Left to themselves, will a human child develop basic mathematic skills?

Good question, not sure.
If a child grew up with no basic mathematical training, 1+1=2 etc. I am sure, the human child would, eventually, make associations with the amounts of particular items, but…with no concept of numbers there would really be no association beyond visual computing. Obviously a pile of a dozen eggs, or buffalo hides or apples would be assimilated on a mental level as more than one but without actual symbolic numbers to denote actual and accurate accounting I don’t think true mathematical ability would evolve out of nowhere. More than likely it would be along the lines of a particular vessel or basket or whatever container that would either be completely full or half full etc.

In other words, a human, primitive or otherwise might invent a mathematical system but not have an actual ability to count so it would be more measurement based I would think. A turtle shell full of berries in trade for a turtle shell full of acorns, that sort of thing. Look at how little children think that 10 pennies are “more” than one Dime. haha

it will learn how to count, how to tell the difference between different and probably how to internally add and subtract quantities..
which makes it only marginally better than other animals

If not, maybe it will become an instinct over time. Like running. Or, breathing.

No

Counting is not ingrained. There are languages that have words for “one”, “two”, and “many”. and none for any other numbers.

And, it is highly unlikely that a natural developed system would be in Base 10. Could very well be Base 4 (one hand but not he thumb, becaus the thumb would be placeholder.)

It’s quite odd. Perhaps we can “pick up” even more advanced understanding by learning it from ???

As long as they have fingers & toes then of course they would.

The chances that “a random human child” will develop mathematical ability (assuming that the culture around her already supports that ability because many people already have the ability) is… dubious. What would be the drive, or the benefit to follow that drive? As a rule, people don’t develop reading ability on their own, and the culture fully supports the ability to read; demands it, even. (Edit to add: Basic reading and writing ability seems to be – to me, anyway – easier by far to learn than the more abstract concepts of mathematics.) And yet we’re covered up with functionally illiterate folks. There isn’t the demand for numerical ability. It’s handy, to be sure! But people can and apparently do function pretty well with next to no computational ability.

But… it’s not impossible, clearly. Two particular (not random) children grew up to independently invent calculus, after all. No one taught them that numerical / computational capability directly, although obviously they had instruction in mathematics that led them to a jumping-off point where it was possible to invent a new means of calculation.

And also obviously, numerical / computational capabilities have been developed “from scratch” over time, as mathematics is an acquired ability, and at one time it simply didn’t exist in any human society. No words for counting, no comprehension of the basic principles of mathematics, calculation, symbolic notation, etc. Those were all invented out of whole cloth by each generation “standing on the shoulders” of the previous generation’s understanding and learning.

So, for a child to be born in the society that @LostInParadise refers to, without even words for numbers, it’s unlikely to the point of impossibility that a child will not only invent a numbering system, the words and concepts for ordering and manipulating these new symbols, nor the language to describe or teach it to others.

I think very simple math probably, other than that probably not.

“Left to themselves” reminds me of feral children. Those are children who grew up away from human contact, either isolated, or living among animals. Those children never learnt human language, which greatly affected the way they thought and perceived the world. A feral child would be able to make a difference between “one” and “many” but if it never made a clear distinction between this many and that many, I don’t think it could count. Anything else above that is, of course, out of the question.

The article posted above explained well that language greatly affects the way we think. Tribes who didn’t have words for numbers couldn’t grasp certain quantities and couldn’t count beyond what they had the words for.

If the child never learnt any words for numbers, it can’t count.

So yeah, math probably needs to be taught.

@CWOTUS My point exactly.

Well, we were left to ourselves. People. Humankind. And apparently we did. Took a long time, though.

A sense of quantity (maybe in terms of volume?) probably predated actual arithmetic by a lot. But ancient inscriptions show record-keeping for barrels of grain, livestock, etc., for purposes of management of wealth and trade. Also travel required a sense of distances and supply. When those things became important to track, people figured out how to do it.

I recently enjoyed a 2015 movie called The Man Who Knew Infinity,(film) a biopic about the self-taught mathematical genius Ramanujan. He went far beyond conventional mathematics by dint of his own reason, instinct, intellectual gifts, and inspiration. No doubt he did learn the fundamentals from someone, but beyond that, one could certainly say he was left to himself.

Every philosopher of whom I am aware (with the possible exception of JS Mill) regards mathematics as a priori rather than a posteriori, meaning it can be derived from logic rather than relying on the “fuzzy logic” of Chomsky’s overlapping spheres of language meanings. But this proposition is reliant on there being a direct 1:1 correlation between mathematics and the Universe, which surprisingly has not been proven. In fact, since different mathematical models can arrive at different answers given the same initial propositions, it’s almost a certainty that at least some models of mathematics do not correlate to the Universe of things.

The answer to your question is therefore going to depend on your definition of mathematics.

Yes, IMO.

I’ve gotta say, even with a lifetime of schooling I still have not developed basic math skills, so I’m dubious. :P

@smashthestate Let’s stick with the identification by the uninitiated in elementary math to the problem of 1+1=2. This could be evidenced by the responding uninitiated mathematician candidate suggesting there were exactly two deer seen on today’s hunt, not one. Demonstrated by the spontaneous abstract use of fingers as counters when quizzed.

Very interesting question!
As a hobby linguist, there are scientists talking about grammar as something that we are more or less born with and develop to some extent naturally.

Even if not having studied verb tenses we can hear or know it is wrong to say “yesterday I buy a pizza”.

Perhaps it’s the same with maths?

Monkey see monkey learn. Curiosity as well. Unless the child is left alone to live in a solitary confinement there would be adults around that’ll take care of the child, such adults will perform daily tasks which may include math and its relevance thus as the child live among those adults they will become role models for the child where he/she can ask to be taught or simply learn by observation. For the child to want to learn/understand math there should be at least an underlying feeling that the need for math is apparent even though the child might not think it’s essential. For example, eventually the child will meet his/her peers that have apparently learned about math, being the only one to not grasp the idea of math will encourage the child to find a way to learn so that he/she won’t be left behind.

Where do you think ALL of our mathematical concepts came from? Obviously, some children have the curiosity/ability to understand and “invent” mathematical concepts.

@YARNLADY this question is more about any given human child. You might expect any given human child to blink, for instance, or to smile. This is somewhat less natural of an instinct, or is it? You seem to think it is indeed. Thanks for weighing in.

I don’t think so. Fluidity and flexibility with quantitative topics may come easier to some of us than others, but it is taught, not instinctual.

So. A lioness with baby lions doesn’t have a concept of math?
She knows that she has 8 cubs,and after she leaves she won’t sleep until she finds all 8 cubs.
Is that math, or just her recognizing each cub?

@MrGrimm888 I’ve read papers on psych studies which suggest that our inherent understanding of numbers consist of one, two, and many. There isn’t actually any conclusive proof that this and this and this and this and this is “five.” Mathematics are a model we use for describing certain phenomena, and models are, by their nature, incorrect. The number “five,” for example, is not five things. It’s a description of o o o o o. The question is whether “fiveness” is qualia or noumena.

Amend my above answer to mean basic as in counting to 10.

Get a ruler in your hands. Measure things until you start to understand how a ruler works. Measure some stuff and figure out where the center is. Say you measure a book and it’s 7/8” thick. You look at your ruler and see that every eighth is divided into two sixteenths, so obviously half of 7/8” is going to be 7/16”. If you write that out you have ½×7/8 = 7/16. And you notice that ½ is divided into 2/4 and then into 4/8 and so on, so you can convert anything to anything by multiplying all the numbers on top and then all the numbers on bottom.

Other rulers are divided into 10 and 100 parts. But an inch is still an inch, so anything on one ruler can be translated to the other ruler. A half inch on one ruler is 5/10 or 50/100 on the other. An eighth inch is just 12.5 marks when you have 100 marks per inch. A metric ruler divides an inch into 25.4 parts, so a half inch would be 12.7 of those parts. Pretty simple, isn’t it? Practice this a bit and people will think you went to wizard school.

I believe there is a basic understanding right from the start, and we gradually learn the names from those around us. A child with no one to teach the names would still develop the concepts independently AS NEEDED. If there was no need, it simply wouldn’t come up so no thought would be given to it, unless the person was also naturally more curious than most.