User:ProboscideaRubber15/sandbox

Evaluating the article ``List of inventions and discoveries by women"
List of inventions and discoveries by women Overall thoughts:

I think this page, in its current incarnation, arguably does more harm than good. In presenting a very short and poorly organized list of inventions and discoveries by women, largely focused on women’s roles as child-rearers and housekeepers, this article leaves the reader thinking that women have contributed very little. While incomplete lists are inevitable, the specific way in which this list is incomplete seems harmful. In particular, while there are many notable omissions (i.e. the section on biology is missing Barbara McClintock, and apparently, nearly another dozen female Nobel Laureates in physiology/medicine), a lot of very minor inventions (i.e. the Hot comb) are included.

More minor issues
 * There’s some inconsistency in formatting between subheads and individual discoveries. For instance, in the mathematics section, words listed in blue bold font refer to subfields of mathematics which notable women have worked in. In the vehicular appliances section, words in blue bold font refer to individual discoveries. Other sections, such at those on computing and physics, are internally inconsistent.


 * There are many small grammatical errors and convoluted sentences, i.e. “The female presence in scientific fields, where such achievements occur, has been largely disproportional compared to male presence; however, this is slowly changing as more women are entering these fields. Moreover, most of the engineering or technical training schools are working towards educating more women.” “ previously a mathematician professor at...”


 * The preamble is a little flowery, and includes some unsourced claims about women in science more generally. Similar pages like List of inventions in the medieval Islamic world or List of Indian inventions and discoveries do not have similar preambles.

physics

 * Réka Albert: Barabási–Albert model
 * Harriet Brooks:Atomic recoil


 * Radon

In 1901, Harriet Brooks and Ernest Rutherford contributed to the discovery of the element Radon by finding evidence that the “emanation” emitted by thorium compounds was likely to be a gas. This follows work in 1899 by Pierre and Marie Curie, who observed that the gas emitted by radium remained radioactive for a month.


 * As a graduate student Phyllis S. Freier found evidence for the existence of elements heavier than helium in cosmic radiation.Her work was published in Physical Review in 1948 with co-authors Edward J. Lofgren, Edward P. Ney, and Frank Oppenheimer.
 * Yvette Cauchois: not totally clear what the discovery is, but seems like she has potential
 * Yvonne Choquet-Bruhat : "From 1951-1952 she worked at the Institute for Advanced Study in Princeton where she proved the local existence and uniqueness of solutions to the vacuum Einstein Equations. "
 * Joan Curran: Chaff (countermeasure)
 * Cécile DeWitt-Morette: "In 1972 Morette and her husband led an expedition to Mauritania to confirm that light was deflected in line with the theory of general relativity. These measurements were made during the solar eclipse there. Comparison of the pictures with those made six months later confirmed that, in line with theory, light was indeed bent when passing by massive objects. Morette and her husband joined the faculty of the University of Texas in 1972. She began to work increasingly in physics rather than in mathematics, and she became a Professor in 1985. "
 * Louise Dolan: String theory stuff
 * Mildred Dresselhaus : carbon stuff
 * Jo Dunkley: unclear from page--origin of universe stuff
 * Eva Ekeblad: "In 1746, Ekeblad wrote to the Royal Swedish Academy of Sciences on her discoveries of how to make flour and alcohol out of potatoes. Potatoes had been introduced into Sweden in 1658, but had been cultivated only in the greenhouses of the aristocracy. Ekeblad's work turned potatoes into a staple food in Sweden, and increased the supply of wheat, rye and barley available for making bread, since potatoes could be used instead to make alcohol. This greatly improved the country's eating habits and reduced the frequency of famines. " (will probably move this to another category)
 * Magda Ericson: "Magda Ericson's contributions have been largely responsible for the development of nuclear pion physics as a subfield of nuclear physics and a large number of papers are based on her work." (http://cwp.library.ucla.edu/Phase2/Ericson,_Magda_Galula@881345678.html) borderline case
 * Gertrude Scharff Goldhaber: "Around this time she also observed that spontaneous nuclear fission is accompanied by the release of neutrons — a result that had been theorized earlier but had yet to be shown.[7] Her work with spontaneous nuclear fission was classified during the war, and was only published after the war ended in 1946.[7]"
 * Fanny Gates: "She made contributions to the research of radioactive materials, determining that radioactivity could not be destroyed by heat or ionization due to chemical reactions, and that radioactive materials differ from phosphorescent materials both qualitatively and quantitatively.[4] More specifically, Gates showed that the emission of blue light from quinine was temperature dependent, providing evidence that the emitted light is produced from phosphorescence rather than radioactive decay.[5] "
 * Melissa Franklin: While working at the Fermi National Accelerator Laboratory in Chicago, her team found some of the first evidences for the existence of the top quark. In 1993, Franklin was elected a fellow of the American Physical Society. She is currently member of the CDF (Fermilab) and ATLAS (CERN) collaborations.
 * Illustrative example: Gerson Goldhaber verus Sulamith Goldhaber
 * Lene Hau: slowing light down to the speed of a bicycle using a bose-einstein condensate
 * He Yizhen: not sure if there's anything for the list. but, this is a fascinating story that I want to read more about. She reminds me a lot of one of the main characters of the Three Body Problem, to the extent that I wonder if she was the inspiration for this character.
 * Ann Heinson: more top quark stuff. I'll need information beyond what is in this article.
 * Shirley Ann Jackson: no obvious discoveries on the page, but I bet I can find one among the stuff vaguely mentioned.
 * Irène Joliot-Curie: Jointly with her husband, Joliot-Curie was awarded the Nobel Prize in Chemistry in 1935 for their discovery of artificial radioactivity. This made the Curies the family with the most Nobel laureates to date.[1] Both children of the Joliot-Curies, Hélène and Pierre, are also esteemed scientists.[2]
 * Lorella Jones: page for improvement. Again, there's an interesting story here, and the page doesn't totally do it justice.
 * Berta Karlik: While working with Ernst Foyn she published a paper on the radioactivity of seawater. She discovered that the element 85 astatine is a product of the natural decay processes. The element was first synthesized in 1940 by Dale R. Corson, K. R. MacKenzie, and Emilio Segrè, after several scientists in vain searched for it in radioactive minerals.
 * Hendrika Johanna van Leeuwen: She studied at Leiden University under the guidance of Hendrik Antoon Lorentz, obtaining her doctorate in 1919. Her thesis [1][2] explained why magnetism is an essentially quantum mechanical effect, a result now referred to as the Bohr–van Leeuwen theorem. (Niels Bohr had arrived at the same conclusion a few years earlier.)
 * Cecilia Payne-Gaposchkin: was a British–American astronomer and astrophysicist who, in 1925, proposed in her Ph.D. thesis an explanation for the composition of stars in terms of the relative abundances of hydrogen and helium.[1]
 * Elizabeth Laird (physicist): likely to be something in here
 * Marguerite Perey: Francium
 * Kathleen Lonsdale: " in 1929, that the benzene ring is flat by using X-ray diffraction methods to elucidate the structure of hexamethylbenzene.[1] She was the first to use Fourier spectral methods while solving the structure of hexachlorobenzene in 1931. "
 * Margaret Eliza Maltby: I think there's something here, but also that there's something fishy about this page
 * Naomi McClure-Griffiths: " is an American astrophysicist and radio astronomer who researches and lives in Australia. In 2004, she discovered a new spiral arm in the Milky Way galaxy. She was awarded the Prime Minister's Malcolm McIntosh Prize for Physical Scientist in 2006 and in 2015 was honored for her research in physics by receipt of the Pawsey Medal from the Australian Academy of Science."
 * Lise Meitner: Meitner and Otto Hahn led the small group of scientists who first discovered nuclear fission of uranium when it absorbed an extra neutron; the results were published in early 1939.[4][5] Meitner and Otto Frisch understood that the fission process, which splits the atomic nucleus of uranium into two smaller nuclei, must be accompanied by an enormous release of energy. Nuclear fission is the process exploited by nuclear reactors to generate heat and, subsequently, electricity.[6] This process is also the basis of the nuclear weapons that were developed in the U.S. during World War II and used against Japan in 1945.
 * Rajaâ Cherkaoui El Moursli : some role in this whole higgs boson thing
 * Sameera Moussa Moussa believed in "Atoms for Peace" and was known to say "My wish is to see nuclear treatment as available and as cheap as Aspirin". She worked hard for this purpose and throughout her intensive research, she came up with a historic equation that would help break the atoms of cheap metals such as copper, paving the way for a cheap nuclear bomb.[2] IDK if there's a thing for the list, but I want to stare at these two sentences for a bit more
 * Marcia Neugebauer: Neugebauer's research are among the first that yielded the first direct measurements of the solar wind and shed light on its physics and interaction with comets.
 * Heidi Jo Newberg: Among her team's findings are that the Milky Way is cannibalizing stars from smaller galaxies[1][2][3] and that the Milky Way is larger and has more ripples than was previously understood.[4]
 * Ida Noddack: She was the first to mention the idea of nuclear fission in 1934.[3] With her husband Walter Noddack she discovered element 75, rhenium. She was nominated three times for the Nobel Prize in Chemistry.[4]
 * Hiranya Peiris: "detailed maps of the early universe."
 * Melba Phillips: Oppenheimer-Phillips effect,
 * Frances Pleasonton: member of the team who first demonstrated neutron decay in 1951.
 * Edith Quimby: as one of the founders of nuclear medicine.
 * Helen Quinn: Peccei-Quinn theory which implies a corresponding symmetry of nature[2] (related to matter-antimatter symmetry and the possible source of the dark matter that pervades the universe)
 * Valerie Thomas: Illusion transmitter
 * Marie-Antoinette Tonnelat: "Her research focused on synthesizing the concepts gravity, electromagnetism, and nuclear forces within the basic framework provided by Einstein's theory of relativity. Along with the help of Einstein and Schrödinger, she played a role in developing Unified Field Theory."
 * Mary Tsingou: She is known in the computational physics community for having helped in the coding of the Fermi–Pasta–Ulam–Tsingou problem at the Los Alamos National Laboratory while working as a programmer in the MANIAC group. The result was an important stepping stone for chaos theory.
 * Chien-Shiung Wu: Wu worked on the Manhattan Project, where she helped develop the process for separating uranium metal into uranium-235 and uranium-238 isotopes by gaseous diffusion.  She is best known for conducting the Wu experiment, which contradicted the hypothetical law of conservation of parity. This discovery resulted in her colleagues Tsung-Dao Lee and Chen-Ning Yang winning the 1957 Nobel Prize in physics, and earned Wu the inaugural Wolf Prize in Physics in 1978.

improvable pages
Alessandra Buonanno

biology/medicine

 * Twelve women have won the prize:
 * The Cori cycle. Gerty Cori received the Nobel Prize in 1947 for the discovery of the mechanism by which glycogen—a derivative of glucose—is broken down in muscle tissue into lactic acid and then resynthesized in the body and stored as a source of energy (known as the Cori cycle).

Rosalyn Yalow (1977), Barbara McClintock (1983), Rita Levi-Montalcini (1986), Gertrude B. Elion (1988), Christiane Nüsslein-Volhard (1995), Linda B. Buck (2004), Françoise Barré-Sinoussi (2008), Elizabeth H. Blackburn (2009), Carol W. Greider (2009), May-Britt Moser (2014) and Tu Youyou (2015). As of 2017, the prize has been awarded to 214 individuals.

Brenda Milner: brain lateralization, HM

math:finalists

 * Ingrid Daubechies : Daubechies wavelet


 * Daubechies wavelet

Ingrid Daubechies introduced the Daubechies wavelet and contributed to the development of the  CDF wavelet, important tools in image compression.


 * Irmgard Flügge-Lotz : discontinuous automatic control
 * Carolyn S. Gordon : that you can't hear the shape of a drum
 * Marion Cameron Gray : Gray graph
 * Maria Hasse : Gallai–Hasse–Roy–Vitaver theorem in graph coloring.
 * Sofia Kovalevskaya: Cauchy–Kovalevskaya theorem
 * Vera Kublanovskaya: QR algorithm
 * Olga Ladyzhenskaya: "She provided the first rigorous proofs of the convergence of a finite difference method for the Navier–Stokes equations."
 * Ruth Lawrence: Lawrence–Krammer representation (braid groups are linear)
 * Rózsa Péter : recursion theory
 * Julia Robinson: "Her work on Hilbert's 10th problem played a crucial role in its ultimate resolution."
 * Kirstine Smith: Optimal design
 * Vera T. Sós: friendship theorem Kővári–Sós–Turán theorem three-gap theorem

math: the half of the list that is due to Emmy Noether...

 * Noether normalization lemma

The Noether normalization lemma is a result of commutative algebra, introduced by Emmy Noether in 1926. It states that for any field k, and any finitely generated commutative k-algebra A, there exists a nonnegative integer d and algebraically independent elements y1, y2, ..., yd in A such that A is a finitely generated module over the polynomial ring S:=k[y1, y2, ..., yd].

The theorem has a geometric interpretation. Suppose A is integral. Let S be the coordinate ring of the d-dimensional affine space $$\mathbb A^d_k$$, and A as the coordinate ring of some other d-dimensional affine variety X. Then the inclusion map S &rarr; A induces a surjective finite morphism of affine varieties $$X\to \mathbb A^d_k$$. The conclusion is that any affine variety is a branched covering of affine space.

The Noether normalization lemma is an important step to proving Hilbert's Nullstellensatz.


 * Noether's theorem

Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proven by mathematician Emmy Noether in 1915 and published in 1918, although a special case was proven by E. Cosserat & F. Cosserat in 1909. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system's behavior can be determined by the principle of least action.

Noether's theorem is used in theoretical physics and the calculus of variations. A generalization of the formulations on constants of motion in Lagrangian and Hamiltonian mechanics (developed in 1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian alone (e.g. systems with a Rayleigh dissipation function). In particular, dissipative systems with continuous symmetries need not have a corresponding conservation law.

Noether's theorem can be stated informally

"If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time."


 * Noether's second theorem

In mathematics and theoretical physics, Noether's second theorem relates symmetries of an action functional with a system of differential equations. The action S of a physical system is an integral of a so-called Lagrangian function L, from which the system's behavior can be determined by the principle of least action.


 * isomorphism theorems

In mathematics, specifically abstract algebra, the isomorphism theorems are three theorems that describe the relationship between quotients, homomorphisms, and subobjects. Versions of the theorems exist for groups, rings, vector spaces, modules, Lie algebras, and various other algebraic structures. In universal algebra, the isomorphism theorems can be generalized to the context of algebras and congruences.

The isomorphism theorems were formulated in some generality for homomorphisms of modules by Emmy Noether in her paper Abstrakter Aufbau der Idealtheorie in algebraischen Zahl- und Funktionenkörpern which was published in 1927 in Mathematische Annalen. Less general versions of these theorems can be found in work of Richard Dedekind and previous papers by Noether.

Three years later, B.L. van der Waerden published his influential Algebra, the first abstract algebra textbook that took the groups-rings-fields approach to the subject. Van der Waerden credited lectures by Noether on group theory and Emil Artin on algebra, as well as a seminar conducted by Artin, Wilhelm Blaschke, Otto Schreier, and van der Waerden himself on ideals as the main references. The three isomorphism theorems, called homomorphism theorem, and two laws of isomorphism when applied to groups, appear explicitly.


 * Lasker–Noether theorem

In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals (which are related to, but not quite the same as, powers of prime ideals). The theorem was first proven by for the special case of polynomial rings and convergent power series rings, and was proven in its full generality by.

The Lasker–Noether theorem is an extension of the fundamental theorem of arithmetic, and more generally the fundamental theorem of finitely generated abelian groups to all Noetherian rings. The Lasker–Noether theorem plays an important role in algebraic geometry, by asserting that every algebraic set may be uniquely decomposed into a finite union of irreducible components.


 * Albert–Brauer–Hasse–Noether theorem

In algebraic number theory, the Albert–Brauer–Hasse–Noether theorem states that a central simple algebra over an algebraic number field K which splits over every completion Kv is a matrix algebra over K. The theorem is an example of a local-global principle in algebraic number theory and leads to a complete description of finite-dimensional division algebras over algebraic number fields in terms of their local invariants. It was proved independently by Richard Brauer, Helmut Hasse, and Emmy Noether and by Abraham Adrian Albert.

math: runners up

 * Mary Ellen Rudin: Dowker space
 * Jean Bartik: fundamentals of programming
 * Christine Darden: some tech to mitigate the effects of sonic booms
 * Olive Jean Dunn: Some of Dunn's 1958 and 1959 work led to the conjecture of the Gaussian correlation inequality, which was only proved by German mathematician Thomas Royen in 2014 and was only widely recognized as proved in 2017.[11]
 * Ratner's theorems
 * Maharam's theorem

math:uncategorized

 * Christine Darden: some tech to mitigate the effects of sonic booms
 * Olive Jean Dunn: Some of Dunn's 1958 and 1959 work led to the conjecture of the Gaussian correlation inequality, which was only proved by German mathematician Thomas Royen in 2014 and was only widely recognized as proved in 2017.[11]
 * Irmgard Flügge-Lotz : She was a pioneer in the development of the theory of discontinuous automatic control,
 * Carolyn S. Gordon : solution to the "can you hear the shape of a drum" problem
 * Marion Cameron Gray : Gray graph
 * Geneviève Guitel: long scale and short scale
 * Maria Hasse : Gallai–Hasse–Roy–Vitaver theorem in graph coloring.
 * Grete Hermann : "She is noted for her early philosophical work on the foundations of quantum mechanics, and is now known most of all for an early, but long-ignored critique of a no-hidden-variable theorem by John von Neumann." " Her doctoral thesis, "Die Frage der endlich vielen Schritte in der Theorie der Polynomideale" (in English "The Question of Finitely Many Steps in Polynomial Ideal Theory"), published in Mathematische Annalen, is the foundational paper for computer algebra. It first established the existence of algorithms (including complexity bounds) for many of the basic problems of abstract algebra, such as ideal membership for polynomial rings. Hermann's algorithm for primary decomposition is still in contemporary use.[1]"
 * Eva Kallin : "One of its results, that not every topological algebra is localizable, has become a "well-known counterexample"
 * Faina Mihajlovna Kirillova : " She discovered and justified (together with R. Gabasov) the quasi-maximum principle for discrete-time control systems and pioneered its application. She also developed a new numerical approach to solving linear programming problems, and she created numerical methods for the solution of linear, quadratic, nonlinear programming, and optimal control problems. "
 * Maria Klawe : a generalization of the Art gallery problem
 * Sofia Kovalevskaya: Cauchy–Kovalevskaya theorem
 * Vera Kublanovskaya: QR algorithm
 * Olga Ladyzhenskaya: "She provided the first rigorous proofs of the convergence of a finite difference method for the Navier–Stokes equations."
 * Ruth Lawrence : " Lawrence's 1990 paper, "Homological representations of the Hecke algebra", in Communications in Mathematical Physics, introduced, among other things, certain novel linear representations of the braid group — known as Lawrence–Krammer representation. In papers published in 2000 and 2001, Daan Krammer and Stephen Bigelow established the faithfulness of Lawrence's representation. This result goes by the phrase "braid groups are linear.""
 * Anneli Cahn Lax: the Lax-Lax polynomial-- http://www.math.ens.fr/~benoist/articles/CarresEMS.pdf is the best reference I can find--I've actually only heard this called the "Lax-Lax polynomial" verbally, but I've heard it enough times to think this is probably a standard term.
 * Dorothy Maharam: Maharam's theorem, Maharam algebra
 * Maryam Mirzakhani: This is hard, and I'm not sure she actually belongs on this list? It seems like a lot of her work is too deep for me to understand, explain, or summarize, and may not fit the discrete "invention" model well. There's no named theorem or object that I can just pull off of wikipedia, but this doesn't mean that there are no named theorems or objects... Also, Mirzakhani's page is actually pretty short and lacking in mathematical detail, given her fame.
 * Caryn Navy: some important counterexamples in low dimensional topology
 * Gabriele Nebe: some cool sphere packings
 * Nataša Pavlović : "she is known for her work with Nets Katz pioneering an approach to constructing singularities in equations resembling the Navier–Stokes equations, by transferring a finite amount of energy through an infinitely decreasing sequence of time and length scales"
 * Lillian Pierce: She was one the first mathematicians to prove nontrivial upper bounds on the number of elements of finite order in an ideal class group.[2]
 * Marina Ratner: "she proved a group of major theorems concerning unipotent flows on homogeneous spaces, known as Ratner's theorems"
 * Ida Rhodes: "Rhodes was responsible for the "Jewish Holiday" algorithm used in calendar programs to this day."
 * Julia Robinson: "Her work on Hilbert's 10th problem played a crucial role in its ultimate resolution."
 * Alice Roth Swiss cheese (mathematics)
 * Alice Silverberg]: With Karl Rubin, she introduced the [[CEILIDH system for torus-based cryptography in 2003.
 * Kirstine Smith: optimal design of experiments
 * Vera T. Sós : friendship theorem  three-gap theorem
 * Birgit Speh : Speh representations, which seem quite important, but are a redlink
 * Ileana Streinu : carpenter's rule problem
 * Bella Subbotovskaya : random restrictions in complexity theory
 * Esther Szekeres: the happy ending problem (I'm not sure if she solved it/contributed to its solution, though.)
 * Daina Taimina: hyperbolic crochet
 * Tan Lei: "Tan obtained important results about the Julia and Mandelbrot sets, in particular investing their fractality and the similartities between the two.[pub 1] For example she showed that at the Misiurewicz points these sets are asymptotically similar through scaling and rotation.[pub 2] She constructed examples of polynomials whose Julia sets are homeomorphic to the Sierpinski gasket[pub 3] and which are disconnected.[pub 4] "
 * Éva Tardos:Tardos function
 * Reidun Twarock: "In the early 2000s, while thinking about the Penrose tiling and different ways of dividing the surface of a sphere, she was able to come up with a model describing the exceptional structure of papovaviridae, answering a question in virology that had been open for more than twenty years.[3] Almost all icosahedral viruses have the proteins on their capsids clustered in fives and sixes, with a structure permitting at most 12 clusters of five; but papovaviridae, including the cervical-cancer-causing HPV, have 72 clusters of five[4] This protein layout did not correspond to any spherical polyhedron known to mathematics. Twarock's model of papovaviridae had to be mathematically as well as biologically novel - it resembles a Penrose Tiling wrapped around a sphere."
 * Maryna Viazovska: "solved the sphere-packing problem in dimension 8[4][5][6] and, in collaboration with others, in dimension 24.[7][8] "
 * Marie-France Vignéras: you can't hear the shape of a hyperbolic drum
 * Karen Vogtmann: Out(Fn)
 * Claire Voisin: "In 2002 Voisin proved that the generalization of the Hodge conjecture for compact Kähler varieties is false."
 * Grace Wahba:Wahba's problem
 * Marion Walter: Marion Walter's Theorem
 * Wang Zhenyi : understanding eclipses
 * Gail Wolkowicz: She is known, among other contributions, for her proof that the competitive exclusion principle holds for inter-species competition in the chemostat.[2]

computing

 * ...probably some particular invention belongs on this list: Frances E. Allen
 * Smalltalk: Adele Goldberg (computer scientist)
 * treap: Cecilia R. Aragon
 * IBM Home Page Reader : Chieko Asakawa
 * MARC format : Henriette Avram
 * Baker's technique : Brenda Baker
 * Scratch programming language : Paula Bonta
 * abstract interpretation : Radhia Cousot
 * some developments in logic programming : Veronica Dahl (something of an edge case--no super clear, unital "discovery" for me to point to)
 * lattice-based access control (LBAC), intrusion detection systems (IDS) : Dorothy E. Denning
 * Sci-Hub : Alexandra Elbakyan
 * currently, this list only covers A-E
 * Shafi Goldwasser : "She is the co-inventor of probabilistic encryption,[12] which set up and achieved the gold standard for security for data encryption. " lots and lots of other stuff too--she should probably appear in both math and computing lists, for different discoveries

=Article 2: Improving Maryam Mirzakhani=

Mirzakhani made several contributions to the theory of moduli spaces of Riemann surfaces.


 * be more specific. Get some more concrete and suggestive words like geometry and dynamics in there. These are also waaay better links to follow if you're a nonmathematician/undergrad/etc.


 * figures! can't steal from her papers, obviously, but can look at them for inspiration and find related images on commons
 * just a picture of a hyperbolic surface would be nice--when you see pictures of her notes there are always lots of many holed tori.


 * also point out that this early work is a PhD thesis.

In her early work, Mirzakhani discovered a formula expressing the volume of the moduli space of surfaces of type (g,n) with given boundary lengths as a polynomial in those lengths. This led her to obtain a new proof for the formula discovered by Edward Witten and Maxim Kontsevich on the intersection numbers of tautological classes on moduli space, as well as an asymptotic formula for the growth of the number of simple closed geodesics on a compact hyperbolic surface, generalizing the theorem of the three geodesics for spherical surfaces.


 * Give this actual result, and why it is interesting and surprising

Her subsequent work focused on Teichmüller dynamics of moduli space. In particular, she was able to prove the long-standing conjecture that William Thurston's earthquake flow on Teichmüller space is ergodic.


 * This is intimidating. I think it makes sense to unpack Teichmüller space a little bit. Ergodicity seems like it might be easier to unpack--it has lots of simple consequences.

In 2014, with Alex Eskin and with input from Amir Mohammadi, Mirzakhani proved that complex geodesics and their closures in moduli space are surprisingly regular, rather than irregular or fractal. The closures of complex geodesics are algebraic objects defined in terms of polynomials and therefore they have certain rigidity properties, which is analogous to a celebrated result that Marina Ratner arrived at during the 1990s. The International Mathematical Union said in its press release that "It is astounding to find that the rigidity in homogeneous spaces has an echo in the inhomogeneous world of moduli space."
 * Being analogous to Ratner's feels pretty meaningless. It would be more meaningful to actually state the analogous result and unpack the analogy a bit.

Resources:

https://www.ams.org/notices/201304/rnoti-p490.pdf

http://www.ams.org/notices/201409/rnoti-p1074.pdf

http://www.ams.org/journals/notices/201803/201803FullIssue.pdf

Article 3? : Nancy Hingston
there is currently literally zero mathematical content on this page