Gottfried Wilhelm Leibniz was born #OTD in 1646. He was one of the great polymaths of the age, and is best known for discovering differential and integral calculus independently of Isaac Newton.
Image: Wellcome Collection An etching of Leibniz, seated for a portrait. He is wearing
Leibniz developed the calculus after Newton, but published first. Newton probably developed the central ideas in the mid-1660s, and circulated unpublished papers (written as early as 1669) among colleagues. Leibniz had his main insights in the mid-1670s, and published in 1684.
However, we still use Leibniz's superior notation: ∫ for integrals, and d for differentials.

∫dx x = ½ x² + constant
Leibniz first used the symbol ∫ in his unpublished manuscript "Analyseos tetragonisticae pars secunda” (1675). The elongated "s" for "summa" replaced the notation "omn," for the latin "omnia" indicating "the sum over all small things."
Image: Gottfried Wilhelm Leibniz Bibliothek
Henceforth, please STOP saying "integrate" and START gravely intoning "I invoke the sum over all small things."
I especially love "sum over all small things" because it sounds like a mid-level D&D spell. The image mimics the layout of a magic user spell from the 1
(I meant to tag @SeamusBlackley in that last tweet.)
Leibniz is also known for his succinct formulation of the Primordial Existential Question. In his 1714 work "La Monadologie," he asked “Why is there something rather than nothing?”

If you’ve ever found yourself wide awake at 3am trying to square that circle, you are my people.
"La Monadologie" was published posthumously, so perhaps Leibniz already had a definitive answer to the question by the time readers appreciated his prehumous arguments.
I don't know who else sits in the little sliver of intersection when you Venn diagram interest in “archaic calculus terminology” and “AD&D first edition hardcover books.” But whoever you are, I tried to get the layout of the spell just right.
For everyone mentioning Neal Stephenson’s “Baroque Cycle,” yes this is one of my all-time faves. My one and only collaboration with Lee Smolin was bringing Neal to the Perimeter Institute for the Quantum to Cosmos festival back in 2009.
My wife introduced me to “Quicksilver.” Before we met, she worked at Harper Collins as the assistant to Neal’s editor. She gave me this when we started dating, it is one of my prized possessions.

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More from @mcnees

30 Jun
The Wilkinson Microwave Anisotropy Probe (WMAP) launched from pad 17B at Kennedy Spaceflight Center #OTD twenty years ago, the start of a three month journey to the L2 Lagrange point 1.5 million km from Earth.
Credit: NASA / Kennedy Space Flight Center
About 10 years earlier the COBE satellite had made the first measurements of tiny anisotropies in the Cosmic Microwave Background.
Image: NASA / COBE Science Team An ellipse covered in small blue, pink, and red blobs showin
WMAP collected about seven years of data, refining the COBE measurements and producing what was, at the time, the most detailed map of the Cosmic Microwave Background.
Credit: NASA / WMAP Team An ellipse with small blue, green, yellow, and orange blobs
Read 6 tweets
10 Jun
Mathematician Bernhard Riemann gave his famous lecture "On the Hypotheses Which Lie at the Foundations of Geometry" #OTD in 1854. He expanded on ideas introduced by his mentor Gauss and introducing what we now call Riemannian geometry.
Image: Familienarchiv Thomas Schilling An oval portrait of Bernhard Riemann as a young man, probabl
Riemann's geometry is broader than the geometry axiomatized by Euclid. He generalizes the infinitesimal version of the Pythagorean theorem describing the distance between two nearby points, and dispenses with the infamous 5th axiom about parallel lines.
(Euclid's 5th postulate basically says that if I give you a straight line and a point not on that line, both in a plane, you can draw a second line through the point that never intersects the first line. That's not true on intrinsically curved surfaces like a globe or a saddle.)
Read 8 tweets
9 Jun
*taps microphone*
Look, I'm not a medical doctor, I'm just a humble physicist. But I can tell you with some assurance that no one is being MAGNETIZED by vaccines.
That is... really something. Image
*Furiously hammering a nail into my own arm*
OH YEAH, THEN EXPLAIN WHY THIS STICKS.
Read 6 tweets
26 Apr
The naturalist and ornithologist John James Audubon was born #OTD in 1785. Go outside and look at some birds.
Portrait: John Syme
If you can’t go outside, or if you go outside but don’t see any birds, you can also look through @BioDivLibrary's online copy of Audubon's beautiful "Birds of America.” It is scanned from the @smithsonian's copy:
biodiversitylibrary.org/item/124835#pa… A plate from Audubon’s “Birds of America.”
Audubon's "Birds of America" was published 180 years ago yet this timeless classic can still surprise and delight the modern reader.
Read 4 tweets
26 Apr
Greg Abbott has been a practicing vegetarian for years, this is so disingenuous.
His family made their fortune off quinoa and other ancient grains.
(None of that is true, but neither is the stuff in his tweet.)
Read 4 tweets
15 Mar
Mathematician Grace Chisolm Young, author or co-author of a host of articles and books on set theory, geometry, topology, and calculus, and the first woman to officially earn a doctoral degree from the University of Göttingen, was born #OTD in 1868.
Image: Sylvia Wiegand / MAA Image
It’s hard to say exactly how many papers and books she produced. She wrote several articles on her own, more as co-author with her husband William, and also worked on many projects where William appeared as sole author. It’s estimated they wrote over 200 papers & books together.
Grace Chisholm Young is best known for her contribution to what is now called the Denjoy-Young-Saks theorem, classifying the possible behavior of the Dini derivatives of arbitrary measureable functions.
Image: Young, Quart. J. Math, 47 (1916)
babel.hathitrust.org/cgi/pt?id=uc1.… Image
Read 4 tweets

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