Dear Yingxu,

I disagree with your statement. I believe that a large part of human knowledge that I would also consider "core" has been archived in prose. I am thinking of history records, for example, literature, etc.

However, to answer your question about the usefulness of mathematics, I will give my opinion on this. I think the key property of mathematics is illustrated by the work of Russell and others in mathematical logic: facts enunciated in mathematical form should be verifiable by anyone who has knowledge of the logical formalism, independently of the content itself.

To elaborate on this, think about my statement about history records. Do we have any way to verify that the war of Troy actually happened, just by looking at the writings that we have? We may go to the site, dig here and dig there, go to museums, but the writings themselves do not have a self-validation mechanism.

Mathematical logic, on the other hand, is amenable to verification in and of itself. Given a set of axioms and a mechanism for deduction, you should be able to verify if the proof of a theorem is correct or not, independently of whether you understand it or its implications.

So, to sum up, I think the key property of mathematics is verifiability (enter now Gödel's theorem, but that's another story).

Just my two cents.

Cheers,

Fernando

In science and engineering, a mathematical model (formula) is worth of a thousand words, because it is a general expression of a set of knowledge in a certain domain. For instance, although a textbook of Physics would be over 1,000 pages, there are only less than 100 formulae as the core knowledge, except those of factors, instances, and descriptions.

Dear Yingxu,

I agree with that, but there still is a gap between (quoting you) "the core of human knowledge" and "science and engineering".

Cheers,

Fernando

There is also a matter of semantics here. A formula is nothing worth without ist "legend" (to say as for maps of geography) - where the legend means an explanation of what do the symbols in the formula mean. [E = mc2, where E total energy, m total mass, c light velocity in vacuum]. Now, for a lot of notions, the right definition is more important as the formulae they are involved in. It is very hard, or almost impossible, to give the right definition of the notions "mass" and "energy", just to give an example. It seems to me that the core of human knowledge can be expressed only in a good mix of formulae and text, and that we probably need much more text than formulae. However, formulae have a magic compacity, and ca be used as a citation of the whole text they are refering to.

I am also agree "the core of human knowledge been mainly archived in mathematical forms".

According to myself ...The Archived mathematical forms are formed by comparative analysis of currently observed events with past acquired knowledge.

For Example:we know how to ride a bike. Initially we ride bike with more precaution and full attention. as the day goes on we dont pay such attention as what we gave initially.Initially we bother one person walking on road while we riding bike. but later on we do many styles by riding without holding hand.

how it is possible?

Simple: Answer is Our body gets trained well cognitively. Based on that all our nervous system bends properly at right time mathematically(functional/expression)

All outside in this world mathematically functioning is nothing but our perspective view from our mind, functioning mathematically.

Similar example like The person practicing Kung fu

only mathematical judging of opponent's fist.

Hence,

I am also agreeing "the core of human knowledge been mainly archived in mathematical forms".

I partly agree with Fernando and Mihai. I disagree with Fernando in that it gives a central role in logic. All mathematics was done without formalisation and formal logic! 

Let take things from the beginning. There are three stages, when we talk about knowledge.

!. We have the knowledge acquired by the humans.

2. Some of these (maybe all) admit mathematisation.

3. From mathematisation we may need a further stage of formalisation,  where most can be checked even by computers.

We should not confuse mathematisation and formalisation.

Has the core of human knowledge been mainly archived in mathematical forms? Well if one thinks that the machine language of a computer is essentially based on mathematics, and if we accept that today we may archive in one or the other way, in a computer, then we answer YES. But this does not mean that a fiction has been archived taking first a mathematical form! 

Mathematics has been referred to as a 'language.' The language of mathematics has consistent rules, much more so than rules of grammar. (That's definitely true of English.) And it is more universally written, as I have seen mathematics I recognized in a paper whose text was in a language I did not know. Much of the information in such a paper is right there in the mathematical expressions. But, though logic is used to break verbal arguments into mathematical-like symbolism, I have to agree with Fernando that it is difficult to believe this covers all human knowledge. The original question, however, was with regard to "sciences," and said "mainly,' for 'core' knowledge archival. The short answer, I think, is "Yes." As to "Why?" I'd say that because, like a picture, as Yingxu said, a formula is "...worth a thousand words." One other point: in statistics, graphs are very helpful. (I found scatterplots to be extremely informative.) Often a graph can tell you much more information, and be far more clearly interpretable than generally accepted statistical measures. Do we include graphics as "mathematical forms?" That would make the "Yes" a more positive one.

But archiving knowledge does not mean creating it. What of the role of mathematics in creating scientific knowledge ... 'Standing on the shoulders of giants?' Oddly, I think the arguments for and against this might be similar.  

Not completely has the core of science knowledge been achieved in mathematical forms, because mathematics is the universal language for science like English for communication. It does not imply that science can only be expressed in math, since there are possibilities for other expressions.

Many non-analytical results in science may not be in mathematical form! This will be corrected until the Theory of Category, a holistic approach, will be more popular!

Not everything is mathematizable, in biology there is relatively little in mathematical

theory or models.

Many frontier or fringe areas of physics seem to use math too much, in detriment of reasoning or evidence. Much understanding can be expressed using no or very simple math, as with  the periodic table of elements.