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history of mathematics morris kline s mathematical thought from ancient to modern times arthur koestler s the sleepwalkers and jacob bronowski s the ascent of man back to the chronological narrative i spent my a level year at the then notorious holland park comprehensive the flagship of the labour government s comprehensive education policy i spent that school year smoking vast quantities of cannabis going to amazing rock concerts in the nights and dropping acid about once a week come on it was the schoolyear 69 70 and holland park ladbroke grove was the centre of the british counterculture in the 1960s and on into the 1970s it is not a surprise that my a level results were to put it mildly bad it s a fucking miracle that i got any a levels at all i still managed to get a place to study archaeology at university college cardiff in those days one of the leading universities for the subject i had spent another summer digging at usk before the a level results came out and a lecturer recommended my selection for a place based on having got to know me on those excavation i think it was more likely that he wanted to make an impression on my father who was much further up the greasy pole than he was so indirect nepotism i studied archaeology metallurgy and mathematics i quite enjoyed the metallurgy but found the mathematics which in that first year didn t go beyond what i had already learnt at school boring i was stimulated by the archaeology but had immense problems with the essays because of my writing problems however all in all i decided it was not where i wanted to be and dropped out at the end of the year over the next decade i continued to teach myself the histories of mathematics and science in 1976 i lived for a time in malmø in southern sweden and in the well stocked public library discovered both stephen körner s the philosophy of mathematics and karl popper s conjectures and refutations as a result of which i added the philosophies of mathematics and science to my private curriculum shortly after i returned to the uk an assistant in a small book shop who knew my somewhat specialised taste in reading matter drew my attention to imre lakatos proofs and refutations which as i ve documented elsewhere was possibly the most influential book in my life throughout the 1970s i did numerous things to pay the rent and buy groceries for several years i spent the summers working as a field archaeologist and at one point for a whole year working on archaeology sites you learn an awful lot about the mechanisms of history i also spent a lot of time time working as a sound and light technician in theatre and as a set designer and constructer i worked concerts as a stagehand and a ticket controller i did a stint as an industrial painter in the docks if somebody offers you work cleaning out the diesel tanks in the keel of a ship so that welding repairs can be carried out politely decline and walk away fast i did the obligatory six months working in cardiff s nineteenth century east moors steel works i worked in the quality control for the ancient coke ovens taking coal samples before they came into the ovens the top of a nineteenth century coke ovens at three o clock on a summer s night is like something out of dante s inferno belching sulphurous fumes and sheets of flame my final occupation before finally leaving cardiff was renovating second hand electric stoves for resale it says something about the economic state of the uk in the 70s that it was a roaring trade in 1980 i moved to germany when people ask why i answer quite honestly i went on holiday and never went back again i ve already documented the events leading up to this move so i won t repeat myself here i couldn t speak the language so i went to evening classes to learn it it was too slow for my taste and i asked if there was anything faster and got told there was a german as a foreign language course in erlangen at the local university i inquired and it turned out that i would have to register as a student to be able to do the german as a foreign language course i had always intended to return to university so i did the german high school system closes with a high school certificate das abitur which qualifies the holder to study anything at university my science a levels only counted as a restricted high school certificate so i registered to study mathematics after one year of the german as a foreign language course i took and passed the final exam and could begin my mathematics degree in those days the first degree at a german university was a master s complete with thesis which was expected to take four to five years but many students took longer in mathematics it was called a diploma and i registered with philosophy as my subsidiary as already related elsewhere my philosophy professor was a historian of logic and mathematics and from the very beginning i followed an intensive history and philosophy of science course of studies with a set of excellent teachers the maths department had absolutely no interest in the history of the discipline so after two and a half years i changed from mathematics to a master s in philosophy in order to do so i required at least one humanities a level so i took german a level courtesy of the british institute in münchen i took english philology and history as my subsidiaries by then i had already been working for some time as one of the researchers in a major research project into the external history of formal logic i now seriously devoted as much time as possible to the study of the history and philosophy of science however i was a mature student without a grant or parental support so i was also working long hours to pay the rent and buy the groceries i won t list all the things i did to earn money but i did quite a lot of work as a stage hand for a large concert promoter in the end i ended up working as the evening manager of a youth and cultural centre with about three thousand guests in its various activities on a friday or saturday night i also worked there as a concert sound a lighting technician in my spare time my hobby was running the jazz club in the centre not surprisingly i was by now suffering from some fairly serious mental illnesses including a full blown alcoholism after a total of ten years at the university i had acquired all the course credits i needed to graduate ma and had written about two thirds of my master s thesis and a very detailed annotated outline for my doctoral thesis the planned doctoral thesis was originally going to be my master s thesis but had got too large and so i took one section out of it as a master s thesis as i have documented elsewhere not surprisingly the wheels fell off and instead of graduating i took a time out in the local loony bin going through withdrawal and trying to get my mental state back onto an even keel when i came out of the clinic it was obvious that i needed to reduce the stress in my life and as it was clear that as a forty year old graduate i would never get a job in the history of science which are as rare as hen s teeth for anybody i dropped out of university for the second time in my life it is often said that alcoholism is a symptom of an underlying phycological disturbance and that was certainly the problem in my case in fact within a year i was back in the loony bin with clinical depression i regularly attended the aa for several years and also had extensive out patient psychotherapy but i still wasn t really getting at the root problem however after a time i started regularly attending my professor s weekly research seminar in which graduate students and lecturers presented their actual research to public scrutiny these weekly sittings had originally been part of the research project in which i had worked for years in those days we often had guest lecturers and i got to meet and converse during the meals following the lectures with some of the world s leading historian of mathematics and logic including ivor grattan guiness martin davis and joe dauben at the ichs conference in hamburg in 1989 i got to chaperone the then ancient but still incredibly sharp legendary historian of mathematics dirk struik 1894 2000 who was the keynote speaker in our section of the conference as well as reconnecting with my professor if only as a guest i also began to hold public lectures on the histories of science and mathematics mostly in nürnberg i also became an active member of a group of historians of astronomy in nürnberg later i became an active member of the simon marius society i also began my legendary history of astronomy tours of nürnberg which in the meantime have been enjoyed by quite a large number of professional historians of science i still had not come to terms with my inability to write i could hold lectures on a myriad of topics without notes which i know from feedback are very good but faced with a blank page i became hopelessly cramped as i have noted elsewhere i finally discovered at about the age of fifty that i have high grade ad h d and suffer from dysgraphia i knew that some of my symptoms were indicative of dyslexia but i had no problems in reading i had had my nose buried in a comic magazine newspaper or book since i taught myself to read at the age of three dysgraphia is a disturbance of the part of the brain that controls writing the solution turned out to be quite simple i don t write i hold a lecture in my head and write it down as i go along hence my narrative style seventeen years ago i started this blog to teach myself to write it was an uphill struggle but the fact that i m still hear seem to indicate that i succeeded i have also over the years accumulated a small but growing number of real dead tree academic papers my work has found favour with a surprisingly large number of the world s leading historians of science a fact that i find mildly embarrassing over the years i have been asked to fact check texts written by quite a few of those historians and surprisingly given my life long struggles with the written word i am employed as a copy editor by historians writing in english who are not native speakers yes i m just some guy with a blog but i hope it is by now clear that that blog is written from a very solid and very real background as a historian of science even though i never managed to get any formal qualifications along the way i also research my blog posts carefully mostly in the circa one thousand academic volumes of the personal research library that line the walls of my apartment what i don t already have at home i borrow from the university library 7 comments filed under autobiographical june 26 2026 7 23 am scientific and mathematical instruments in the early modern period anybody who has been following this series will be aware that in england in the early modern period mathematical and scientific instruments played a central role in the world of practical mathematics as we have seen from small beginnings in the middle of the sixteenth century the business of instrument making expanded to become a significant factor in the mathematical community by the middle of the seventeenth century of course scientific and mathematical instruments had been in existence since antiquity but in the early modern period the number of different types of instruments and the number of each type of instrument produced expanded immensely one could argue that the production and use of such instruments was one of the defining aspects of the scientific and mathematical culture of the period however instruments didn t just define the period they also could be said to have defined the roles of the mathematical practitioners mathematical practitioner if not the name or definition of a career or profession but is a catch all term for all the diverse professions which were based on practical mathematics i e mathematics that is put to practical uses surveyors navigators gunners architects shipwrights sundial makers military engineers and book keepers many of whom we have met in the earlier posts in this series these people often in their publications added the title mathematical practitioner or a variant to their job description in their publications e g for instance henry bond s a new booke of gauging is written by henry bond practitioner in the mathematicks similar attributions appear in seth partridge s rabdologia written by seth partridge surveyor and practitioner in themathematicks and william purser s compound interest and annuities in which purser describes himself as mariner and practitioner in the mathematicks 1 gauging is determining the volume of full barrels or ship s holds for purposes of charging customs duty which relies on some form of approximation based on the use of special instruments and mathematical calculation as direct measurement and calculation is not possible because of the shapes literature on gauging and literature on dialling the construction of sundials were the most prolific form of mathematical literature published in the sixteenth and seventeenth centuries in england johannes kepler wrote a book on gauging in which he describes the determination of the volume of barrels using the method of exhaustion an early form of integration rabdologia is instruction in the use of napier s bones a simple calculating device invented by john napier the inventor of logarithms the fuller title of partridges book is rabdologia or the art of numbering by rods with many examples for the practice of the same first invented by lord napier baron of merchiston and since explained and made useful for all sorts of men by seth partridge surveyor and practitioner in the mathematicks 2 source a set of napier s bones source wikimedia commons this change in the role and status of practical mathematics can be clearly observed in the world of the surveyor in the high middle ages surveying was still carried out with the simplest of methods ropes and measuring poles to determine distances or even simple pacing by trained walkers the areas were then computed with simple geometrical methods to a very low level of accuracies boundaries were often vague and inaccurate this would all change radically over the fifteenth and sixteenth centuries first came a demand for better more accurate surveying created by a series of factors at the beginning of the fifteenth century the mathematical cartography of ptolemaeus re entered europe with the translation of his geographia into latin by giacomo or jacopo d angelo of scarperia better known in latin as jacobus angelus from a greek manuscript found in constantinople in about 1406 jacobus angelus latin translation of ptolemaeus geographia early 15th century source via wikimedia commons by the beginning of the sixteenth century ptolemaic cartography had come to dominate throughout europe secondly changes in the legalities of land ownership demanded better and more accurate estate maps with clearly defined accurate legal bou...
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