Monday Morning Math: Fractals in the News!

Good morning! The semester is winding down and so this will be the last Monday Morning Math until mid-September (ummm, except for the bonus one I post because I forgot to hit submit one week). Today’s post features a Sierpinski triangle that just showed up in nature! We do love the Sierpinski triangle, whether in cookies or cake or cards or chapels, and so it was a delight to learn that (cyano)bacteria love it just as much! From the abstract of “Emergence of fractal geometries in the evolution of a metabolic enzyme” by Sendker et al. in Nature:

Here we report the discovery of a natural protein, citrate synthase from the cyanobacterium Synechococcus elongatus, which self-assembles into Sierpiński triangles. Using cryo-electron microscopy, we reveal how the fractal assembles from a hexameric building block. 

That’s right, this molecule forms triangles as it grows, and they assemble into Sierpinski Triangles. It came as a complete surprise, and the scientists still don’t fully understand what is going on. And that is the best, this kind of unexpected discovery of mathematical objects in nature.

If you want to see the photos, and you do, there’s an article by Katy Spalding in IFL Science and also nice 12-minute YouTube explanation by Anton Petrov with lots of fractal images:

I hope your own summer is just as full of discoveries!

Monday Morning Math: the Abel Prize

Good morning! The 2024 Abel Prize, named after Niels Abel, was announced last month: it will go to Michel Talagrand for his work in stochastic (random) processes in mathematics and physics. Even though the processes are random, a lot can be predicted and described.

Dr. Talagrand showed his strength in mathematics at a young age. Despite that, and despite his current accomplishments, he shared with the magazine New Scientist:

I’m not able to learn mathematics easily. I have to work. It takes a very long time and I have a terrible memory. I forget things. So I try to work, despite handicaps, and the way I worked was trying to understand really well the simple things. Really, really well, in complete detail. And that turned out to be a successful approach.

And that seems like a good thing for us all.

You can see a half hour video about the mathematics and the mathematician here:

Sources:

• “Why 2024 Abel prize winner Michel Talagrand became a mathematician” by Alex Wilkins
• “Mathematician Who Made Sense of the Universe’s Randomness Wins Math’s Top Prize” by Christian Thorsberg
• The Official Abel Prize site

Monday Morning Math: What’s a good guess?

I was listening to a podcast, and one of the hosts, Karen, asked the other, Georgia, how much $1 million in 1914 (or maybe 1920) — the value of the Carolands Estate when it was built — would be worth today. Georgia guesses $36 million, but the correct answer was $28 million.

That got me wondering – how close would a guess have to be to be a good guess? My first thought for a good guess that was too low was that anything above about $14½ million is pretty good, because it’s more than halfway to the correct number. So, roughly speaking, if $A is now worth $B, a guess that was too low, but above the average (A+B)/2, is pretty good.

But then I started to wonder if the arithmetic mean is really the right choice. The arithmetic mean (A+B)/2 is equally far from A and B in terms of addition: for example, the arithmetic mean of 2 and 8 is 5, and it has the pattern that 2+3=5 and 5+3=8. But money grows exponentially, so in thinking about how much things are worth it’s probably more natural to think of how many times over an amount has increased (as in, it’s worth 36 times as much as it used to me, not 35 million dollars more). That suggests that the geometric mean might be more relevant. The geometric mean is √(AB), and it is equally far between A and B in terms of multiplication. So the geometric mean of 2 and 8 is only 4, because √(2·8)=4, and it has the pattern that 2·2=4 and 4·2=8. This would mean that anything above about $5½ million was a pretty good guess.

If those numbers seem low, maybe instead of being more than halfway correct, you’d want to be something like 80% right. Using the arithmetic mean, 80% of the way from 1 million to 28 million would be 1+(80% of 27 million) — that is, A+0.8*(B-A) — so a low guess above about $22½ million is pretty good. Using the geometric mean, though, you’d want to multiply A by (B/A)^0.8, which in this case is (28)^0.8 so a low guess above $14½ million is pretty good.

But Georgia’s guess was too big! So what makes sense for a too-large guess? Using the arithmetic mean I might say anything between $14½ million and $41½ million is good, because both are $13½ million away [the arithmetic mean of 1 and 28]. Or if I wanted to be 80% correct, anything between $22½ and $33½ is a good guess, because both those numbers are within $5½ of the answer. Oh no! Georgia’s guess was just outside of that range.

But what if I used the geometric mean? In that case it seems more natural to use multiplication, rather than addition. If I look from (28)^0.5 to (28)^1.5 I get $5½ million to $148 million, which is a huge range. Even focusing on being 80% correct, I’d look from (28)^0.8 to (28)^1.2, so anything between $14½ million and a still-pretty-big $54½ million is pretty good. And Georgia’s guess falls well within both those ranges. Yay!

Monday Morning Math: Mary Golda Ross

Good morning! It’s an exciting day – a total solar eclipse in a race with the cloud cover that is so frequent here. So far it’s looking like cloud cover will win, but the sun is pretty powerful and we should still see the impacts of the eclipse, if not the actual sight.

With such an exciting celestial event happening, it’s also a good day to talk about Mary Golda Ross. She was born in Oklahoma in 1908; both of her parents were Cherokee citizens. Mary Ross earned bachelor’s and master’s degrees in mathematics and taught for many years. During World War II she begin working for Lockheed Aircraft Corporation and, after the end of the war, went back to school to study engineering. She developed important theories about interplanetary space travel and earth-orbiting flights, and said that in her job she combined her mathematical knowledge with qualities from her Cherokee heritage. Despite the importance of what she did, a lot of her work is still classified, and so remains unknown.

Mary Ross gave considerable support to others even after her retirement through the Society for Women Engineers, the American Indian Science and Engineering Society, and the Smithsonian’s National Museum of the American Indian. The Smithsonian museum opened only 20 years ago, in 2004, and Mary Ross (then 96 years old) attended the opening. She passed away in 2008, a few months before her 100th birthday.

Sources:

• “Mary Golda Ross: Aerospace Engineer, Educator, and Advocate” by Emily A. Margolis, Anya Montiel for the National Air and Space Museum on February 11, 2022.
• Google Doodle for “Mary G. Ross’s 110th birthday” from August 9, 2018.

Monday Morning Math: How to win the lottery. Or your bracket.

The role of morning this fine April the First will be played by…later in the morning.  Because that happens sometimes.  But as a treat to make up for the trick of not getting this out first thing, I’ll let you know how to win the lottery!  

For most lottery winnings, where you pick some numbers, the odds of winning really are the same no matter which number you choose.  So, umm,  you can’t pick a number that helps you win the lottery.  Sorry about misleading you.  But what you can do is pick a number that helps you maximize your winnings!  To do this, you want to pick a number that other people are unlikely to pick, so that if you do win, you won’t have to share.  This means you want to avoid mathy combinations like 314 (sorry about that, π) or number progressions like 123 or things that could be dates (also 123, or 04-01-24).   You want as boring a number as possible.*

The same idea applies to picking teams for a bracket, if you’re trying to figure out who will win a tournament!  You might want to pick the team that is leading, and in terms of winning that’s a good bet, but other people will think so too so even if you do win, you’re more likely to have to share.  Instead, you want to avoid that team.  Pick a good team, but not the top team.   Admittedly a little late for this season’s March Madness, although you can still follow along as see if that would have been a good strategy this year.

*You could look for the first integer that is not interesting but, unfortunately, that makes the number interesting.  Better look for the second most boring number.

This post was inspired by “The Team You Should Pick to Win Your NCAA Tournament Bracket Pool; It’s not UConn. The smartest thing you can do this March Madness is bet against the most popular national championship pick.” by Andrew Beaton and Ben Cohen in the Wall Street Journal, which reads like one of those journal articles from the 1800s.  Thanks, MK, for passing along this article from JM!

Monday Morning Math: Naive Bayes

Good morning! Last week I talked about Bayes’ theorem, which is a way of using the probability of B (assuming that you already know A) to find the probability of A (assuming that you already know B). As an example, you can use the probability that a person with a disease gets a positive test for that disease to find the probability that a person with a positive test actually has the disease, and (still and always surprising to me) those are not the same.

It turns out that Bayes theorem can also be used to determine if an email is spam! Here’s how it works. The email in question is made up of a bunch of words, and matters order the. But for this process, all the words are treated as independent, just a bunch of words in a pile — this is what is behind the word “naive”. The Naive Bayes algorithm looks at this bunch of words, figures out the probability that a piece of spam has those words in it, and then uses Bayes’ theorem to turn that around and find the probability that an email with those words is spam! The math involved is about one step more complicated than Bayes’ theorem, maybe two (something called Laplace smoothing plays a role), but it’s still the same basic idea of flipping probabilities around, in a modern application!

Thanks, S, for sharing this with me!
Sources: “Speech and Language Processing” by Daniel Jurafsky and James H. Martin, as explained by S.

Monday Morning Math: Bayes’ theorem

Good morning! Today’s post is the first of a two-parter, starting with Bayes’ theorem, named after the Reverend Thomas Bayes, who lived in England in the 1700s. Bayes’ theorem is a rule that lets you calculate probabilities that are sometimes surprising.

Let’s do an example. (I love this example – I use it each time I teach stats.) Let’s say that there is a disease that affects 1% of the population, and you have a test that is 95% accurate. This means if a person has the disease, there’s a 95% chance that the test is positive, and if the person doesn’t have the disease, there’s a 95% chance that the test is negative.

Now suppose someone takes the test and it comes back positive. What is the chance that person has the disease? It might seem like it’s 95% but it isn’t! It’s actually less than 25%. To find the probability, we can use Bayes’ theorem. Bayes’ theorem is usually written as P(A|B)=P(B|A)P(A)/P(B), but I’m going to replace A with 🤒 (for having the disease) and B with + (for having a positive test) and write it as
P(🤒| +) = P (+ | 🤒) P(🤒) / P(+)

Here’s what everything means:

• P( 🤒 | +) is the probability that a person has the disease if they got a positive test. That’s what we’re trying to figure out.
• P( + | 🤒) is the probability that a person gets a positive test if they have the disease. That’s 95% because the test is 95% accurate.
• P(🤒) is the probability that a person has the disease. That’s 1%, since 1% of the population has the disease.
• P(+) is the probability that a person gets a positive test. That’s a little more complicated: If a person has the disease there’s a 95% chance they get a positive test, but if they don’t have the disease there’s still a 5% chance that the test would (incorrectly) come back positive. So P(+) is 95% of 1% plus 5% of 99%, which turns out to be 4.75%.

Putting this all together, we get that P( 🤒 | +)=95%*1%/4.75%, which is 16.1%. In other words, even though the test is 95% accurate, if a person gets a positive test there’s only a 16.1% chance that they have the disease! This is about 1 out of 6, because out of every 100 people, only 1 person will have the disease (and they probably get a positive test) but there will also be about 5 people without the disease will also (incorrectly) get a positive test result.

Isn’t that amazing? Next week we’ll go one step further, and see how this applies to your computer deciding whether an email is spam…

How many digits of π should NASA use?

Good morning! I’ve been looking up space things lately in honor of our upcoming Total Eclipse 🌑🌞, and ran across an article by NASA/JPL on how many digits of π are necessary for accurate calculations with space travel. It’s an interesting read, but was last updated in 2022, which means it’s out of date. Or is it? Let’s do some calculations in anticipation of ✨ Pi Day ✨ this coming Thursday and find out!

The driving force behind the question is Voyager 1. Fun fact: Voyager 1 was launched on September 5, 1977, two weeks after Voyager 2, but it took a faster route into space and by mid-December that year was further away from Earth than Voyager 2’s, and fourteen months later got to discover that Jupiter had a ring! (Don’t feel too bad for Voyager 2, though, since V2 is still the only spacecraft to have visited Uranus and Neptune. Everyone gets to contribute.) In 1998 Voyager 1 overtook Pioneer 10, which had been launched in 1972, and with that Voyager 1 became the furthest spacecraft from Earth. At this point, after over 46 years on the (space)road, Voyager 1 is about 15.14 billion miles from Earth, which is almost 24.36 billion kilometers. We’ll round up to 25 billion kilometers to be safe. And, umm, because that makes the math easier.

Speaking of math, let’s do some calculations! If we think of r as Voyager 1’s distance from Earth, the circumference of a circle with that radius would be 2πr. Now let’s think of π as being made up of an approximation p plus some small error ∆p. This means the circumference would be 2(p+∆p)r=2pr+2r∆p, making our error for the circumference is 2r∆p. We’re using circumference here as a proxy for thinking of how far off our estimates of the exact location of V1 could be by potentially rounding too much in our approximation for π.

So to figure out how accurate our approximation for π needs to be in space travel computations, we can decide how much error we’re OK with, and divide that by 2r. If we want the circumference using Voyager 1’s distance to be accurate to 1 millimeter, which honestly is pretty good after close to 50 years of travel, then we’ll take that 1 millimeter and divide by 50 billion kilometers (which is twice the 25 billion km that V1 is from Earth). Putting everything in meters for an easier calculation, that’s 1×10^-3 meters divided by 50×10¹² meters. Division gives (1/50)x10^-15. Since 1/50 is 0.02=2×10^-2, our allowable error in the approximation for π is 2×10^-17.

What does all this mean? Well, it means that if our approximation for π is accurate to 17 decimal places, than our computations involving Voyager 1’s distance will be accurate to within a millimeter! (Even more, I think, because that 1mm is spread over the whole circumference, but we’re trying to keep things simple). In other words, NASA can use 3.141 592 653 589 793 24. That last digit is rounded up from a 3, but we’re still OK whether we use a 3 or a 4 in that last spot. We can still know where Voyager 1 is.

HAPPY PI DAY!!!

Motivation: https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/
(although they approached it in the opposite way – picking 15 decimal places and seeing how far off the circumference using Voyager 1 would be, and similarly looking at distances over Earth or over the known universe!).

Monday Morning Math: Kathaleen Land

Good morning! Our mathematician this morning is Kathaleen Land, one of the Hidden Figures who worked at NASA.  Kathaleen Land was the Sunday School Teacher of Margot Lee Shetterly, the author of the book  (and then movie) Hidden Figures, and she is sometimes referred to as the inspiration for the book. According to Shetterly, in 2010 she and her husband were visiting her parents in Hampton, Virginia, and had gone to her church where she caught up with her former teacher.  After leaving, Shetterly’s father – himself a research scientist at the National Aeronautics and Space Administration’s Langley Research Centre — pointed out that Mrs. Land had been a computer (someone who computes) at NASA.  Shetterly had grown up knowing many of the computers, but now, as an adult, she found it compelling in a new way.  Kathaleen Land was one of the first women Margot Lee Shetterly interviewed, and she pointed the way to other women whose contributions were not widely known.  

Kathaleen Land herself was born Bonnie Kathaleen Pleasants in northern Virginia and moved to Hampton, Virginia, in 1941 around the time she married her husband Stanley Land. They had three daughters and lived in Hampton, where Langley is located, the rest of their lives.  Kathaleen Land passed away in 2012 at the age of 93.

Sources:

• “Hidden figures: the history of Nasa’s black female scientists” by Margot Lee Shetterly in The Guardian 
• Sarah Mirk’s 16-minute interview with Margot Lee Shetterly in “In ‘Hidden Figures’ NASA’s African American Mathematicians Will Land on the Big Screen” (though I’m getting a warning now that the security certificate has expired, so 
• “Kathaleen Land” on Wikipedia
• Bonnie Kathaleen Land obituary on legacy.com

Monday Morning Math: You are Here

Here’s a fun map trick: open up a map app on your phone and choose a view that includes your location. The view can be as zoomed in or as zoomed out as you’d like. If you hold your phone horizontally, so the map appears parallel to the ground, then there will be a point on the map that is directly above the point it represents. That’s direct in a mathematical term: it won’t be even a millimeter off. If you walk around a bit, or zoom in or out more, the relevant point will change, but there will always be some point on the map that is directly above the place it shows.

This result doesn’t just work with phones, but with paper maps, should you have one handy to unfold and hold parallel to the ground. That map doesn’t have to be perfectly flat either: you could crumple it up and then uncrumple it, or hold it at an angle, and there would still be a point over the spot it represents. Or you could print your map on stretchy fabric or on silly putty, stretch it out and, after you’ve laughed at how funny the map looks, there would STILL be a point that woks! Furthermore, you could send your crumpled up silly putty map to a friend (as long as that friend also is somewhere shown on the map) and it would work for them, too.

This is an example of Brouwer’s Fixed Point Theorem, which says that if you have a continuous map from a nonempty compact convex closed set to itself, there will always be a fixed point – a point where f(P)=P.

Monday Morning Math: x=+

Good morning! One of the best things about math is noticing something and thinking, “Huh – I wonder how often that happens?” Maybe it’s a complicated answer, maybe easy, but I love that that question can be asked and often explored when you least expect it.

For example, you might notice that 2+2=2·2 and wonder if that happens with other numbers. A quick check shows that if x+x=x·x, then x²=2x so 0=x²-2x=x(x-2) so the only numbers that work are x=0 and x=2. Well, maybe. What if you switch into modular arithmetic? Then you just need x²=2x mod n, so you end up with a quadratic equation: x²-2x-kn=0 and using the quadratic formula you get x=(2±√(4+4kn))/2, which simplifies nicely to x=1±√(1+kn). In Base 3, for example, letting n=3 and k=1, one solution is x=1-2=-1, and a quick check verifies that (-1)+(-1) is the same as (-1)·(-1) since both equal 1 mod 3. And in Base 8, setting n=8 and k=3, one solution is x=1+5=6. Sure enough 6+6=6·6 in Base 8, since both equal 4 mod 8. Are there an infinite number of possibilities? Probably?

Since we’re already in modular arithmetic, here’s a similar thing that came up recently in Abstract Algebra. We were working with the integers mod 5, and it turns out that 2 and 3 are both additive inverses of each other (since 2+3=0 mod 5, and 0 is the identity using addition) and multiplicative inverses of each other (since 2·3=1 mod 5, and 1 is the identity under multiplication). And that got me wondering – are there other pairs like that, where x+y=0 mod n but x·y=1 mod n? The answer is Yes! For example, in mod 10 the numbers 3 and 7 are both additive inverses and multiplicative inverses. But wait, there’s more! The numbers 4 and 13 are additive and multiplicative inverses, mod 17. And I bet you can find even more! And come up with another interesting puzzle waiting around the corner.

Enjoy!

Math Mistakes that Make the News: Optimization

Good morning! It’s been a while since we had a Math Mistake featured here, but thanks to an article sent my way (thanks MM!), we have some breaking news. Well, “breaking” might be a stretch – the error happened in 1945 and was revealed in 1989, so it’s been a while. But still, it’s an error I hadn’t heard of before and it involves *Calculus*, and specifically checking if your critical point is a max or a min.

So what happened? In 1945 William R. Sears and Irving L. Ashkenas, who worked for the Northrup Corporation, wrote a report comparing the range of a traditional bomber to one that didn’t have a tail and was essentially all-wing (looking a bit like a boomerang). As part of the justification they used CALCULUS to find the shape that gave the best range: set up a function, take the derivative, and see what the critical points are. In this case, there were two: one where almost all the weight was in the wings, and one where it wasn’t. They stated that the all-wing design gave the maximum range.

The problem? That was actually the minimum. A test like the second derivative test can help with that – if the second derivative is negative, then the critical point is a maximum, like ⋂. But if the second derivative is positive, it’s a minimum, like ⋃. 

This mistake was caught within a few years, when Engineer Joseph V. Foa checked the math and told the authors. They admitted it, but also said it didn’t really change things because that was only part of the story. Foa thought that this did too change things, and if this were a couple hundred years earlier there might have been a duel. Instead, the army canceled an all-wing aircraft they’d been working on, supposedly for budget reasons.

So that’s that! Or maybe not – sometimes endings aren’t so clear. Wayne Biddle’s 1989 article below refers to a new B-2 bomber by Northrup that uses the same all-wing design. 

Main source: “Skeleton Alleged in the Stealth Bomber’s Closet” by Wayne Biddle, Science, New Series, Vol. 244, No. 4905 (May 12, 1989), pp. 650-651. (There was a follow-up: “B-2 comes up short” by Wayne Biddle, Science, Vol. 246, Issue 4928 (October 20, 1989), p. 322.)

Monday Morning Math: Honoring Black Mathematicians

Good morning!!!  e-day (February 7, for 2.7….) is almost here, which makes this a very mathematical week.  We’re celebrating with cookiEs in the Math Center on Wednesday.  

But that’s not the only day of celebration – we have a whole month’s worth!  The site Mathematically Gifted & Black honors a new mathematician each day in February! The honoree for February 1 was Toka Diagana.  Dr. Diagana studied mathematics in Mauritania and France, and is now a professor at Howard University; he has published seven books and well over a hundred research articles, mostly related to Differential Equations. Other honorees for February are

• Dr. Lakeshia Legette Jones, Associate Professor of Mathematics at Clark Atlanta University 
• Dr. Adrian Cartier, Cofounder and Chief Data Officer of Freight Science, Inc.
• Dr. Tai-Danae Bradley, Research Mathematician at SandboxAQ, Visiting Research Professor of Mathematics at The Master’s University, and creator of Math3ma.

Happy reading!

Monday Morning Math: Sizes of Squares

Good morning!  Classes have started, and that means More Monday Morning Math!  Today’s topic is based on a reader suggestion (Thanks Q!) and it’s a pretty neat problem.

Imagine that you have a grid – you could think about the xy plane, using only integers for x and y, or thinking of a giant geoboard.     If you make a square with all four corners at these (integer) points, what are the possible areas of the square?

You might guess 1 using a 1×1 square, and 4 using a 2×2 square, and 9 using a 3×3 square, etc.  And those are correct, but there are more in between, if you tilt the square.  The image below shows squares with area 1, 2, 4, and 5. 

At those point you might be thinking a couple things:  Why did I skip 3, and is this related to the Pythagorean Theorem?  And the answers are “I couldn’t do it” and “Yes!”

Here’s one way to think about it.  Look at the second and fourth square above: you can picture the side length as the hypothenuse of a right triangle whose legs have integer length (since the vertices of the square are on the integer grid). 

The legs of those triangles are integers, and using the Pythagorean Theorem that means that the hypotenuse squared will be the sum of integers, and therefore itself an integer.  So Interesting Thing #1 is that all these squares have integer area (since the area is going to be the same as the square of the hypotenuse)! 

Interesting Thing #2 is the pattern of which areas can be formed. 1, 2, but not 3.  4, 5, but not 6 or 7.  Based on the above description, the areas are those integers that can be written as   for integers  and  (and by allowing one of those to be 0, you get the perfect squares as well). It turns out this is sequence A001481 in the Online Encyclopedia of Integer Sequences, and it has a few interesting properties:

• It is closed under multiplication.  This means that if you multiply two numbers in the sequence, you get another number in the sequence!
• These numbers have more 4k+1 divisors than 4k+3 divisors.  For example, The number 9 has two divisors that are equal to 1 mod  (1 and 9) but only one that is equal to 3 mod4 (3).  
• If you factor these numbers into primes, the power of any prime-that-is-equal-to-3mod4  must be even.  For example, .  The number 13 is equal to 1 mod4 so we don’t have to worry about it, but 11 is equal to 3 mod4 and 11 isn’t raised to an even power, so there isn’t a square of area 2024.  Bummer!  But  and the factor 3 (which is equal to 3 mod 4) is raised to an even power, so there is a square with area 2025!  [Actually,  so maybe that’s not a surprise.]
• Finally, the way to draw the squares isn’t unique: the aforementioned 2025 could also be written as  so it’s possible to draw a square with non horizontal/vertical sides whose area is 2025. ]

Happy Squaring!

Monday Morning Math: Evelyn Boyd Granville

Good morning!  It’s Finals Week here, and so this week will be the last MMM until after the Spring Semester starts in late January. We will use this final Monday Morning Math of 2023 to celebrate a mathematician who passed away this year at the age of 99:  Evelyn Boyd Granville, the second African American woman to receive a PhD in mathematics.  Evelyn Boyd was born in Washington, DC, on May 1, 1924. She loved school and graduated high school as valedictorian and Smith College, where she studied mathematics, theoretical physics and astronomy, summa cum laude. In 1949 she earned her PhD in Mathematics at Yale University, studying functional analysis. She worked as a postdoc for a year before becoming a university professor, but after two years returned to Washington, DC, to work at the National Bureau of Standards.  In 1956 Dr. Boyd joined IBM, where she worked on the space program.  She was part of NASA’s Project Vanguard (to launch a satellite), Project Mercury (to put a person into Earth orbit) and Project Apollo (to put a person onto the moon).

Dr. Granville (as she was known after her marriage to Edward Granville) continued with IBM for nearly 20 years before returning to teaching as a university professor.  She wrote a college textbook and taught math and computer science in California and Texas before returning again to Washington, DC, in 2010.    Evelyn Boyd Granville passed away in her home in Silver Springs, Maryland, on June 27, 2023.  Dr. Granville received many awards during her lifetime, including the Golden Anniversary Legacy Award from NAM (the National Association of Mathematicians) in 2019.   [I was at that ceremony, in the back of a very crowded room, and the love and admiration for Dr. Granville were palpable.]

For more information, see

• “My Life as a Mathematician” by Evelyn Boyd Granville in SAGE: A Scholarly Journal on Black Women
• “The Legacy of Evelyn Boyd Granville” by J. L. Huston in the NAM Newsletter (pp. 14+)
• “Pioneering NASA ‘Hidden Figure’ Evelyn Boyd Granville dies at age 99” by Josh Dinner at space.com

I wish you all a good December, and a happy and peaceful New Year!