A publication by mathematics historian Viktor Blåsjö has been included in ‘The Best Writing on Mathematics 2016’ by Princeton University Press. The 2016 edition includes a selection of the year’s best and most beautifully written scientific publications. As a result, the edition reaches an international public with a broad interest in science. Blåsjö has also recently been informed that another of his articles has been selected for the 2017 edition.
Selection of the year’s best and most beautifully written scientific publications
Publication by Viktor Blåsjö in ‘The Best Writing on Mathematics’
Blåsjö’s article selected for publication in ‘The Best Writing on Mathematics’ was ‘The Myth of Leibniz’s Proof of the Fundamental Theorem of Calculus’. It was published last year in the Dutch Nieuw Archief voor Wiskunde, but it has made it into the international spotlight. This is a major honour for Blåsjö, because he is a mathematician with a mission. “If you haven’t studied history, it’s as if you’ve never travelled”, he says, paraphrasing Descartes.
Four hundred years old
“The 400-year-old mathematics that my article deals with is still just as true today”, Blåsjö explains. “But it is still interesting to know how it has developed from a historical perspective. A broader perspective often results in a less dogmatic attitude. In science and education, it is especially useful to learn how insights have developed over time, instead of thinking: that’s just the way it is.” Unfortunately, few universities teach the history of mathematics today.
Blåsjö earned his PhD last year for his research on the 17th-century mathematician, physicist and philosopher Gottfried Wilhelm Leibniz, and he now has a tenure track position at the History of Mathematics research group. Utrecht University is the only university in the Netherlands with a chair group for the History of Mathematics, and in Blåsjö’s home country of Sweden there is not a single professor in the field. “Despite the fact that universities often have several professors for the history of philosophy”, he says in comparison. The philosophical works by Leibniz are available in English, but one must be fluent in Latin to read his writings on mathematics.
In Blåsjö’s article selected for publication in ‘The Best Writing on Mathematics’, he deals with a major misconception about one of Leibniz’ works. The article in question is generally considered to be the proof of the fundamental theorem of calculus, but Blåsjö shows that this is not in fact the case. “In this article, Leibniz deals with situations in which finding a formula is no trivial matter”, Blåsjö explains.
Leibniz and his contemporaries were the first mathematicians to work with formulas. Until then, mathematics was based on ‘tangible’ geometry. The reliability and meaning of formulas was therefore strongly related to geometrical problems. “In order to interpret this article correctly, you have to have a good understanding of the historical context”, Blåsjö elucidates.
For the 2017 edition of ‘The Best Writings on Mathematics’, the editors selected Blåsjö’s article ‘How to Find the Logarithm of Any Number Using Nothing But a Piece of String’, which was published in the American periodical The College Mathematics Journal. “This article is also a form of converting tangible geometry into formulas. It is a fun recipe for finding logarithms by using measurements of a chain that is held up on two points.”
PhD research of Viktor Blåsjö