There are a lot of extremely questionable assertions and premises in the article referred to.

Before I comment further, may I point out that this theme has been quite extensively covered in RG before, and that it would behoove you to actually look up the relevant threads? I'm also slightly baffled at your behest to 'google' the names of the quoted individuals - believe you me, RG users as a rule know science, including names and sources....

This being said,

1- The referred article begins with a fallacy, nay a falsehood: mathematics is demonstrably NOT a human invention. Not only can many animal species count (aka use arithmetics) : https://www.nytimes.com/2018/02/05/science/animals-count-numbers.html

but they can even use simple mathematical modelling: e.g., in 'The Global Brain', Howard Bloom shows how bees have been known to seamlessly use predictive mathematics to find sources of food.

2- Now the thrust of the subsequent analysis and of the article itself - to wit, 'There is no Truth in Mathematics' actually totally misses the point.

The essence of mathematics is not truth or untruth: it is vocabulary definitions. The very core of mathematics is numbers theory, and number theory is a set of lexicon definitions - robust, WYSIWYG word definitions, not laying claim to any truth. From the existence of 1, whenever we put 1 and 1 together we create a whole different thing, a different entity, which we choose to call 2: from this very simple, robust, language-independent definition, at once arise seamlessly & unavoidably a whole exotic zoo of numbers - integers, real, rational, irrational, complex, quaternions, aleph, beth, Graham's number, prime, etc. upon which the whole edifice of modern physics is built - and hence our understanding of reality.

3- The article's contention that there is no such thing as two identical things in the universe and that hence that the assembling of numbers into ensembles is untenable is simply arrantly false. The building blocks of nature - photons, neutrons, electrons, protons, and so on - are all identical, and behave identically whenever put into the same environments (such as fields or chemical bonds etc.etc.)

4- Hence, unsurprisingly, the power of mathematics to map with external reality is both immense, surprising, and has never been falsified, irrespective of how baffling its predictions may have on occasion been - such as e=mc² and many other such equations, which have proven to work in reality for no other apparent reason that applicable mathematics shall not be falsified. And indeed, correct, applicable mathematics has never been falsified (by correct is meant not silly, content-free models that keep adding on as many new variables as there are new data points.)

There are so many misconceptions and outright errors in this text that I would simply dismiss it.

Hmm. Does mathematics exist? Does logics exist?

If me and you have two volvo v90 cross country cars(I love it thats the reason I am using it) and we want to have to divide it equally then we each get one each (two divided by two).

Now from this example let me take you to the world of aircrafts and space engineering where everything works because human have defined existing logics with the help of mathematics so that machines can understand it and help us make calculations faster.

If you understand a topic well enough then does not matter google or university professor comes to you, you will stick to the logics. The mathematical experiments that you have performed will always prove as a source to counter nonsense.

I will advise you to take these questions on a different social platform called Quora where a lot of brilliant minds can give good examples to clear confusions about such things.

Ok

Dear Ravi

In every subject there are variation in ideas especially among philosophiers, and with respect to mathematics, it is a science interact with all other sciences and has a wide applications in the real world.

Some time our criteria for existance related with material sense, but in mathematics I think it is related with logic.

Good Luck

Thanks

There are a lot of extremely questionable assertions and premises in the article referred to.

Before I comment further, may I point out that this theme has been quite extensively covered in RG before, and that it would behoove you to actually look up the relevant threads? I'm also slightly baffled at your behest to 'google' the names of the quoted individuals - believe you me, RG users as a rule know science, including names and sources....

This being said,

1- The referred article begins with a fallacy, nay a falsehood: mathematics is demonstrably NOT a human invention. Not only can many animal species count (aka use arithmetics) : https://www.nytimes.com/2018/02/05/science/animals-count-numbers.html

but they can even use simple mathematical modelling: e.g., in 'The Global Brain', Howard Bloom shows how bees have been known to seamlessly use predictive mathematics to find sources of food.

2- Now the thrust of the subsequent analysis and of the article itself - to wit, 'There is no Truth in Mathematics' actually totally misses the point.

The essence of mathematics is not truth or untruth: it is vocabulary definitions. The very core of mathematics is numbers theory, and number theory is a set of lexicon definitions - robust, WYSIWYG word definitions, not laying claim to any truth. From the existence of 1, whenever we put 1 and 1 together we create a whole different thing, a different entity, which we choose to call 2: from this very simple, robust, language-independent definition, at once arise seamlessly & unavoidably a whole exotic zoo of numbers - integers, real, rational, irrational, complex, quaternions, aleph, beth, Graham's number, prime, etc. upon which the whole edifice of modern physics is built - and hence our understanding of reality.

3- The article's contention that there is no such thing as two identical things in the universe and that hence that the assembling of numbers into ensembles is untenable is simply arrantly false. The building blocks of nature - photons, neutrons, electrons, protons, and so on - are all identical, and behave identically whenever put into the same environments (such as fields or chemical bonds etc.etc.)

4- Hence, unsurprisingly, the power of mathematics to map with external reality is both immense, surprising, and has never been falsified, irrespective of how baffling its predictions may have on occasion been - such as e=mc² and many other such equations, which have proven to work in reality for no other apparent reason that applicable mathematics shall not be falsified. And indeed, correct, applicable mathematics has never been falsified (by correct is meant not silly, content-free models that keep adding on as many new variables as there are new data points.)

There are so many misconceptions and outright errors in this text that I would simply dismiss it.

Mathematics exists in the same form that energy exists or other fundamental concepts of Science. Without Mathematics Physics or other fields of knowledge simply would not exist. And even the physical reality would not discovered, for instance the electromagnetic wave spectra or the gravitational waves found in 2015 as an outcome of the solutions of Einstein's gravitational equations.

The origins of math has become a hot topic of debate as neuroscientists continue to uncover mathematical abilities we seem to be born with, and have pinpointed regions in the brain responsible for mathematical thinking. Other scientists are finding that certain math capabilities vary by culture and depend on how we interact with the world. Both types of findings suggest math is a human construct rather than a phenomenon that determines how the cosmos is constructed. For more info visit here, http://www.kavlifoundation.org/science-spotlights/brain-or-universe-%E2%80%93-where-does-math-come#.W0Y2ctIza00

Most of the mathematical basics have born associated to real problems and after that extended to more abstract properties. For instance the Pythagorean theorem was taking initially as a property of certain trieangles, but later was the fundamental of geometry (Euclidean metric) and many other generalizations. The infinitessimal calculus was made absolutly close to Physics and so on.

Thus I think that the neuroscientists have very few characteristic things to find in mathematics if they restric its knowledge to pure logic created only in our brains. Without nature the mathematics were very different without any kind of doubt, even the logic mathematic.

Mathematics is about as real as things get. It is a logical system that builds an internally consistent set of rules that are amazingly useful in describing the world around us. It begins with simple counting and the assessment of value, then algebra, geometry, and so forth.

Different cultures may do things slightly differently. Our number system is base 10, but some had base 60 or other bases. With computers, we now have four number systems in use: binary, octal, decimal, and hexadecimal. The value of adding 1 and 1 may change depending on the number system, but the logical constructs remain unchanged and values can be converted if you know the number base used in calculations.

You could argue that mathematics is a construct of the human mind. In that case, you should be able to change the value of pi simply by force of will or have the angles in a triangle sum to 274 degrees. I think I will take my chances and stick with the old math.