At the Airspeed Velocity of an Unladen Swallow
Women In Mathematics #4: Sofia Kovalevskaya


A common theme amongst female mathematicians is breaking down gender barriers — Sofia Kovalevskaya was not only the first major Russian female mathematician, but the first woman appointed to a full professorship in ALL OF NORTHERN EUROPE.

Born in 1850 in Moscow, and living 41 years, Ms. Kovalevskaya’s work was mainly devoted to advanced differential equations and the modeling of mechanics as such. When she was 11, she was prepped for tutoring in calculus, eventually showing an obvious talent in mathematics. However, due to the sexist laws dampening women’s education at the time, she forged a marriage with one Vladimir Kovalevsky to allow emmigration (a future collaborator of Charles Darwin), and moved to Germany in 1867. After 2 years in Heidelberg, she moved to Berlin, taking private lessons from the famous Weierstrass, father of Analysis (if you’ve taken Real Variables/Real Analysis, you know him from any one of the bazillion things named after him, such as the Bolzano-Weierstrass, Weirstrass-Casorati, etc). 

By 1974, she made her mark on partial differential equations (PDEs), the dynamics of Saturn’s rings and on elliptic integrals, all as a doctoral thesis, giving her the distinction of being the first woman in all of european history to have a doctorate’s in mathematics. 

However, despite her obvious talent and knowledge, she was denied even the right to teach for free. Returning back to Russia in 1879, she failed once again to obtain professorship because of their radical political views, and turned back to head to Germany. However, after giving birth to a daughter, and leaving her in the care of her sister, she traveled to Sweden, getting a position at the University of Stockholm. It was here, she died of the flu, in 1881, after returning from a vacation in Genoa. She is celebrated in Russia for her achievements. 


20 Things You Didn’t Know About Relativity

Galileo invented it, Einstein understood it, and Eddington saw it.

1  Who invented relativity? Bzzzt—wrong. Galileo hit on the idea in 1639, when he showed that a falling object behaves the same way on a moving ship as it does in a motionless building.

2  And Einstein didn’t call it relativity. The word never appears in his original 1905 paper, “On the Electrodynamics of Moving Bodies,” and he hated the term, preferring “invariance theory” (because the laws of physics look the same to all observers—nothing “relative” about it).

3  Space-time continuum? Nope, that’s not Einstein either. The idea of time as the fourth dimension came from Hermann Minkowski, one of Einstein’s professors, who once called him a “lazy dog.”

4  But Einstein did reformulate Galileo’s relativity to deal with the bizarre things that happen at near-light speed, where time slows down and space gets compressed. That counts for something.

5  Austrian physicist Friedrich Hasenöhrl published the basic equation E = mc2 a year before Einstein did.

6  Never heard of Hasenöhrl? That’s because he failed to connect the equation with the principle of relativity. Verdammt!

7  Einstein’s full-time job at the Swiss patent office meant he had to hash out relativity during hours when nobody was watching. He would cram his notes into his desk when a supervisor came by.

8  Although Einstein was a teetotaler, when he finally completed his theory of relativity, he and his wife, Mileva, drank themselves under the table—the old-fashioned way to mess with the space-time continuum.

9  Affection is relative. “I need my wife, she solves all the mathematical problems for me,” Einstein wrote while completing his theory in 1904. By 1914, he’d ordered her to “renounce all personal relations with me, as far as maintaining them is not absolutely required for social reasons.”

10  Rules are relative too. According to Einstein, nothing travels faster than light, but space itself has no such speed limit; immediately after the Big Bang, the runaway expansion of the universe apparently left light lagging way behind.

11  Oh, and there are two relativities. So far we’ve been talking about special relativity, which applies to objects moving at constant speed. General relativity, which covers accelerating things and explains how gravity works, came a decade later and is regarded as Einstein’s truly unique insight.

12  Pleasure doing business with you, chum(p): When Einstein was stumped by the math of general relativity, he relied on his old college pal Marcel Grossmann, whose notes he had studied after repeatedly cutting class years earlier.

13  Despite that, the early version of general relativity had a major error, a miscalculation of the amount a light beam would bend due to gravity.

14   Fortunately, plans to test the theory during a solar eclipse in 1914 were scuttled by World War I. Had the experiment been conducted then, the error would have been exposed and Einstein would have been proved wrong.

15  The eclipse experiment finally happened in 1919 (you’re looking at it on this very page). Eminent British physicist Arthur Eddington declared general relativity a success, catapulting Einstein into fame and onto coffee mugs.

16  In retrospect, it seems that Eddington fudged the results, throwing out photos that showed the “wrong” outcome.

17  No wonder nobody noticed: At the time of Einstein’s death in 1955, scientists still had almost no evidence of general relativity in action.

18  That changed dramatically in the 1960s, when astronomers began to discover extreme objects—neutron stars and black holes—that put severe dents in the shape of space-time.

19   Today general relativity is so well understood that it is used to weigh galaxies and locate distant planets by the way they bend light.

20   If you still don’t get Einstein’s ideas, try this explanation reportedly from The Man Himself: “Put your hand on a hot stove for a minute and it seems like an hour. Sit with a pretty girl for an hour and it seems like a minute. That’s relativity.”


If you know anything about computers and their history, you know Charles Babbage’s name. What many DON’T know is that without Ada Lovelace, Mr. Babbage might not have gotten anywhere.

Born December 10, 1815 and living to be just shy of 37, she is probably best known for working…


(via Saturday Morning Breakfast Cereal)


‘Rock Star Cosmic Pioneers’ - Megan Lee 

Hypatia (355-415 CE)



Life is an unfoldment, and the further we travel, the more truth we comprehend. To understand the things that are at our door is the best preparation for understanding those that lie beyond.


Hypatia was an eminent mathematician, philosopher, astronomer and astrologer who was head of the Neoplatonist school at Alexandria.  She is considered the first woman to significantly contribute to the field of mathematics.  She was also famous for her skills as an orator – people traveled far and wide to hear her speak.  Unfortunately, her career was flourishing at a bad time.  Christianity had just recently become the official religion of the Roman Empire, and mathematics and astrology became associated with Hellenic paganism and therefore were considered heretical. In 412, a new Archbishop, Cyril, came to power.  The previous Archbishop seems to at least tolerated Hypatia, but Cyril was, quite frankly, a fanatical nutball whose main platform was the extermination of Neoplatonists and Jews.  He perceived Hypatia as a threat, not just because of her occupation, but because of her popularity with the non-Christians of Alexandria and, of course, the fact that she was a woman (GASP).  To get rid of her, he began a vicious smear campaign, depicting her as an evil witch who regularly engaged in black magic and cast spells on anyone she wanted.  But despite the number of people turning against her, Hypatia refused to leave the city.  In 415, she was abducted by a group of Christian zealots, dragged from behind a carriage to a church, and flayed alive.  Her body was then torn apart and burned.  The false image of her as a witch stayed with her after her death.  John of Nikiu, a 7th century bishop, described her as “devoted at all times to magic, astrolabes and instruments of music, and…beguiling many people through her Satanic wiles.”  Aren’t we all, John.  Aren’t we all.


Further reading:

“Hypatia and Her Mathematics” by Michael A. B. Deakin -


Scientists are a famously anonymous lot, but few can match in the depths of her perverse and unmerited obscurity the 20th-century mathematical genius Emmy Noether.

She is the most important mathematician who ever happened to physics. Even if this sentence doesn’t make sense.