Issue 6. Discovering the work of your past self

 

Preamble

I write this, honestly, in surprise. But to explain that, I need to tell you a very brief story. It started about this time last year, somewhat ironically, with me doomscrolling. I came across a video talking about how we accredit scientific discoveries to people by name, but that this can overshadow the fundamental work of the people that came before them. I was inspired, albeit angry, and this combined with the desire to do something meaningful before the end of the academic year: I set out to complete a study. A research paper, in its entirety. Hindsight, wow, what a miscalculation of what was achievable with no funding or real time to dedicate.

The thesis of my paper? That educational curricula are systemically racist. Hmm. Definitely bit off more than I could chew. Do I still believe this? In some (much smaller) amount, but the important part is that I didn't find data to prove it. 

It took me about 3-4 months to complete, and at the end I honestly hated what I'd made. It was full of waffle, and didn't find out anything useful. I left it alone for the foreseeable future, happy to say it was never to be returned to again. 

A few days ago, I was reinspired to do something.  I'd hypothesised a statement, done a small study, and found data that showed a correlation. You know what, I have something here, I'm going to do something with it. Now, I kind of have (had) only 2 options. The first, is to write it up as an article more than a paper, and entirely removing any mention of misinformation or racism (which is true for either option), and submit it to an online STEM journal for high schoolers called TSS. The second option I’m going to refrain from discussing because explaining my plan increases my fail rate by about 1000‰, and it is also currently what I intend to do going ahead.

Back to TSS, (the story is almost over hang in there) I re-go over their submission layouts and tips, and start outlining in a Word document as to what the hell I’m going to write. The article contains a figure, and I was looking back through my computer for it when I happen across a pdf dated in August called ‘Shining a light on the ancestors of science and mathematics’. Corny name aside (as I had come up with the far better ‘Looking at how learning shapes language’ moments earlier), this means I had already written this up for a second time, and already submitted it to TSS, and—most annoyingly—already been rejected. What was I gonna do now?

Maybe this is the universe telling me to move on already; maybe I’m being extremely naïve, but some way or another I’m convinced there is something of value in what I did, and I have dreams for it. Believe me, this project isn’t dead. At least, not yet. I still have plans for this but I’m happy to release this failed article, maybe as some kind of historical archive, maybe as some kind of sentimental metaphor for the journey of chasing your goals or something of similar sappiness. “The reason for release is left as an exercise to the reader.”

Below follows the pdf that I found, edited only to fix grammar or typos, but with no other changes. Comments from November-me to August-me are pointed as endnotes, indicated by a symbol in yellow.

Endnotes will appear in this order: * then † then ‡ then § then || then ¶ then # then Δ then ◊ then ↓

The document

Shining a light on the ancestors of science and mathematics

27 August, 2025

Coming across an issue

There is no time like the present, and never has that been more true for the areas of science, technology, engineering, and mathematics. More than ever, we are seeing breakthrough developments across these fields that open our eyes to the marvel that is the world around us, and what we still have left to learn. In this era of looking forwards, it is just as important to remember to look behind us, to the scientists of the past who — just as we do now — * pushed the limits of what was thought to be possible.

It is with regards to this that my story here started, towards the tail-end of 2024. A video online, from whom I cannot remember, was explaining the lesser-known pioneers of the past that had discovered crucial mathematical concepts. For example, Al-Karaji of Persia, who is the earliest person in recorded history to be accredited with the conception of what many today refer to as ‘Pascal’s Triangle’, as well as the production of the Binomial Theorem (Rashed, 1994). Al-Karaji made his discovery around 1,000 years before Blaise Pascal described the triangle in his Traité du triangle arithmétique, yet due to factors such as imperialism, and the lack of communication internationally, Pascal’s attribution became commonplace in Europe, which spread across the Atlantic to the North Americas (Fowler, 1996). This video planted a mental seed into my head that grew into the desire to find out other examples of these cases. †

Okay, let’s do something about it

In the months that followed, and into the New Year, I researched into 3 cases: Pascal’s Triangle, Pythagoras’ Theorem, and Gutenberg’s accreditation to being the inventor of the printing press. Each one being as insightful and interesting to me as the others.

While Pascal indeed defines his Triangle in his treaty of 1679, it had also seen mention in 1556 in Italy by Tartaglia (Tartaglia, 1556; Edwards, 2013), and elsewhere across Europe by Jordanus de Nemore 200 years prior in the 13th Century (Barnabas, 1989). At the same time, across the globe in Ancient China, the Song dynasty’s Yang Hui had defined the structure of the triangle. And, 200 years before that, the Persian mathematician Omar Khayyám theorised the triangles in his algebraic treaties (Weisstein, 2002; Coolidge, 1949). That’s a range of roughly 600 years!

As for the printing press, while indeed ‡ Johannes Gutenberg popularised movable-type printing across Europe (Meggs, 2016), allowing the widespread sharing and communication of information to the masses like never before, the origins trace back to the Song dynasty yet again, where Bi Sheng had developed movable-type in both wooden block and fired ceramic forms, circa 1041 AD (Tsuen-Hsuin, 1985).

These two cases were fascinating for me to discover, but leave nothing to the Pythagorean theorem. Pythagoras' contribution to the theorem is highly contested, though he is credited with its first proof in the sixth century BC (Euclid, 1956). Once more, the writings of the chinese text Zhoubi Suanjing in the 1200s BC predate the discoveries of Europe’s earliest mention of the theorem, with Euclid providing the oldest existing axiomatic proof in his book Elements, in the third century BC (Cullen, 1996; Aaboe, 1997). However, the knowledge that a2+b2=c2 predates Pythagoras by over 1,000 years, as clay tablets from the Old Babylonian period display lists of integer values that satisfy the theorem, also known as ‘Pythagorean triplets’ (Neugebauer, 1969). §

Statistical analysis and exciting prospects

My interest now thoroughly piqued, I felt a recurring intrigue into the nature of these cases that aren’t misattributions — many concepts are credited to a scientist by other scientists, who recognise their valuable work in that field (e.g. it was not Max Planck himself who named it ‘Planck’s constant’ but his peers) — but surely felt under-representative to the vital work of those before them, who had either already made that discovery or provided the required foundation to be built upon.

And so I conducted a small, internet questionnaire study with 24 respondents from various demographics and backgrounds to test what I hypothesised: the longer an individual spends in formal education, the more likely they are to identify scientific and technological concepts as according to typical curricula. I did this by using the three aforementioned cases of the printing press, the Pythagorean theorem, and Pascal’s Triangle — which I referred to in the analysis process as the binomial coefficient array.

Respondents were asked to ‘Please identify the name of the man who invented the printing press’, and were then shown respective images of the Pythagorean theorem and Pascal’s triangle, and asked to ‘Please identify what is being shown in the picture below’.

I did, in fact, find that within my small sample size the hypothesis remained true, with no respondents mentioning the works of anyone before Gutenberg, Pascal, or Pythagoras. The individual's resident continent seemed to have no identifiable influence across the sample, but may differ with larger groups. ||

 

¶

My findings act as a preliminary study to show the existence of value in further research into identifying why these prior discoveries of equal, or greater, importance are not commonly known or taught, and — more generally speaking — into discovering more of these scientific trailblazers of the past.

As we look forwards into the future, what else will we discover of the past behind us, of the great discoveries of Ancient China, India, the Islamic Golden Age, and more? #

References Δ

● Rashed, R. (1994). The Development of Arabic Mathematics: Between Arithmetic and Algebra. Boston Studies in the Philosophy of Science, 156, 63. ISBN 9780792325659

● Fowler, D. (1996). The Binomial Coefficient Function. The American Mathematical Monthly, 103(1), 11. https://doi.org/10.2307/2975209

● Tartaglia, N. (1556). General Trattato di Numeri et Misure, Part II. 69.

● Edwards, A. (2013). Combinatorics: Ancient and Modern. Oxford University Press, 171-174. ISBN 9780198739050

● Barnabas, H. (1989). The arithmetical triangle of Jordanus de Nemore. Historia Mathematica, 16(3), 213-223. https://doi.org/10.1016/0315-0860(89)90018-9

● Weisstein, E. (2002). CRC Concise Encyclopedia of Mathematics, Second Edition. Taylor & Francis, 2169. ISBN 9781584883470

● Coolidge, J. (1949). The Story of the Binomial Theorem. The American Mathematical Monthly, 56(3), 147-157. https://doi.org/10.2307/2305028

● Meggs, P. (2016). History of Graphic Design, Sixth Edition. John Wiley & Sons, 70. ISBN 9781118772058

● Tsuen-Hsuin, T. (1985). Science and Civilization in China, Vol 5 Part 1. Cambridge University Press, 201–217. ISBN 9780521086905

● Euclid. (1956). The Thirteen Books of Euclid's Elements, Translated from the Text of Heiberg, with Introduction and Commentary, Vol. 1 (Books I and II), Translated by Heath, Thomas L. Dover Publications, 351-352. https://archive.org/details/euclid_heath_2nd_ed

● Cullen, C. (1996). Astronomy and Mathematics in Ancient China: The ’Zhou Bi Suan Jing’. Cambridge University Press, 206-217. ISBN 9780521550895

● Aaboe, A. (1997). Episodes from the Early History of Mathematics, Volume 13. Mathematical Association of America, 52. ISBN 0883856131

● Neugebauer, O. (1969). The exact sciences in antiquity (2nd ed.). Courier Dover Publications, 36. ISBN 0486223329

Endnotes

Well that was rough, let me tear into it. This is why we don’t submit things that haven’t had a few more revisions.

 

* This is just poor grammar, either use an em—dash, or an en - dash with spaces between. Other than that this is a strong opening, it sets an informal-formal tone that's right at place in an article.

 

† Most of this paragraph is, fine, if cluttered with quotes and citations and italics that just kind of look gross all too close together. But, "it is with regards to this"?, "by whom I cannot remember"? Who talks like this?

 

‡ I was holding off from commenting on the use of "indeed" in the previous paragraph, but to use it two paragraphs in a row is just egregious. This kind of language is for revealing big plot-twists, and communicates an odd self-superiority. Not to mention the nauseatingly fake excited tone - I'm not presenting a children's show. Calm down, August-me.

 

§ While I think I know what I was trying to say here, this sentence just seems... incomplete? It's like I wrote the beginning and then never came to a conclusion. The tone for this sentence to make sense relies on it being read aloud, which isn't an amazing prerequisite for a written text. The rest of the paragraph is similarly hard to read; was I allergic to proofreading?

 

|| This whole section isn't criminal, but again some of the holier-than-thou (or smarter-than-thou, in this case) language is trying to creep in like, "now thoroughly piqued" and "a reoccuring intruige". There are worse sins to commit in writing but this isn't great. And that parenthetical ", in fact," is another attempt at building excitement around the topic, but just comes off as oozing with ego. Once again, calm down, August-me.

 

¶ This figure is tolerable to look at, but far from perfect. If I was serious about publication, I really should have tidied up the visible gridlines, and formatted it smarter (i.e. not in Google Sheets). Something like this.

 

  Maybe a little misleading but it shows the key trend.

 

# I set the 'children's entertainer' tone to 100% here and it shows, this part is unbearably optimistic. It's like reading a science book you'd get for a 10 year old.

 

Δ (Was I putting in zero effort at all?) This is a really poor attempt at APA 7th ed. referencing. I mean, the smaller stuff like not writing volumes in italics is somewhat excuseable, but it's not even written alphabetically. I would reject this paper! I can easily see why they [TSS] did.

Takeaways

What did I learn from this experience?

1. Don't allow yourself to rush a project just because you're enthusiastic about it: your outcome will be worse.
2. If you're thinking of writing something for serious publication, you must spend serious time editing, revising, editing, and revising again. Especially to catch such rookie errors.

Thanks for bearing-with in today's issue. Aside from the momentous, maybe-unachieveable, plan I have in mind for this project, there's another long essay project set to be out hopefully sometime within the next year that I'm really excited to work on. Let me just get this out the way first. Thanks for reading!