@WillOrrick Thank you for the point you brought up. I wanted to discuss it here, if that's okay. Yes, that point was largely based on Wikipedia but I did use their source. I considered this acceptable as it is a question to gather information. If this were a scientific paper, I would likely not do this.

@WillOrrick Please can you provide sources and/or points as to whether the ancient Chinese, Indians or Arabs utilised our concept of negative numbers / subtraction. I would genuinely like to know.

*Circa 300 B.C.E.

You are also welcome to discuss whether, in this instance, it was good to use Wikipedia for information.

The second half of page 11 of Zetetics and the Art of Mathematical Enquiry by Peter Merrotsy discusses counting boards.

Page 13 discusses four suggestions as to how the tablet could have been used. Suggestions 3,4 rely on orders of magnitude except with allocations for multiples of 5 (a somewhat 'half-step', despite $\sqrt{10}≠5$.)

Regarding Stephen Kent Stephenson, Ancient Computers does reference 300 BCE with the Salamis Tablet in the figure title on page 6 and footnote 13 on page 41.

I often use Wikipedia; in many instances it's the first source I go to. It's good to remain skeptical, of course, and to check the reliability of the sources Wikipedia cites. I also contribute to Wikipedia where I can, so I have some familiarity about how Wikipedia articles develop and what the standards are.

Statements in Wikipedia are supposed to be backed by reliable sources, but standards are enforced by volunteers and material that should not have been added may remain in place for long periods of time, especially in articles that are not watched by a large number of editors.

Since Stephenson's arXiv preprint does not appear to have been published in a journal, which suggests it never underwent any kind of peer review, it is the kind of source that is often questioned, and sometimes removed, on Wikipedia. Previously the Salamis tablet article presented the use of negative numbers as an established fact, but the article has been modified recently to clarify that this is only a hypothesis.

Earlier this year the claim about the Salamis tablet was also added to Wikipedia's article on negative numbers, but was immediately questioned by other editors. It has not, however, been removed. My personal feeling is that it should be removed until a source can be found that has passed a sufficiently rigorous level of peer review.

As for the Chinese, the place to look is the book "Nine Chapters on the Mathematical Art". The dating of this is complicated. A version with extensive commentary was produced by the brilliant Liu Hui in the third century CE, but it is considered certain that the work in some form goes back at least to the first half of the second century BCE.

Most Chinese manuscripts were destroyed by order of the emperor Qin Shi Huang late in the third century BCE, but there appears to be strong evidence that the "Nine Chapters" are based, at least in part, on fragments of older material that people managed to save from the destruction, perhaps on much older material.

At any rate, the part to look at is Chapter 8, which presents the Gaussian elimination algorithm as we know it today. Example problems include systems of linear equations with negative coefficients. The rules for adding and subtracting signed quantities are also given in this chapter.

The rules for multiplication involving negative numbers do not appear to have been known in China until much later. The "Nine Chapters" are known to have influence the mathematics of neighboring cultures, such as Korea and Japan. I am unclear on what is known about possible Chinese influence on India.

The first person known to have recorded the rules for multiplying with negative quantities as Brahmagupta in the seventh century CE. The lines of influence linking India to the Arabic speaking world and the Arabic speaking world to Europe are well established.

I appreciate your points here, Will Orrick. I admit I have been underwhelmed so far with the research I have done on this topic; euro-centrically. I started the question as "Why are integers before rationals" but has veered off from there. Thank you for this information as I now have some reading to do.

@WillOrrick How much of an influence do you think Asian mathematics has had on the present-day maths used worldwide? In my opinion, the other continents have had, at least, fairly strong connections to European academia and influence - after colonisation.

And corresponding lines of open communication, academically.

I do resonate with the idea of an ancient alternative to deducing propositions stemming from axioms.

Actually a better question might be what value does the history of Asian mathematics have for us today?