Mars mission: A confident Isro gearing up for insertion

 

Press Trust Of India  |  Bangalore

September 15, 2014 Last Updated at 20:40 IST

As India's Mars Orbiter Mission (MOM) raced for its tryst with the red planet on September 24, Indian space scientists are gearing up for the critical manoeuvre of the spacecraft, sounding confident about the mission's success.

The spacecraft has covered 98 per cent of its 300-day odyssey and the critical manoeuvre would be performed when the scientists restart the onboard liquid engine which is in sleep mode for nearly 10 months.

The MOM, India's first interplanetary mission, was launched on November 5, 2013 by India's workhorse Polar Satellite Launch Vehicle(PSLV) from the spaceport of Sriharikota in Andhra Pradesh.

At a media briefing, ISRO said today it was confident about the MOM's success going by its performance so far.

Commands for inserting the Mars spacecraft into the Red Planet's orbit were being uploaded since yesterday and were expected to be completed today, it said.
"The remaining crucial thing is Mars Orbit Insertion (MOI), and if you see some missions have failed because of failures in estimates in the distance from the mars, and if you see the history they were at very early stages....," Isro scientific secretary V Koteswara Rao said.

"We are very confident; there is no reason, not to be confident going by the performance of the system so far. We have covered 98 per cent of the journey and another 2 per cent we are going to complete soon. We are very confident, teams are all very confident," he said.

If the Rs 450 crore MOM mission turns out to be a success, Isro would be the fourth space agency in the world to have sent a mission to Mars. European Space Agency (ESA) of European consortium, National Aeronautics and Space Administration (NASA) of the US and Roscosmos of Russia are the only three agencies which have so far sent their missions to the red planet. Only 21 of the total of 51 missions sent to Mars by various countries have been successful.

In the final critical manoeuvre, the space scientists would use the commands to fire the spacecraft's propulsion system for 24 minutes to slow it down just enough to be captured into the Martian orbit. The now shut off Liquid Apogee Motor (LAM) engine has to be fired again for MOI, Rao said.

The engine stored in the orbit for about 300 days without operation has to be restarted which "is very essential for MOI." MOI will be performed on September 24 at around 7:30 AM, Rao said.

"When we go there, the distance between earth to the spacecraft will be 224 million km. Today, the distance between earth and Mars orbital spacecraft is 215 million km. The present one way communication is approximately 12 minutes."

He said out of the 666 million km, the spacecraft had covered 653 million km so far. "We are yet to go another 13 million km which tells us that 98 per cent of the journey has been covered so far." "The distance between Mars and MOM is 2.496 million km approximately now; all the subsystems of the space craft are in good health and payloads health is also normal," he added.

Rao said "If you see the history of the failed missions- they have failed at various stages, some have failed during the launch which we have crossed, some of them have failed during trans Mars injection which we have crossed, some of them were lost on the way- we have completed 98 per cent of the journey."

"The remaining crucial thing is Mars Orbit Insertion, and if you see some mission have failed because of failures in estimates in the distance from the Mars, and if you see the history they were at very early stages....," he added.

India would be the first Asian country to go to Mars and also the first to succeed in the maiden attempt if the mission is successful, Rao said.

Nothing Vedic in ‘Vedic Maths’

September 3, 2014

Updated: September 3, 2014 15:52 IST

 

Illustration by Satwik Gade.

Advocating ‘Vedic mathematics’ as a replacement for traditional Indian arithmetic is hardly an act of nationalism; it only shows ignorance of the history of mathematics

Gujarat has made it compulsory for school students to read the texts of Dinanath Batra, endorsed by Prime Minister Narendra Modi. According to news reports, Mr. Batra has now proposed a non-governmental education commission which will Indianise education through, for instance, Vedic mathematics. The Minister for Education has also mentioned Vedic mathematics as part of her agenda.

Ignorant of tradition

One appreciates the desire of these people to work for Indian traditions. But where in the Vedas is “Vedic mathematics” to be found? Nowhere. Vedic mathematics has no relation whatsoever to the Vedas. It actually originates from a book misleadingly titled Vedic Mathematics by Bharati Krishna Tirtha. The book admits on its first page that its title is misleading and that the (elementary arithmetic) algorithms expounded in the book have nothing to do with the Vedas. This is repeated on p. xxxv: “Obviously these formulas are not to be found in the present recensions of Atharvaveda.” I have been pointing this out since 1998. Regrettably, the advocates of “Vedic mathematics,” though they claim to champion Indian tradition, are ignorant of the actual tradition in the Vedas. Second, they do not even know what is stated in the book — the real source of “Vedic mathematics.” Third, they are unaware of scholarly writing on the subject. When education policy is decided by such ignorant people, they only end up making a laughing stock of themselves and the Vedas, and thus do a great disservice to the very tradition which they claim to champion.

Everyone learns how to add, subtract, multiply and divide in school. Why should we replace those algorithms with “Vedic mathematics”? Will that Indianise education? No. The standard arithmetic algorithms actually originated in India, where they were known by various names such as patiganita (slate arithmetic). However, the word “algorithm” comes from “algorithmus”: the Latinised name of al Khwarizmi of the 9th century House of Wisdom in Baghdad. He wrote an expository book on Indian arithmetic called Hisab al Hind. Gerbert d’Aurillac (later Pope Sylvester II), the leading European mathematician of the 10th century, imported these arithmetic techniques from the Umayyad Khilafat of Córdoba. He did so because the primitive Greek and Roman system of arithmetic (tied to the abacus), then prevailing in Europe, was no match for Indian arithmetic. However, accustomed to the abacus (on which he wrote a tome), Gerbert was perplexed by algorithms based on the place-value system, and foolishly got a special abacus (apices) constructed for these “Arabic numerals” in 976 CE. Hence the name “Arabic numerals” — because a learned pope amusingly thought there was some magic in the shape of the numerals which made arithmetic efficient.

Later, Florentine merchants realised that efficient Indian arithmetic algorithms conferred a competitive advantage in commerce. Fibonacci, who traded across Islamic Africa, translated al Khwarizmi’s work, as did many others, which is why they came to be known as algorithms. Eventually, after 600 years, Indian algorithms displaced the European abacus and were introduced in the Jesuit syllabus as “practical mathematics” circa 1570 by Christoph Clavius. These algorithms are found in many early Indian texts, such as the Patiganita of Sridhar or the Ganita Sara Sangraha of Mahavira, or the Lilavati of Bhaskara II. So, advocating “Vedic mathematics” as a replacement for traditional Indian arithmetic is hardly an act of nationalism. On the contrary, it only shows ignorance of the history of mathematics. Spreading this ignorance among future generations will weaken the nation, not strengthen it.

The techniques of “Vedic mathematics” are designed for mental arithmetic, traditionally used by lower caste artisans such as carpenters or by people like Shakuntala Devi. There are many other such systems of mental arithmetic today. If that is what we intend to promote, we should first do a systematic comparison. We should also be honest and refrain from using the misleading label “Vedic” which is the main selling point of Bharti Krishna Tirtha’s system, and which attracts gullible people who infer value just from the wrapper.

Suppressing real Mathematics

Promoting the wrongly labelled “Vedic mathematics” suppresses the mathematics that really does exist in the Vedas. For example, Yajurveda 17.2 elaborates on the decimal place value system (the basis of Indian algorithms) and some of those names for numbers are still in use, though terms such as arab (arbudam) have changed meaning. That passage shows that the place value system extends back to Vedic times, and it was a late acquisition only in mathematically backward Europe.

Likewise, the theory of permutations and combinations is built into the Vedic metre (and Indian music in general), as explained in various texts from Pingala’s Chandahsutra to Bhaskar’s Lilavati. The aksa sukta of the Rgveda gives a beautiful account of the game of dice, which is the foundation of the theory of probability. The romantic story of Nala and Damayanti in the Mahabharata further relates dice to sampling theory (to count the number of fruits in a tree).

More details are in my article on “Probability in Ancient India” available online and published in the Elsevier Handbook of the Philosophy of Statistics. However, all these scholarly efforts are jeopardised, for they too are viewed with suspicion.

We need to change the Western and colonial education system, especially with regard to mathematics. Traditional Indian ganita has much to offer in this process, but “Vedic mathematics” is definitely not the right way.

Wrong solutions like “Vedic mathematics” persist because an insecure political dispensation values the politically loyal over the learned who are loyal to the truth. (“Merit” apparently is important only in the context of reservations.) Such political processes are historically known to damage real traditions.

As I wrote over a decade ago in my book The Eleven Pictures of Time, those who attain or retain state power through religion are the worst enemies of that religion, whatever be the religion they claim to represent: Christianity, Islam, or Hinduism.

(C.K. Raju is author of Cultural Foundations of Mathematics. He was professor of mathematics, and Editorial Fellow of the Project of History of Indian Science, Philosophy and Culture.)

http://www.thehindu.com/opinion/op-ed/nothing-vedic-in-vedic-maths/article6373689.ece

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The Fraud of Vedic Maths

14 August 2010

Those who seriously still think ancient India had devised a parallel mathematical system need to acquaint themselves with an inventive Shankaracharya called Bharti Krishna Tirthaji.

BY Hartosh Singh Bal

The sutras, unfortunately, only reveal how little Tirathji knew of maths. But his quest was still forgivable

In 1965, a book titled Vedic Mathematics was published in English. Since then, the subject has become an industry that shows no sign of diminishing. In its latest manifestation, parents who know no better are shelling out serious money in the hope that their children will become scientific geniuses. They really shouldn’t bother. The subject amounts to nothing more than a few cheap parlour tricks, and there is nothing Vedic about it. But the story of how it came to be makes for a fantastical tale. 

Bharti Krishna Tirthaji was born in 1884 with some talent for science and mathematics. But he eventually paid heed to a passion for Sanskrit and philosophy, and joined the Sringeri math in Mysore to study under its Shankaracharya. In 1925, he became a Shankaracharya himself. All through these years, he’d kept up his interest in science and mathematics. Many scholars before him had dismissed the Atharva Veda as arcane and difficult to understand, but Tirathji decided to spend time studying it in the belief that he could excavate the knowledge that he felt must lie there. 

After eight years of ‘deep’ contemplation, he claimed to have found 16 sutras which explained all of mathematics. He, it is said, then wrote 16 volumes on Vedic mathematics, one on each sutra. Mysteriously, just before their publication, the manuscripts were lost. But in 1960, the last year of his life, Tirathji managed to rewrite one volume which was published in 1965 as Vedic Mathematics.

As stories go, this is not a bad one, but the evidence does nothing to support it. The 16 sutras expounded by Tirathji do not appear in any known edition of the Atharva Veda. Tirathji’s defenders have claimed that Tirathji was so immersed in Vedic thought that he was able to glean what the Vedic seers had in mind even if it was not explicitly so stated anywhere in the Vedic corpus. If one were to actually concede this meeting of minds between Tirathji and the ancient Vedic seers, it would have the unfortunate consequence of implying that not just Tirathji but even these seers were limited in their mathematical understanding.

All the sutras largely do is make the burden of addition and multiplication faster (though never nearly as fast as the cheapest pocket calculator), and even that, they do at a cost. Students studying the traditional method of multiplication should ideally understand (and bad teachers themselves fail to grasp this) what multiplication is, how it works, and how it is in essence an act of repeated addition. Tirathji’s methods are just rules that make mathematics seem like a bunch of tricks which are easy to implement but difficult to understand.

Take, for example, the multiplication of 9 and 7. Line them along with their difference from 10. That is:

9–10 = –1 and 7–10 = –3

9–1

7–3

——

6   3

You obtain the answer in the following fashion: the unit’s digit is the two differences multiplied together, –1 x –3 = 3 and the other digit 6 is just either of the diagonals added together, that is, 9–3 = 7–1 = 6. This method can be extended to much larger numbers. It is a neat trick, but it does not make multiplication easier to fathom, quite the contrary.

Let us then set Tirathji’s claims aside. The 16 sutras expound all of mathematics no more than astrology expounds all of modern astronomy. So what drove him and his followers (who brought out the book) to make a claim so extreme based on so little? 

The answer lies in Tirathji’s times. The man was an early nationalist, and he worked with GK Gokhale in 1905 when the latter was president of the Indian National Congress. Among Gokhale’s initiatives was an effort to spread education among the Indian masses. Tirathji was caught between his devotion to the math and Gokhale’s vision. In 1908, he actually left the math to head a National College in Rajamahendri. 

Three years later, he went back to the math, but the experience would have left Tirathji with little choice but to confront the message that Englishmen such as Macaulay had so forcefully fashioned, that the ancient history and knowledge of India were worth nothing when set against the most elementary aspects of Western thought.  

To men like Tirathji, it was clear that if the secret of Western domination over India lay anywhere, it lay in the knowledge of the sciences, and mathematics stood at the heart this knowledge. What better answer to such hubris than to show that in fact all of mathematics had already been revealed in the Vedas? 

The sutras, unfortunately, only reveal how little Tirathji knew of mathematics. Today, they only symbolise the strivings of a colonised mind searching for some self-respect, and we can find their equivalent in the Sangh Parivar’s absurd attempts to search for the technology of the jet engine in the udankhatola of The Ramayan. At least Tirathji’s quest was far more understandable and forgivable, given his times, but that we Indians should still take it seriously only shows the extent to which our creative imagination remains colonised. How much better off we would be if we could forgo the portentous name given to these tricks and learn to enjoy them as a Shankaracharya’s fancy.

http://www.openthemagazine.com/article/art-culture/the-fraud-of-vedic-maths

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Neither Vedic Nor Mathematics
http://www.sacw.net/DC/CommunalismCollection/ArticlesArchive/NoVedic.html
We, the undersigned, are deeply concerned by the continuing attempts to thrust the so-called `Vedic Mathematics' on the school curriculum by the NCERT. 

As has been pointed out earlier on several occasions, the so-called 'Vedic Mathematics' is neither 'Vedic' nor can it be dignified by the name of mathematics. 'Vedic Mathematics', as is well-known, originated with a book of the same name by a former Sankracharya of Puri (the late Jagadguru Swami Shri Bharati Krishna Tirthaji Maharaj) published posthumously in 1965. The book assembled a set of tricks in elementary arithmetic and algebra to be applied in performing computations with numbers and polynomials. As is pointed out even in the foreword to the book by the General Editor, Dr. A.S. Agarwala, the aphorisms in Sanskrit to be found in the book have nothing to do with the Vedas. Nor are these aphorisms to be found in the genuine Vedic literature.

The term "Vedic mathematics'' is therefore entirely misleading and factually incorrect. Further, it is clear from the notation used in the arithmetical tricks in the book that the methods used in this text have nothing to do with the arithmetical techniques of antiquity. Many of the Sanskrit aphorisms in the book are totally cryptic (ancient Indian mathematical writing was anything but cryptic) and often so generalize to be devoid of any specific mathematical meaning. There are several authoritative texts on the mathematics of Vedic times that could used in part to teach an authoritative and correct account of ancient Indian mathematics but this book clearly cannot be used for any such purpose. The teaching of mathematics involves both the teaching of the basic concepts of the subject as well as methods of mathematical computation. The so-called "Vedic mathematics'' is entirely inadequate to this task considering that it is largely made up of tricks to do some elementary arithmetic computations. Many of these can be far more easily performed on a simple computer or even an advanced calculator.

The book "Vedic mathematics'' essentially deals with arithmetic of the middle and high-school level. Its claims that "there is no part of mathematics, pure or applied, which is beyond their jurisdiction'' is simply ridiculous. In an era when the content of mathematics teaching has to be carefully designed to keep pace with the general explosion of knowledge and the needs of other modern professions that use mathematical techniques, the imposition of ``Vedic mathematics'' will be nothing short of calamitous.

India today has active and excellent schools of research and teaching in mathematics that are at the forefront of modern research in their discipline with some of them recognised as being among the best in the world in their fields of research. It is noteworthy that they have cherished the legacy of distinguished Indian mathematicians like Srinivasa Ramanujam, V. K. Patodi, S. Minakshisundaram, Harish Chandra, K. G. Ramanathan, Hansraj Gupta, Syamdas Mukhopadhyay, Ganesh Prasad, and many others including several living Indian mathematicians. But not one of these schools has lent an iota of legitimacy to `Vedic mathematics'. Nowhere in the world does any school system teach "Vedic mathematics'' or any form of ancient mathematics for that matter as an adjunct to modern mathematical teaching. The bulk of such teaching belongs properly to the teaching of history and in particular the teaching of the history of the sciences.

We consider the imposition of `Vedic mathematics' by a Government agency, as the perpetration of a fraud on our children, condemning particularly those dependent on public education to a sub-standard mathematical education. Even if we assumed that those who sought to impose `Vedic mathematics' did so in good faith, it would have been appropriate that the NCERT seek the assistance of renowned Indian mathematicians to evaluate so-called "Vedic mathematics" before making it part of the National Curricular framework for School Education. Appallingly they have not done so. In this context we demand that the NCERT submit the proposal for the introduction of `Vedic mathematics in the school curriculum to recognized bodies of mathematical experts in India, in particular the National Board of Higher Mathematics (under the Dept. of Atomic Energy), and the Mathematics sections of the Indian Academy of Sciences and the Indian National Science Academy, for a thorough and critical examination. In the meanwhile no attempt should be made to thrust the subject into the school curriculum either through the centrally administered school system or by trying to impose it on the school systems of various States.

We are concerned that the essential thrust behind the campaign to introduce the so-called 'Vedic mathematics' has more to do with promoting a particular brand of religious majoritarianism and associated obscurantist ideas rather than any serious and meaningful development of mathematics teaching in India. We note that similar concerns have been expressed about other aspects too of the National Curricular Framework for School Education. We re-iterate our firm conviction that all teaching and pedagogy, not just the teaching of mathematics, must be founded on rational, scientific and secular principles.

S.G.Dani Professor of Mathematics, Tata Institute of Fundamental Research, Mumbai
Madhav M. Deshpande Professor of Sanskrit and Linguistics Department of Asian Languages and Cultures, University of Michigan
Indranil Biswas Professor of Mathematics at TIFR.
Nirmala B. Limaye Professor of Mathematics University of Mumbai
B.V. Limaye Professor of Mathematics Indian Institute of Technology Bombay
Alladi Sitaram, Indian Statistical Institute, B'lore
S. Ramasubramanian, Indian Statistical Inst.,B'ore
V. Pati, Indian Statistical Inst., B'lore
G. Misra, Indian Statistical Inst., B'lore
Jishnu Biswas, Indian Statistical Inst., B'lore
D. P. Sengupta, Indian Inst. of Science(Retd.), B'lore
Alladi Uma, Dept. of English, Univ. of Hyderabad
M. Sridhar, Dept. of English, Univ. of Hyderabad
Amitava Bhattacharya
S.Subramanian, Tata Institute of Fundamental Research Mumbai
Professor Nitin Nitsure,Tata Institute of Fundamental Research, Mumbai

ISRO's Mars Orbiter Mangalyaan Just A Month Away From Rendezvous With Red Planet

Aug 25, 2014, 06.03 PM

The countdown of India's much talked-about Mars Orbiter Mission, better known as Mangalyaan, has begun with just a month to go before it is placed in orbit around the red planet on September 24.

According to Indian space agency Isro's Facebook profile, the orbiter is nine million kilometres away from Mars and 189 million kilometres away from Earth. It also added that the orbiter will take 33 more days to complete its mission to Mars.

The engine firing for the crucial Mars Orbital Insertion (MOI) will take place in September to place India's first space voyager in orbit around Mars.The orbiter was launched on November 5, 2013 from India's spaceport at the Satish Dhawan Space Centre in Andhra Pradesh's Sriharikota. It is ISRO's tried and tested warhorse.

The probe, which Weighs about 1350 kilograms (2980 pounds), will fire its engines on September 24 to be placed into an elliptical orbit around Mars, approaching the closest at 377 kilometres and going as far away as 80,000 kilometres.

The probe did not even require the scheduled trajectory correction this month.It has been moving as planned by the ISRO. The last such manoeuvre was performed on June 11 by firing the spacecraft's thrusters for 16 seconds.

The Indian Deep Space Network on the outskirts of Bangalore and NASA JPL's Deep Space Network have been constantly monitoring the Mars Orbiter Mission.

The Mars orbiter has been designed and developed by ISRO at a cost of $69m. The probe will study the atmosphere and the soil of the planet.

http://www.businessinsider.in/ISROs-Mars-Orbiter-Mangalyaan-Just-A-Month-Away-From-Rendezvous-With-Red-Planet/articleshow/40868638.cms

Astronomers measure rare black hole

Washington, August 18, 2014

Updated: August 18, 2014 18:24 IST

 

Researchers, including one of Indian-origin, have accurately measured and confirmed the existence of an elusive black hole, 400 times the mass of our Sun, in a galaxy 12 million light years from Earth.

Ranging from a hundred times to a few hundred thousand times the Sun’s mass, these intermediate-mass black holes are so hard to measure and even their existence is sometimes disputed.

Little is known about how they form. And some astronomers question whether they behave like other black holes.

University of Maryland astronomy graduate student Dheeraj Pasham and colleagues succeeded in accurately measuring — and thus confirming the existence of — a black hole about 400 times the mass of our Sun in a galaxy 12 million light years from Earth.

Co-author Richard Mushotzky, a UMD astronomy professor, said the black hole in question is a just-right-sized version of this class of astral objects.

“Objects in this range are the least expected of all black holes,” said Mushotzky.

While the intermediate-mass black hole that the team studied is not the first one measured, it is the first one so precisely measured, Mushotzky says, “establishing it as a compelling example of this class of black holes.”

“For reasons that are very hard to understand, these objects have resisted standard measurement techniques,” said Mushotzky.

Pasham focused on one object in Messier 82, a galaxy in the constellation Ursa Major.

Messier 82 is our closest “starburst galaxy,” where young stars are forming.

Beginning in 1999 a NASA satellite telescope, the Chandra X-ray Observatory, detected X-rays in Messier 82 from a bright object prosaically dubbed M82 X-1.

Astronomers, including Mushotzky and co-author Tod Strohmayer of NASA’s Goddard Space Flight Centre, suspected for about a decade that the object was an intermediate-mass black hole, but estimates of its mass were not definitive enough to confirm that.

Between 2004 and 2010 NASA’s Rossi X-Ray Timing Explorer (RXTE) satellite telescope observed M82 X-1 about 800 times, recording individual X-ray particles emitted by the object.

Pasham mapped the intensity and wavelength of X-rays in each sequence, then stitched the sequences together and analysed the result.

Among the material circling the suspected black hole, he spotted two repeating flares of light. The flares showed a rhythmic pattern of light pulses, one occurring 5.1 times per second and the other 3.3 times per second.

The study was published in the journal Nature.

http://www.thehindu.com/sci-tech/science/astronomers-measure-rare-black-hole/article6329004.ece

Ten Historic Female Scientists You Should Know

 

Before Marie Curie, these women dedicated their lives to science and made significant advances

By Sarah Zielinski

smithsonian.com
September 19, 2011

12.2K 398 9 118 283 8 20.2K

12.2K 398 118 283 9 20.2K

When it comes to the topic of women in science, Marie Curie usually dominates the conversation. After all, she discovered two elements, was the first women to win a Nobel Prize, in 1903, and was the first person to win a second Nobel, in 1911. But Curie was not the first female scientist. Many other brilliant, dedicated and determined women have pursued science over the years.

Emilie du Chatelet (1706 – 1749)

Gabrielle-Emilie Le Tonnelier de Breteuil, the daughter of the French court’s chief of protocol, married the marquis du Chatelet in 1725. She lived the life of a courtier and bore three children. But at age 27, she began studying mathematics seriously and then branched into physics. This interest intensified as she began an affair with the philosopher Voltaire, who also had a love of science. Their scientific collaborations—they outfitted a laboratory at du Chatelet’s home, Chateau de Cirey, and, in a bit of a competition, each entered an essay into a contest on the nature of fire (neither won)—outlasted their romance. Du Chatelet’s most lasting contribution to science was her French translation of Isaac Newton’s Principia, which is still in use today. At age 43, she fell in love with a young military officer and became pregnant; she died following complications during the birth of their child.

Caroline Herschel (1750 – 1848)

Herschel was little more than the household drudge for her parents in Hanover, Germany (she would later describe herself as the “Cinderella of the family”), when her older brother, William, brought her to England in 1772 to run his household in Bath. After she mastered the art of singing—to accompany William, who was the organist for the Octagon Chapel—her brother switched careers and went into astronomy. Caroline followed. In addition to assisting her brother in his observations and in the building of telescopes, Caroline became a brilliant astronomer in her own right, discovering new nebulae and star clusters. She was the first woman to discover a comet (she discovered eight in total) and the first to have her work published by the Royal Society. She was also the first British woman to get paid for her scientific work, when William, who had been named the king’s personal astronomer after his discovery of Uranus in 1781, persuaded his patron to reward his assistant with an annual salary. After William’s death in 1822, Caroline retired to Hanover. There she continued her astronomical work, compiling a catalogue of nebulae—the Herschels’ work had increased the number of known star clusters from 100 to 2,500. She died in 1848 at age 97 after receiving many honors in her field, including a gold medal from the Royal Astronomical Society.

Mary Anning (1799 – 1847)

In 1811, Mary Anning’s brother spotted what he thought was a crocodile skeleton in a seaside cliff near the family’s Lyme Regis, England, home. He charged his 11-year-old sister with its recovery, and she eventually dug out a skull and 60 vertebrae, selling them to a private collector for £23. This find was no croc, though, and was eventually named Ichthyosaurus, the “fish-lizard.” Thus began Anning’s long career as a fossil hunter. In addition to ichthyosaurs, she found long-necked plesiosaurs, a pterodactyl and hundreds, possibly thousands, of other fossils that helped scientists to draw a picture of the marine world 200 million to 140 million years ago during the Jurassic. She had little formal education and so taught herself anatomy, geology, paleontology and scientific illustration. Scientists of the time traveled from as far away as New York City to Lyme Regis to consult and hunt for fossils with Anning.

Mary Somerville (1780 – 1872)

Intrigued by the x’s and y’s in the answer to a math question in a ladies’ fashion magazine, 14-year-old Mary Fairfax of Scotland delved into the study of algebra and mathematics, defying her father’s injunction against such pursuits. Her studies were sidetracked by a marriage, in 1804, to a Russian Navy captain, but after his death she returned to Edinburgh and became involved in intellectual circles, associating with people such as the writer Sir Walter Scott and the scientist John Playfair, and resumed her studies in math and science. Her next husband, William Somerville, whom she wed in 1812, supported these efforts, and after they moved to London, Mary became host to her own intellectual circle, which included the astronomer John Herschel and the inventor Charles Babbage. She began experimenting on magnetism and produced a series of writings on astronomy, chemistry, physics and mathematics. She translated astronomer Pierre-Simon Laplace’s The Mechanism of the Heavens into English, and although she was unsatisfied with the result, it was used as a textbook for much of the next century. Somerville was one of the first two women, along with Caroline Herschel, to be named honorary members of the Royal Astronomical Society.

Maria Mitchell (1818 – 1889)

Young Maria Mitchell learned to observe the stars from her father, who used stellar observations to check the accuracy of chronometers for Nantucket, Massachusetts, whalers and taught his children to use a sextant and reflecting telescope. When Mitchell was 12, she helped her father record the time of an eclipse. And at 17, she had already begun her own school for girls, teaching them science and math. But Mitchell rocketed to the forefront of American astronomy in 1847 when she spotted a blurry streak—a comet—through her telescope. She was honored around the world, earning a medal from the king of Denmark, and became the first woman to be elected to the American Academy of Arts and Sciences. In 1857 Mitchell traveled to Europe, where she visited observatories and met with intellectuals, including Mary Somerville. Mitchell would write: “I could not help but admire [her] as a woman. The ascent of the steep and rugged path of science has not unfitted her for the drawing room circle; the hours of devotion to close study have not been incompatible with the duties of wife and mother.” Mitchell became the first female astronomy professor in the United States, when she was hired by Vassar College in 1865. There she continued her observations, particularly those of the Sun, traveling up to 2,000 miles to witness an eclipse.

Lise Meitner (1878 – 1968)

When Lise Meitner finished school at age 14, she was barred from higher education, as were all girls in Austria. But, inspired by the discoveries of William Röntgen and Henri Becquerel, she was determined to study radioactivity. When she turned 21, women were finally allowed into Austrian universities. Two years of tutoring preceded her enrollment at the University of Vienna; there she excelled in math and physics and earned her doctorate in 1906. She wrote to Marie Curie, but there was no room for her in the Paris lab and so Meitner made her way to Berlin. There she collaborated with Otto Hahn on the study of radioactive elements, but as an Austrian Jewish woman (all three qualities were strikes against her), she was excluded from the main labs and lectures and allowed to work only in the basement. In 1912, the pair moved to a new university and Meitner had better lab facilities. Though their partnership was split up physically when she was forced to flee Nazi Germany in 1938, they continued to collaborate. Meitner continued her work in Sweden and after Hahn discovered that uranium atoms were split when bombarded with neutrons, she calculated the energy released in the reaction and named the phenomenon “nuclear fission.” The discovery—which eventually led to the atomic bomb (“You must not blame scientists for the use to which war technicians have put our discoveries,” Meitner would say in 1945)—won Hahn the Nobel Prize in 1944. Meitner, overlooked by the Nobel committee, refused to return to Germany after the war and continued her atomic research in Stockholm into her 80s.

Irène Curie-Joliot (1897 – 1956)

The elder daughter of Pierre and Marie Curie, Irène followed her parents’ footsteps into the lab. The thesis for her 1925 doctor of science was on the alpha rays of polonium, one of the two elements her mother discovered. The next year, she married Frédéric Joliot, one of her mother’s assistants at the Radium Institute in Paris. Irène and Frédéric continued their collaboration inside the laboratory, pursuing research on the structure of the atom. In 1934, they discovered artificial radioactivity by bombarding aluminum, boron and magnesium with alpha particles to produce isotopes of nitrogen, phosphorus, silicon and aluminum. They received the Nobel Prize in chemistry the next year, making Marie and Irène the first parent-child couple to have independently won Nobels. All those years working with radioactivity took a toll, however, and Irène died of leukemia in 1956.

Barbara McClintock (1902 – 1992)

While studying botany at Cornell University in the 1920s, Barbara McClintock got her first taste of genetics and was hooked. As she earned her undergraduate and graduate degrees and moved into postdoctoral work, she pioneered the study of genetics of maize (corn) cells. She pursued her research at universities in California, Missouri and Germany before finding a permanent home at Cold Spring Harbor in New York. It was there that, after observing the patterns of coloration of maize kernels over generations of plants, she determined that genes could move within and between chromosomes. The finding didn’t fit in with conventional thinking on genetics, however, and was largely ignored; McClintock began studying the origins of maize in South America. But after improved molecular techniques that became available in the 1970s and early 1980s confirmed her theory and these “jumping genes” were found in microorganisms, insects and even humans, McClintock was awarded a Lasker Prize in 1981 and Nobel Prize in 1983.

Dorothy Hodgkin (1910 – 1994)

Dorothy Crowfoot (Hodgkin, after her 1937 marriage) was born in Cairo, Egypt, to a pair of British archaeologists. She was sent home to England for school, where she was one of only two girls who were allowed to study chemistry with the boys. At 18, she enrolled in one of Oxford’s women’s colleges and studied chemistry and then moved to Cambridge to study X-ray crystallography, a type of imaging that uses X-rays to determine a molecule’s three-dimensional structure. She returned to Oxford in 1934, where she would spend most of her working life, teaching chemistry and using X-ray crystallography to study interesting biological molecules. She spent years perfecting the technique, for which she was awarded a Nobel Prize in 1964, and determined the structures of penicillin, vitamin B12 and insulin. In 2010, 16 years after her death, the British Royal Mail celebrated the 350th anniversary of the Royal Society by issuing stamps with the likenesses of 10 of the society’s most illustrious members, including Isaac Newton and Benjamin Franklin; Hodgkin was the only woman in the group.

Rosalind Franklin (1920 – 1958)

James Watson and Francis Crick get credit for determining the structure of DNA, but their discovery relied on the work of Rosalind Franklin. As a teenager in the 1930s, Franklin attended one of the few girls’ schools in London that taught physics and chemistry, but when she told her father that she wanted to be a scientist, he rejected the idea. He eventually relented and she enrolled at Cambridge University, receiving a doctorate in physical chemistry. She learned techniques for X-ray crystallography while in Paris, returning to England in 1951 to work in the laboratory of John Randall at King’s College, London. There she made X-ray images of DNA. She had nearly figured out the molecule’s structure when Maurice Wilkins, another researcher in Randall’s lab who was also studying DNA, showed one of Franklin’s X-ray images to James Watson. Watson quickly figured out the structure was a double helix and, with Francis Crick, published the finding in the journal Nature. Watson, Crick and Wilkins won a Nobel Prize in 1962 for their discovery. Franklin, however, had died of ovarian cancer in 1958.

Read more: http://www.smithsonianmag.com/science-nature/ten-historic-female-scientists-you-should-know-84028788/#pqgRp4yMMHXRL7QZ.99

Five Historic Female Mathematicians You Should Know

 

Albert Einstein called Emmy Noether a "creative mathematical genius"

By Sarah Zielinski

smithsonian.com
October 7, 2011

Sofia Kovalevskaya, Emmy Noether and Ada Lovelace are just three of the many famous female mathematicians you should know. (Wikicommons)

If you haven’t yet read my story “Ten Historic Female Scientists You Should Know,” please check it out. It’s not a complete list, I know, but that’s what happens when you can pick only ten women to highlight—you start making arbitrary decisions (no living scientists, no mathematicians) and interesting stories get left out. To make up a bit for that, and in honor of Ada Lovelace Day, here are five more brilliant and dedicated women I left off the list:

Hypatia (ca. 350 or 370 – 415 or 416)

No one can know who was the first female mathematician, but Hypatia was certainly one of the earliest. She was the daughter of Theon, the last known member of the famed library of Alexandria, and followed his footsteps in the study of math and astronomy. She collaborated with her father on commentaries of classical mathematical works, translating them and incorporating explanatory notes, as well as creating commentaries of her own and teaching a succession of students from her home. Hypatia was also a philosopher, a follower of Neoplatonism, a belief system in which everything emanates from the One, and crowds listened to her public lectures about Plato and Aristotle. Her popularity was her downfall, however. She became a convenient scapegoat in a political battle between her friend Orestes, the governor of Alexandria, and the city’s archbishop, Cyril, and was killed by a mob of Christian zealots.

Sophie Germain (1776 – 1831)

When Paris exploded with revolution, young Sophie Germain retreated to her father’s study and began reading. After learning about the death of Archimedes, she began a lifelong study of mathematics and geometry, even teaching herself Latin and Greek so that she could read classic works. Unable to study at the École Polytechnique because she was female, Germain obtained lecture notes and submitted papers to Joseph Lagrange, a faculty member, under a false name. When he learned she was a woman, he became a mentor and Germain soon began corresponding with other prominent mathematicians at the time. Her work was hampered by her lack of formal training and access to resources that male mathematicians had at the time. But she became the first woman to win a prize from the French Academy of Sciences, for work on a theory of elasticity, and her proof of Fermat’s Last Theorem, though unsuccessful, was used as a foundation for work on the subject well into the twentieth century.

Ada Lovelace (1815 – 1852)

Augusta Ada Byron (later Countess of Lovelace) never knew her father, the poet Lord Byron, who left England due to a scandal shortly after her birth. Her overprotective mother, wanting to daughter to grown up as unemotional—and unlike her father—as possible, encouraged her study of science and mathematics. As an adult, Lovelace began to correspond with the inventor and mathematician Charles Babbage, who asked her to translate an Italian mathematician’s memoir analyzing his Analytical Engine (a machine that would perform simple mathematical calculations and be programmed with punchcards and is considered one of the first computers). Lovelace went beyond completing a simple translation, however, and wrote her own set of notes about the machine and even included a method for calculating a sequence of Bernoulli numbers; this is now acknowledged as the world’s first computer program.

Sofia Kovalevskaya (1850 – 1891)

Because Russian women could not attend university, Sofia Vasilyevna contracted a marriage with a young paleontologist, Vladimir Kovalevsky, and they moved to Germany. There she could not attend university lectures, but she was tutored privately and eventually received a doctorate after writing treatises on partial differential equations, Abelian integrals and Saturn’s rings. Following her husband’s death, Kovalevskaya was appointed lecturer in mathematics at the University of Stockholm and later became the first woman in that region of Europe to receive a full professorship. She continued to make great strides in mathematics, winning the Prix Bordin from the French Academy of Sciences in 1888 for an essay on the rotation of a solid body as well as a prize from the Swedish Academy of Sciences the next year.

Emmy Noether (1882 – 1935)

In 1935, Albert Einstein wrote a letter to the New York Times, lauding the recently deceased Emmy Noether as “the most significant creative mathematical genius thus far produced since the higher education of women began.” Noether had overcome many hurdles before she could collaborate with the famed physicist. She grew up in Germany and had her mathematics education delayed because of rules against women matriculating at universities. After she received her PhD, for a dissertation on a branch of abstract algebra, she was unable to obtain a university position for many years, eventually receiving the title of “unofficial associate professor” at the University of Göttingen, only to lose that in 1933 because she was Jewish. And so she moved to America and became a lecturer and researcher at Bryn Mawr College and the Institute for Advanced Study in Princeton, New Jersey. There she developed many of the mathematical foundations for Einstein’s general theory of relativity and made significant advances in the field of algebra.

Read more: http://www.smithsonianmag.com/science-nature/five-historic-female-mathematicians-you-should-know-100731927/#94sm4uQgeI5yceWQ.99
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http://www.smithsonianmag.com/science-nature/five-historic-female-mathematicians-you-should-know-100731927/?no-ist

For the first time ever, a woman wins mathematics' highest honor

 

By Ben Brumfield, CNN

August 13, 2014 -- Updated 1358 GMT (2158 HKT) | Filed under: Innovations

Maryam Mirzakhani is the first woman to win mathematics' highest honor, the Fields Medal.

STORY HIGHLIGHTS

• The Fields Medal is often nicknamed the Nobel Prize of mathematics
• Since it was established in 1936, it previously had gone only to men
• Maryam Mirzakhani helped bring unexpected order to an area considered chaotic by many
• She hopes her receiving the award will encourage young women in the field

(CNN) -- For the first time in history, a woman has received the highest honor in mathematics, often nicknamed the Nobel Prize of mathematics.

Since it was established in 1936, the Fields Medal had gone only to men, until Wednesday, when Maryam Mirzakhani received it in Seoul, South Korea, from the International Mathematical Union.

"This is a great honor. I will be happy if it encourages young female scientists and mathematicians," Mirzakhani said, according to a statement from Stanford University, where she is a professor.

For those of us less versed in the uppermost echelons of mathematics and geometry than Mirzakhani, it's mind-twisting to understand the abstract accomplishments that got her field's highest recognition.

Mirzakhani has delved into the depths of geometry, helping bring unexpected order to an area that many of her colleagues considered chaotic and hardly tamable. And her peers have found this very exciting.

The International Mathematical Union called her long list of accomplishments in Reimann surfaces and moduli spaces "stunning."

What are those?

Simply put, those are complex geometric forms.

Anyone who has had high school algebra and geometry may remember that shapes like squares, triangles, circles and spheres are described by mathematical formulas.

But jump to more complex, roundish, theoretical objects, like perfectly formed doughnuts, ultra-warped, crisscrossed potato chips, undulating geometric pretzels or uneven blobs like amoebas.

That's getting close to the kind of math and geometry Mirzakhani works with. Go deeper, and things can appear to descend into infinite chaos.

Find that intimidating? Some bright mathematical minds do, too.

"Because of its complexities and inhomogeneity, moduli space has often seemed impossible to work on directly," the International Mathematical Union said. "But not to Mirzakhani."

But even she finds those theoretical depths challenging.

"It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out," she said.

What's it good for?

Mirzakhani's work was not driven by any practical purpose -- like engineering -- but purely to satisfy mathematical curiosity, to create more knowledge. The implications of her work go beyond just the description of shapes.

Since her area of math also informs physicists, her work could help advance scientists' understanding of the origins of the universe and the workings of subatomic particles, which could have implications for engineering.

The International Mathematical Union praised Mirzakhani for her mastery of various contrasting aspects of mathematics.

Equally as impressive is how Mirzakhani got to where she is today.

From Tehran to Stanford

She discovered her knack for numbers in high school in her native Iran, where she grew up in the capital, Tehran. Media in Iran are also reporting about her achievement.

"It is fun -- it's like solving a puzzle or connecting the dots in a detective case," she said.

As a teenager, she gained international attention when she won gold medals in two International Math Olympiads, achieving a perfect score in one of them.

Mirzakhani got her undergraduate degree at Sharif University of Technology, then moved to the United States, where she went to work on her doctorate at Harvard University.

She was an assistant professor at Princeton University before moving to Stanford.

The Fields Medal, officially called the International Medal for Outstanding Discoveries in Mathematics, is awarded every four years. The past 52 recipients were men.

This year's medal went to four recipients in total. The other three were also men.

http://edition.cnn.com/2014/08/13/tech/innovation/first-woman-highest-math-prize/