did it. The Babylonians did it. It then took us a few thousand years to mechanize that knowledge and invent computers as we know them. As for physics being “understandable” - I think you are conflating the ability to exploit nature with the ability to understand it. Physics isn’t something “out there”. Available to birds and apes. It it is the body of knowledge (texts, ideas, concepts, formulas, narratives) instrumental to humans navigating nature. There would be no physics without humans inventing it just like there would be no language without humans inventing it. I am not at all concerned about the contents; or the structure of the pyramid. I am simply expressing a fact about the pyramid. That which people call science is not founded upon science. It is founded upon the liberal arts, humanities and social constructs (logic, philosophy, mathematics, computation, language) - the pyramid is founded upon human invention.