It is said that the hierarchy of sciences goes like this: Physics > Chemistry > Biology > Psychology > Sociology. One wouldn’t be developed without the predecessor. But to understand Physics would be unimaginable without Math. In this fascinating essay, Professors Bo and Hannes Malmberg take us through the history of Mathematics and how it has been instrumental in almost every stage of mankind’s progress.

Geometric calculations led to breakthroughs in painting, astronomy, cartography, surveying, and physics. The introduction of mathematics in human affairs led to advancements in accounting, finance, fiscal affairs, demography, and economics – a kind of social mathematics. All reflect an underlying ‘calculating paradigm’ – the idea that measurement, calculation, and mathematics can be successfully applied to virtually every domain. This paradigm spread across Europe through education, which we can observe by the proliferation of mathematics textbooks and schools. It was this paradigm, more than science itself, that drove progress. It was this mathematical revolution that created modernity.”

As with everything else, we owe it Gutenberg for the invention of the printing press which democratised knowledge including the spread of mathematics.

“Advances in geometry began with the rediscovery of Euclid. The earliest known Medieval Latin translation of Euclid’s Elements was completed in manuscript by Adelard of Bath around 1120 using an Arabic source from Muslim Spain. A Latin printed version was published in 1482. After the mathematician Tartaglia translated Euclid’s work into Italian in 1543, translations into other vernacular languages quickly followed: German in 1558, French in 1564, English in 1570, Spanish in 1576, and Dutch in 1606.

Beyond Euclid, the German mathematician Regiomontanus penned the first European trigonometry textbook, De Triangulis Omnimodis (On Triangles of All Kinds), in 1464. In the sixteenth century, François Viète helped replace the verbal method of doing algebra with the modern symbolism in which unknown variables are denoted by symbols like x, y, and z. René Descartes and Pierre de Fermat built on Viète’s innovations to develop analytic geometry, where curves and surfaces are described by algebraic equations. In the late seventeenth century, Isaac Newton and Gottfried Leibniz extended the methods of analytic geometry to the study of motion and change through the development of calculus.

…Computation was aided by the adoption of Hindu-Arabic numerals and the popularization of decimal notation. In 1614, John Napier’s introduction of the logarithm transformed multiplication into addition, and it was followed a decade later by the invention of the slide rule that could efficiently perform multiplication and division”

The essay takes us through how math was central to the scientific revolution in the seventeeth century which in turn lead to the industrial revolution and also how math helped develop the social sciences including the study of economy and business. Mathematics continues to influence our lives dramatically even today – the greatest disruption facing humanity – the large language models behind ChatGPT and other Artificial Intelligence (AI) tools wouldn’t be possible without Mathematics.

“The last 200 years have seen the influence of mathematics deepen across almost all domains of human activity, amply supported by torrents of data and dramatic increases in computing power. Now we use math to model nuclear wars, pick players for baseball teams, track changes in literature, and forecast presidential elections. Sometimes, it seems the paradigm has reached its limits; that every field that can benefit from math has been introduced to it. But we may now be nearing the computational paradigm’s greatest success of all: modeling intelligence through math using large language models. In that sense, the computational paradigm may be reaching its logical conclusion: turning us all into math.”

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