Hot answers tagged

79

Emmy Noether comes first to mind, as one of the most influential mathematicians in abstract algebra, specifically in the development of Noetherian rings (along with many properties of ideals). One aspect of her work that high school students might like is from another area, analysis. Noether's theorem says that every symmetry of the laws of nature (or the ...


51

Julia Robinson! I recommend her for a high school audience for a few reasons: Mathematical reasons: She is best known for her work towards the solution of Hilbert's 10th Problem, regarding an algorithm for solving Diophantine Equations. High school students can absolutely recognize and solve particular Diophantine Equations. Furthermore, and more relevant ...


48

Perhaps not strictly a mathematician in the traditional sense, but I think Ada Lovelace might be a great woman to start with in today's digital world. She even has an important programming language named after her: Ada. Augusta Ada King, Countess of Lovelace (10 December 1815 – 27 November 1852), born Augusta Ada Byron and now commonly known as Ada ...


39

Sophie Germain and her work on Fermat's Last Theorem.


31

Maryam Mirzakhani, who just won the Fields Medal, and also was the first Iranian student to win a gold medal in the IMO in 1995 with a perfect score. My colleague Mohammad Javaheri was on Iran's IMO team with her in 1995. He told us the other day that after Maryam won the gold, when the rest of the team went up to congratulate her she said "next, the Fields ...


29

Any Living One who is friendly enough to come talk with them. Seriously, learning about "people in books" can sometimes be inspiring. But actual live role models are best. Write a local college, university, or business to find a woman who self-identifies as a mathematician. Invite her to your school to spend some time with your students. You want a real ...


28

In the first place, the impetus to "reform" math education was motivated by politics, not by any serious observed deficit. By coincidence, there was a "new" style in higher mathematics, reflecting the previous 50-60 years assimilation of set theory and rewriting of many things in terms of set theory. But until the "sputnik scare" no one had incentive to ...


26

Edit (Jan 2018) I recommend checking Annie Perkins' page: The Mathematicians Project: Mathematicians Are Not Just White Dudes If you scroll down, then you will find a section entitled Women (alphabetical by last name). There are some great sources/names there, and - as a bonus - the project keeps evolving! $$ $$ $$ $$ $$ $$ Edit: Marjorie Rice has ...


25

Sonya Kovalevsky, correspondent of Weierstrass, for example.


25

Vi Hart, the self-termed Mathemusician. I especially enjoy her Doodling in Math Class YouTube series.


25

What are some examples of math history that can be mentioned in calculus classes, either to liven things up or to provide additional perspective / insight on the material being learned? You mention two different goals here. Personally, I have used anecdotes about and discussion of historical events/people in calculus courses to... provide some context for ...


21

If your main interest is to provide a role model that students can identify with, you might want to look at Danica McKellar. According to her Wikipedia entry: McKellar studied mathematics at UCLA, graduating summa cum laude in 1998. As an undergraduate, she coauthored a scientific paper with Professor Lincoln Chayes and fellow student Brandy Winn ...


20

Opinion. There never was a generation of high school students in the US who could jump right into Rudin. There would be (and still is) a small portion of the top high school graduates who could. And maybe a larger portion of the graduates from a few elite high schools. But that's it. Baby Rudin would be used (if at all) for advanced undergraduates or ...


20

This is also borderline not-an-answer, but it might be a nice broadening of your students' worldview to know that the "$m$" and the "$b$" are not universally accepted. Showing them this map (even though I do not know its original source, so it may not be accurate in its details) could help their thinking out a bit: Substantial edit: I now no longer believe ...


19

Classically speaking, Maria Agnesi is the best classical mathematician to study. She published calculus texts that expanded and reflected upon the works of Leonhard Euler.


17

Adm. Grace Hopper earned a Ph.D. in mathematics at Yale (1934), helped program the Mark I (1944), developed the first compiler (1952) and some early computer languages, and worked on the development of the UNIVAC I.


16

You might want to read Kline (1973). I haven't read the book, but according to Wikipedia, In 1973, Morris Kline published his critical book Why Johnny Can't Add: the Failure of the New Math. It explains the desire to be relevant with mathematics representing something more modern than traditional topics. He says certain advocates of the new topics "...


15

In Germany, there recently was a Project at two universities which tried to strengthen historical connections in analysis courses, especially for teacher education. For them, history can be an important source of motivation if used with real interest. (Bad use: "Even Leibniz made these mistakes" - no learning from history. Good use: "The concept of ...


14

Maria Gramegna, the brilliant student of Giuseppe Peano. When you use matrices to solve systems of differential equations, you rely in many ways to her ideas. She defined the exponential function of a matrix through its power series and used it as we do it now. Though this is not strictly speaking high school mathematics, you can mention her story to every ...


13

My experience with giving history and chronology and people-involved has mostly (but not entirely) been disheartening: many students, from calculus to grad students, don't count that material (and the perspective it affords) as having much value. Some do value it, but the more-typical response is more-or-less polite waiting for the "real content" to begin. ...


13

I disagree wholeheartedly with Nicola. I can only speak to the US' and Canada's mathematics systems so it may not be broadly true. Mathematics is largely taught in a vacuum. In every other field of study (physics, chemistry, economics, literature, etc.), we learn about the people, the history, and the ideas. In math, we might learn the names of some ...


12

I think very roughly speaking: "new math" (also known in europe as a fearful period of time, especially for parents) followed a mathematical construction of mathematical knowledge rather than a psychological one. Mathematically, you would introduce an abstract concept like an equivalence relation first and then introduce concept like terms or fractions as ...


12

I think for young girls Ruth Lawrence is a great role model since she got her phd at age of 17: At the age of 9, Ruth Lawrence gained an O-level in mathematics, setting a new age record. Also at the age of 9 she achieved a Grade A at A-level Pure Mathematics. In 1981 Ruth Lawrence passed the Oxford University interview entrance examination ...


11

Alicia Boole Stott, the daughter of George Boole (Boolean Algebra), had a deep understanding of 4D geometry. She got married and lived the life that entailed back then (1890s and on). Coxeter gives her husband some credit for connecting her to Pieter Schoute. They worked together and published some papers on 4D polytopes. Coxeter's book, Regular ...


11

Grace Chisholm Young seems overlooked so far (13 answer so far) and in my opinion she is worth considering. She worked mostly in real analysis and what is sometimes called classical point set theory (among other things, she's the "Young" in the Denjoy-Young-Saks theorem and she wrote a well known survey paper on nowhere differentiable continuous functions in ...


11

The notation exists since a long time. It was used already by Irving Stringham in 'Uniplanar Algebra (1893).' This is claimed to be the earliest use on http://jeff560.tripod.com/trigonometry.html giving Cajori vol. 2, page 133 as reference. In this book, Uniplanar Algebra, the notation is used first, as far as I can see, in chapter III (The algebra of ...


10

More famous for computer science than maths, but a strong mathematician none the less and creator of the Liskov substitution principle (the L in SOLID), Barbara Liskov.


10

A quintessential example of a cultural clash over math education in US schools, I would say, is the entire Math Wars, an ongoing struggle over standards and pedagogy in K-12 schools. It is a struggle of curriculum reformers trying to bring research-based innovations of mathematics thinking, learning, and teaching over the last three decades into schools ...


10

I had my students in Math for Elementary Teachers doing arithmetic in the Babylonian, Mayan, and Egyptian systems. It's not beyond them at all, and it helps them understand place value more deeply. I don't have recommendations for a text for the whole course, but you may find a lot of useful material in Count Like an Egyptian. I hope to run a math circle ...


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