Tag Archives: History of Mathematics

Roasted lamb shank, mashed potatoes, and vegetables cooked by the author in May 2025.

On Little Things

This week, recent events have inspired me to think about the wide, wide world on a smaller scale.—Click here to support the Wednesday Blog: https://www.patreon.com/sthosdkane—Click here to buy a copy of my book Travels in Time Across Europe which tells the stories from my year living in London that began 10 years ago this week.


This week, recent events have inspired me to think about the wide, wide world on a smaller scale.


Last Wednesday, after publishing “On Democracy, Part II” I took my place in the driver’s seat of my car, the Mazda Rua, and went out on a day trip to Jefferson City to join the protest against the congressional redistricting underway here in Missouri. I wanted to drive long distance at highway speeds again like I used to four times a year on my Long Drives East and West between Kansas City and Binghamton. There’s a lot of little things about those drives that I miss now that I’m more rooted here in Brookside. Today, I don’t drive every day. Often times if I can I’ll choose to walk to wherever I want to go in the neighborhood. It’s healthier to be sure, and I get the same free time away from the obligations that crowd my desk to listen to music, podcasts, birdsong, or to just think. These walks aren’t terribly taxing, Apple Fitness likes to remind me that the difficulty is “easy” to “moderate,” yet each one adds up into a sum which says that I am healthier today in mid-September than I was in mid-February or mid-March, let alone a year ago now. Moreover, I loved driving even just about town for that free time. Drivetime was often my podcast time. Now, I’m also reassured that I’m not operating a large and potentially dangerous vehicle while I’m listening to an engaging conversation or story; instead, I can focus on the story itself and not split my attention between that and the road.

So, last Wednesday I did try to recreate the things I loved most about those road trips that marked the beginning of this decade. On the outbound drive I listened to a fascinating discussion about political philosophy and space policy on Planetary Radio and on my return trip I listened to the pilot of the new audio drama Star Trek: Khan. Yet as much as I was thrilled to be back on the road and experiencing things that I felt like I had lost, even at my own volition, I still found that some of the little things got to me. For one, I was annoyed at getting stuck behind a semi-truck on the outbound drive for about 10 miles east of Sedalia and even more frustrated that I couldn’t pass a pair of semis that were ahead of me on the return drive as we transitioned from the two-lane divided highway in Cole County back to the one-lane country road that is US 50 in between the state capital and Sedalia. I know well that I control how I react to things, and therefore that I ought to react better to most things today than I did in my younger years, yet getting stuck behind those larger, slower vehicles on the stretch where passing was far more difficult really annoyed me. The beauty of a country drive is lost somewhat when you’re staring at the same big box retailer’s advertisement on the back of their vehicle for mile after mile.

These little things are what give our experiences life. The great, grand gestures that get remembered are one thing, yet they cannot be sustained without the small tokens of affection or whispered advice that comes from living and making the choices that define who we are. I believe that we are fundamentally formed by our experiences for good or ill. I’ve often ended up resorting to grand actions to try and solve questions or puzzles that find their way onto my desk. Marking something off a checklist is one of the most satisfying things I can do in my life. Those grand acts often become boxes which I can fill with the little things that I undertake. Currently, I am working on editing my translation of André Thevet’s (1516–1590) book Les Singularitez de la France Antarctique to send its book proposal off to an academic press. I have enough of my translation edited to send to them now, the first 16 chapters to be precise, yet there’s more still I need to do. This publisher prints page-facing translations and requires that the original text be sent alongside the translation. So, now I am spending my time typing out the original Middle French text of these first 16 chapters to be included in my proposal. There is a Wikisource page for this book, taken from the 1878 French edition that I could copy and paste from, yet it lacks the folio numbers from the original that are vital signposts to navigate the text and has enough nineteenth-century re-renderings of the sixteenth-century French original that I decided it was better if I just went ahead and typed it out myself. The first chapter took me about an hour to do, so I figure in all I might be able to have most of this typing done by the time I publish The Wednesday Blog next week.

Each character here is a little thing that together add up to the surviving thoughts and memories of a man who lived 450 years ago who exists in the scholarly memory of his time yet rarely in the spotlight. In my work, I hope to turn that spotlight on him and demonstrate his erudition and centrality to the cosmographic profession as it existed in the 1550s and 1560s. All this boils down to the same solution I’ve used to get through big projects for years. On Monday I smiled hearing a friend say essentially the same thing with her work in the history of mathematics, that the best way to solve a problem is to break it down into its constituent parts and figure it out piece by piece. A decade ago, this week when I moved to London, I found that the only way that the move was not overwhelming was to think of each thing I needed to do separately. My frustration rose when I found that I couldn’t make sense of a particular facet of one of the things I needed to do. One particular moment of note here was when I was summoned to the international student office to provide visa papers to confirm that I could legally study in the United Kingdom well after I’d started my coursework. Something got lost in the shuffle, but it was serious enough to scare me a little. When I moved to Binghamton, I had similar bureaucratic problems from issues getting my New York residency owing to my Missouri driver’s license having cracked in two, to a year later having big issues proving my residency to my university because I forgot to cross a t somewhere on a form.

Again, I choose how I react, and in the years since I’ve learned to take little things in stride and think of them in the broader context in which they exist. I believe doing the little things can show fidelity to a greater cause because it shows that I’m there for the long run, not just in the good moments. That’s something I learned from Robin Williams in Good Will Hunting, one of the finest movies I’ve ever seen. I think perhaps the best metaphor to explain what I’m trying to say to you, dear Reader, is that we should approach the things in life like we approach cooking. Recipes break down the task of cooking into smaller pieces that are more easily attainable. In May I made an Easter roast for some of my best friends that comprised several recipes I’d never tried before that day, and I truly didn’t know if it had worked until I finally sat down and took a bite of it. The roasted lamb shanks were perfect, as were the mashed potatoes, and the flourless chocolate cake that I rounded things out with was excellent and just as good the following day. In each recipe, I not only took things one at a time but even experimented a bit here or there based on my own experience from cooking similar things. For one, I had to quickly rethink how I was going to cook the lamb shanks because they were larger than nearly all of the pans I had. For another, I realized later than I wanted that in melting the chocolate chips for the cake I should’ve encouraged the process along with a spatula here and there. Each of these little things rounded out with a fine Tempranillo wine from Rioja to make one of the best dinners I’ve yet cooked.

I have a lot to do right now, and in every respect I’m on course to complete the things I have in my docket. The work would be overwhelming if I looked at it as a great mass, yet it is far easier to approach in small bites. That’s the big reason why I’m ending the Wednesday Blog one month from this week on 15 October. I’ve said what I wanted to say, and looking ahead I can use the time that I devote to writing this blog and recording the podcast working on other things great and small that need my attention. This publication is made up of a great many little things, small ideas that flower with their peers and culminate in an essay each week that I usually feel proud of writing. Little things make the lives we live.


A figure from Raphael's "The School of Athens" variously identified as Francesco Maria della Rovere, Pico della Mirandola, or Hypatia of Alexandria.

On Knowledge

This week, I want to address how we recognize knowledge in comparison to the various fields of inquiry through which we refine our understanding of things.—Click here to support the Wednesday Blog: https://www.patreon.com/sthosdkaneArtRaphael, The School of Athens (1509–1511), Apostolic Palace, Vatican Museums, Vatican City. Public Domain.Sources“On Writing,” Wednesday Blog 6.27.Surekha Davies, Humans: A Monstrous History, (University of California Press, 2025).Marcy Norton, The Tame and the Wild: People and Animals After 1492, (Harvard University Press, 2024), 307.Dead Poets Society, (1989) "What will your verse be?" Video on YouTube.


This week, I want to address how we recognize knowledge in comparison to the various fields of inquiry through which we refine our understanding of things.


Lately my work has been dedicated to a thorough review of the historiography within which I’m grounding my dissertation. I wrote about this two weeks ago in an essay titled “On Writing.”[1] My research is historical, yet it touches on secondary literature which operates within various fields within the discipline of history. These include Renaissance history, and its larger sibling early modern history, the history of cartography, the history of animals, the history of botany, and more broadly the history of early modern science. Methodologically, I owe a great deal to two great twentieth-century Francophone anthropologists, Alfred Métraux (1902–1963) and Claude Lévi-Strauss (1908–2009). While Métraux and Lévi-Strauss aren’t considered directly in the historiographic section of the new introduction that I’m writing for my dissertation, which is limited to sources published since the millennium, they nevertheless stand tall in the background of my history.

Today we often talk within academia about a desire for interdisciplinarity in our work and our research. We’ve found ourselves too narrowed by our ever shrinking fields and seek greener common pastures for grazing as our intellectual and pastoral ancestors alike once knew. In my case, this interdisciplinarity lies more in my efforts to incorporate historical zoology into my work, a methodology which seeks to use zoological methodology and theory to explain historical animals. I have friends who study many things. Among them is one whose passion for history, classics, and mathematics has come together to craft a dissertation which seeks to demonstrate the intersections between those three to better understand the great transitions in human inquiry. Another seeks to follow the medical connections across oceans between disparate regions in the Americas and Europe that nevertheless existed even if they seem remarkable today. Still more, I have a friend who applies basic economic need to explain a complex diplomatic situation that once existed between the Venetian Republic and the Ottoman Empire in the Adriatic Sea. All of these historians of whom I write are applying a degree of interdisciplinarity to their work that reflects their own disparate interests and curiosities. In early modern history we talk about curiosities as objects which were collected from disparate and exotic lands into cabinets to display the erudite collector’s prestige and wealth. I say our curiosity is something to be collected by those worthy archives, libraries, museums, or universities that will employ us in the near future and for us to feed with new ideas and avenues of investigation that we will never be bored with life.

In all of these things, there is an underlying genre of knowledge which I am addressing. I’ve written thus far about history alone, yet it is the same for the anthropologists, astronomers, planetary scientists, and physicists who I know. Likewise for the literature scholars and the linguists. Our fields of inquiry all grow on the same planet that comprises of our collected knowledge. In English, this word knowledge is somewhat nebulous. To me, it says that we know things broad or specific. In London, for instance, the Knowledge is the series of tests which new cabbies must complete in order to learn every street within a certain radius of Charing Cross. The Latin translation of this word, scientia, makes things even more complicated as that is the root of the English word science. Thus, when we refer to Renaissance science, there is always a caveat in the following sentence explaining that “this is not science as we know it but a sort of protoscience.” I was advised, similarly, after a particularly poorly received presentation at a workshop at the Museum of Natural Sciences in Brussels in October 2023 that I shouldn’t refer to “sixteenth-century conservation” because no such concept existed at the time; instead, it would be better to discuss a “genealogy of conservation.” This sense that modern terms, in use since the Enlightenment of the eighteenth century, ought not to be pulled further back into the past I think loses some of the provenance of those terms and how the Enlightenment philosophes first came across them. 

I find it telling that the Ancient Greek translation of knowledge, γνῶσις (gnôsis), is a word with which I’m more familiar from theology and the concept of Gnosticism whereas scientia reminds me of philosophy and the other fields of inquiry which grew from that particular branch of the tree of human curiosity. One might even say that philosophy and theology are a pair, siblings perhaps? They seek to understand similar things: on the one hand an inquiry into thought, and ideally wisdom, and on the other a search for the nature of the Divine, which at least in my Catholicism we can know because we are made in the Image of God. The division here between the Ancient Greek term being affiliated with faith and the Latin one with reason I think speaks to the Latin roots of my own education in Catholic schools and at a Jesuit university, where I learned about Plato and Aristotle, yet I recognized Aristotle’s Historia animalium (History of Animals) by its Latin name by which it was generally known in Western Europe for centuries before the rise of vernacular scholarship rather than by its Greek original Τῶν περὶ τὰ ζα ἰστοριῶν (Ton peri ta zoia historion). Note that the English translation of this title, History of Animals reflects better the Latin cognate of ἰστοριῶν rather than the better English translation of that Greek word, Inquiry.

Added onto these classical etymologies, in my first semester Historiography class at Binghamton University I was introduced to the German translation of scientiaγνῶσις, and knowledge. Wissenschaft struck me immediately because I saw the German cognate for the English word wizard in its prefix, and because I knew that the -schaft suffix tends to translate into English as -ship. Thus, my rough Anglicization of Wissenschaft renders Wizardship, which is rather nifty. Yet this word Wissenschaft instead was seen in the nineteenth century as a general word which could be translated into English as science. This is important for us historians trained in the United States because our own historiographic tradition, that is our national school of historians traces our roots back to German universities in the early and middle decades of the nineteenth century. I remember long sessions of my historiography class at UMKC discussing the works of Leopold von Ranke (1795–1886), the father of research-based history. I felt a sense that this concept of Wissenschaft seemed relatable, and as it turned out that was because Irish has a similar concept. 

Whereas in English we tack on the suffix -ology onto any word to make it the study of that word, in Irish you add the suffix -ocht. So, geology is geolaíocht and biology is bitheolaíocht. Yet note with the second example that the suffix is not just -ocht but an entire word, eolaíocht. This is the Irish word for science, added onto the end of bitheolaíocht to demonstrate that this word refers to the study of bith- a prefix combining form of the word beatha, meaning life. So, biology then is the science of life itself. Powerful stuff. I appreciate that Irish linguists and scholars have sought overall to preserve our language’s own consistency with its scientific terminology. It means that these fields of study, these areas of knowledge, can exist purely within the purview of the Irish language without any extra need to recognize that their prefixes or suffixes come from Latin, Greek, or English. There are some exceptions of course: take zó-eolaíocht, the Irish word for zoology, which effectively adopts the Greek word ζῷον perhaps through the English zoo into Irish. Would it not have been just as easy for whoever devised this hyphenated word to instead write ainmhíeolaíocht, translated into English as the science of animals? Here though I see more influence from English because this language adopts as much as it can from other languages out of prestige and a desire for translingual communicability. As an English speaker, I find scholarly works often easier to read because we share common etymologies for our words relating to knowledge. English’s sciencegeology, biology, and zoology are French’s sciencegéologie,biologie, and zoologie. In English, we drop any pretense of Englishness to clothe ourselves in a common mantle familiar to colleagues from related cultures around the globe. In academia this is to our mutual benefit, after all so much of our work is international. I’m regularly on webinars and Zoom calls with colleagues in Europe for instance. I believe this is the lingering spirit of the old scholarly preference for Latin as a lingua franca which at least to me seems close enough in the past that it’s tangible yet realistically it’s surely been a very long time since any serious scholarly work beyond classics was published in Latin for the benefit of a broad translingual readership?

I for one admire the Irish word eolaíocht and its root eolas, which translates into English as knowledge, that is an awareness of things because eolaíocht represents a universal concept while retaining its own native nature. So often in my research I am discussing the early assimilation of indigenous cosmovisions, to borrow a Spanish word put to good use by Surekha Davies in her latest book, into the nascent global world centered on Europe.[2] I see how these cosmic conceptions faded until they were rendered in Gothic or Latin letters on the voluminous pages of encyclopedic Renaissance general and natural histories which remain among the most often cited primary sources for these indigenous cultures who Marcy Norton argued in her 2024 book The Tame and the Wild: People and Animals After 1492 had their own classical past made remote from their colonial present by European contact, conquest, and colonization.[3] Seeing these indigenous perspectives fade into their categorized and classified statuses within the cosmos defined by Europe’s natural philosophers I feel fortunate that my own diaspora (which was also colonized) has retained this element of our individual perspective. I first came across the -ocht suffix in the word poblacht, the Irish word for republic. A famous story from the birth of the Irish Free State during the Anglo-Irish Treaty negotiations in 1921 tells of British Prime Minister David Lloyd-George, a Welsh speaker, remarking to Michael Collins, an Irish speaker, that their choice of a republic was unusual because none of the Celtic languages naturally have a word for republic. That word evokes its Roman roots in the ancient Res publica Romana, the Roman Republic, whose northward expansion across the Alps led to the gradual death of the Continental Celtic languages, whose speakers’ descendants today are largely the Western Romance speakers of French, Romansh, Occitan, Catalan, Spanish, Galician, and Portuguese, among others. Romance languages are noted for their common descent from Latin, whence they all derive variations on the Latin word scientia; English gets science through Old French. “How are you going to name your new government in the Irish language?” Lloyd-George asked. Collins replied something along the lines of “a kingdom is called a ríocht, so this government of the people (pobal) will be called a poblacht. Thus, the Republic of Ireland is named in Irish Poblacht na hÉireann. Naturally, this word pobal derives from the Latin populus, so the shadow of Rome hovers even over unconquered Hibernia. Yet that is another topic for a different essay.

Let me conclude with a comment on the difference between knowledge and wisdom, as I see it. The former is far more tangible. We can know things through learning embodied best in living and in reading. I know for instance to look both ways before crossing a street because plenty of people in the last 140 years have been hit by cars, buses, and trucks, and you can never be too careful. Likewise, I know everything I do about the things I study through reading what others have written about these topics. It’s my job then to say what I will. In Whitman’s words made immortal by our recitation, the answer to the eternal question, “that the powerful play goes on, and you may contribute a verse.” That’s history, people! Reading the powerful play of what others have written and summoning up the courage to take the podium and have your say. I first heard this particular poem, as did many in my generation, recited by Robin Williams in the 1989 film Dead Poets Society. Knowledge is the recitation of these facts we’ve learned. Wisdom is understanding how these facts fit together and speak to our common humanity. What makes us human? I believe it’s as much what we know as what we remain ignorant of. Our ignorance isn’t always a curse, rather it’s another foggy field we’ve yet to inquire about, a place where someone’s curiosity will surely thrive someday. It is another evocation of eolas still to come in our long human story. How wonderous is that?


[1] “On Writing,” Wednesday Blog 6.27.

[2] Surekha Davies, Humans: A Monstrous History(University of California Press, 2025).

[3] Marcy Norton, The Tame and the Wild: People and Animals After 1492, (Harvard University Press, 2024), 307.