Related to your query, I suggest you to follow : https://www.quora.com/What-is-the-difference-between-mathematics-and-science

Dear @Raju Chiluvuri

To my opinion, mathematics is the precursor to all the disciplines of science. And, in fact, mathematics is also a science.

Thanks!

Discipline is equally required but in case of science we mostly dealing with living ones hence more care is needed

Dear Friends,

Thank you. I agree that both are very impotent and compliment each other. But, I feel that by knowing basic differences would help us leverage each of them better for gaining new knowledge and/or using existing knowledge better.

My goal is just for creating more discourse and debate for improving clarity and insights. I need this clarity for my research to improve computer science.

For example, if we can create math from scratch now, would you use decimal system, octal or hexadecimal system? My guess is that mankind choose 10-based system, since we have 10 fingers in both hands. If we choose 12-based system, it can be divisible by 3 also, but not divisible by 5.

Also, I don’t think axioms are invented - it is also not right term, but I can’t find a better terminology. I hope someone can find a better terminology or insights.

Even if we can’t find better term, we can have better understanding about foundational principles for math.

Intelligent species in another planet having 4 fingers for hand may define octa decimal system or hexadecimal system. My point is, it is possible to create different set of axioms as foundation for mathematical disciplines such as Arithmetic.

In that case, can we call it invention of Axioms? They are constrained by some kind of greater reality.

Best Regards,

Raju Chiluvuri

Dear Raju Chiluvuri

Soon I will give you a detailed answer including some questions.

First I think you should read some of my papers which are (by selection) published at RG to have more basis for dicussion.

Regards, Peter

Science is based on observation. But maths is proving science using equations.

Beena G Pillai

Science — per definition — doesn´t exclude mathematics. Math should be the formalism.

Extension: "... observation ...” / Do you think on nature-sciences? But there are others — social-, historical-sciences ... for example.

Dear Mr. Peter,

Let me clarify my question. In one perception, science is knowledge about physical things acquired and accumulated by conforming to scientific method.

Scientific method is a tool for acquiring scientific knowledge, where scientific knowledge imply knowledge about physical things in the natural world.

Mathematics is another tool for acquiring knowledge, where the knowledge includes collaborative and/or quantitative scientific knowledge.

In case of mathematics, it is possible for a person-A to define set of axioms for a discipline. Another person-B can define another set of axioms for creating internally consistent system for the same discipline.

To give you an analogy, we normally use chairs having four legs. But, it is possible to create a chair having only two legs. Both can offer same kind of stability. Please see the attached PDF for other kinds of chairs that also can provide similar internal consistence (so to speak).

We can define or invent axioms that are foundational first principles for each of the mathematical disciplines, but it is not possible to define or invent first-principles for any scientific disciplines.

Best Regards,

Raju

Dear Raju, so far no answer at the level of mathematical science but in respect to your clarification:

Stability of which is called `a chair´ is on three legs minimum (physics).

[Every idealized (correction: every real) thing stays stable on an idealized plane surface by three points of connection.]

Your pdf-examples don´t tell any different. All is on special art in (engineers) stabillity.

Dear Raju, I had a look at your homepage. I see a very good basis for talking together (at the level of science / math).

R. 0011, posted 2020/10/28

Now on math:

1. Mathematics is defined as the science of quantities and their relation — agreeing?

2. Speech was first — agreeing?

3. No number (of amont) exists in reality — agreeing?

4. Mathematics is a formalism — agreeing?

5. Speech knows two different meanings for `number´. Position or amount. Mathematics uses position (the first, the second ...) at syntax but only is on number (of amount) when calculating — agreeing?

6. Every kind of mathematics uses algebra — agreeing?

Dear Mr. Kepp,

My goal for using the analogy for chairs is to show that it is possible to achieve internal consistence in each of the disciplines of matamatas, by defining different set of Axioms (so is it Invented). But they need to satisfy a condition for reality of stability (i.e. internal consistency). So are they kind of discovered?

But, we all agree that first-principles for science are certainly must be discovered and can never be invented or defined. My goal is to understand differences between scientific disciplines and mathematics disciplines. This kind of knowledge is very useful.

For example, the root cause for software crisis is failure of software researchers to understand the difference between reusability and modularization. Both are important but, it is impossible to solve infamous software crisis without understanding the fundamental difference: http://real-software-components.com/raju/TwoKindsOfParadigms.pdf

Likewise, I feel science and math are two mutually independent dimensions for gaining deeper insights.

First time since the subversion of geocentric paradox in 17th century, a scientific discipline ended up in a fake science phase and created such a paradox: http://real-software-components.com/raju/ModifiedKuhnBlackHolePhase.pdf

Best Regards,

Raju