Almost 300 years ago, a single letter exchanged between two brilliant minds gave rise to one of the most enduring mysteries in the world of number theory. 

In 1742, Christian Goldbach penned a letter to fellow mathematician Leonhard Euler proposing that every even integer greater than 2 can be written as a sum of two prime numbers. This statement is now known as Goldbach’s Conjecture (it is considered a conjecture, and not a theorem because it is unproven). While neither of these esteemed mathematicians could furnish a formal proof, they shared a conviction that this conjecture held the promise of being a "completely certain theorem." The following image demonstrates how prime numbers add to all even numbers up to 50:

From its inception, Goldbach's Conjecture has enticed generations of mathematicians to seek evidence of its legitimacy. Though weaker versions of the conjecture have been proved, the definitive proof of the original conjecture has remained elusive. There was even once a one-million dollar cash prize set to be awarded to anyone who could provide a valid proof, though the offer has now elapsed. While a heuristic argument, which relies on the probability distribution of prime numbers, offers insight into the conjecture's likelihood of validity, it falls short of providing an ironclad guarantee of its truth.

The advent of modern computing has emerged as a beacon of progress. With vast computational power at their disposal, contemporary mathematicians like Dr. Tomàs Oliveira e Silva have achieved a remarkable feat—verification of the conjecture for every even number up to an astonishing 4 quintillion, a number with 18 zeroes.

Lazar Paroski’s Goldbach Conjecture Document on Maple Learn offers an avenue for users of all skill levels to delve into one of the oldest open problems in the world of math. By simply opening this document and inputting an even number, a Maple algorithm will swiftly reveal Goldbach’s partition (the pair of primes that add to your number), or if you’re lucky it could reveal that you have found a number that disproves the conjecture once and for all.

A salesperson wishes to visit every city on a map and return to a starting point. They want to find a route that will let them do this with the shortest travel distance possible. How can they efficiently find such a route given any random map?

Well, if you can answer this, the Clay Mathematics Institute will give you a million dollars. It’s not as easy of a task as it sounds.

The problem summarized above is called the Traveling Salesman Problem, one of a category of mathematical problems called NP-complete. No known efficient algorithm to solve NP-complete problems exists. Finding a polynomial-time algorithm, or proving that one could not possibly exist, is a famous unsolved mathematical problem.

Over years of research, many advances have been made in algorithms that can solve the problem, not in perfectly-efficiently time, but quickly enough for many smaller examples that you can hardly notice. One of the most significant Traveling Salesman Problem solutions is the Concorde TSP Solver. This program can find optimal routes for maps with thousands of cities.

Traveling Salesman Problems can also be used outside of the context of visiting cities on a map. They have been used to generate gene mappings, microchip layouts, and more.

The power of the legendary Concorde TSP Solver is available in Maple. The TravelingSalesman command in the GraphTheory package can find the optimal solution for a given graph. The procedure offers a choice of the recently added Concorde solver or the original pure-Maple solver.

To provide a full introduction to the Traveling Salesman Problem, we have created an exploratory document in Maple Learn! Try your hand at solving small Traveling Salesman examples and comparing different paths. Can you solve the problems as well as the algorithm can?

we have recieved lots of great sumissions, but we want your great submission and now you have more time.

The deadline for submissions to the Art Gallery and Showcase for the 2023 Maple Conference is rapidly approaching. We really want to see your art! It doesn't have to be incredibly impressive or sophisticated, we just want to see what our community can create! If you've been working on something or have a great idea, you still have a few days to get it together to submit.

Submission can be made by email to gallery@maplesoft.com but be sure to visit the visit our Call for Creative Works for details on the format of the submission.

What are planes? Are they aircraft that soar through the sky, or flat surfaces you'd come across in your geometry textbook? By definition yes, but they can be so much more. In the world of math, observing a system of equations with three variables allows us to plot them as planes in ℝ³. As we plot planes, these geometric entities can start intersecting, creating captivating visualizations. However, the intersection of planes is not just an abstract mathematical concept present only in the classroom. Throughout our daily lives, we come into contact with intersecting planes everywhere. Have you ever noticed the point where two walls and the floor in your room converge? That’s an intersection in its simplest form! And the line where the pages of a book are bound together? Another everyday intersection!
 

Room image: https://unsplash.com/photos/0H-aJ06IZw4, Book image: https://unsplash.com/photos/6H9H-tYPUQQ 

However, just seeing plane intersections is but a tiny piece of the puzzle. After all, how can we delve into the intriguing properties of these intersections without quantifying them? Enter the focus of Maple Learn's newest collection: Intersection of Planes. Not sure about how you can identify the different scenarios that three planes can form in ℝ³? Check out the eight documents that provide complete walk-throughs for solving each individual case that three planes can form! With cases ranging from three parallel and distinct planes to three planes forming a triangular prism to three planes intersecting in a line, you’ll gain a mastery of understanding the intersection of planes by the time you’re finished with the examples.

Once you’ve gained an understanding of how to identify and solve the cases that three planes can form, it’s time to test your knowledge! This quiz-like document takes you through the steps of solving for the intersection of three planes with guiding questions and comprehensive feedback. Once you successfully find the intersection or identify the case, you’ll be provided with an interactive 3D plot that allows you to see what the math you’ve been doing looks like. This opportunity to solve any of the 16 different possible systems of equations allows you to prove that you’re on another level!

With your newfound mastery of solving systems of equations, check out similar documents in the recently added linear algebra collection! Try calculating the volume of a parallelepiped or deriving the formula for the distance between a point and a plane. 

What are you waiting for? Gear up and join us on Maple Learn today! Whether you're diving deep into the world of linear algebra or merely dabbling, there’s a world of discovery waiting for you.

Jill is walking on some trails after a long and stressful day at work. Suddenly, her stress seems to be lifted off her shoulders as her attention gets drawn to nature's abundant beauty. From the way the flowers blossom to the way the leaves grow on their stems, it is stunning.

When many think of mathematics, what comes to mind is often numbers, equations, and calculations. While these aspects are essential to math, they only scratch the surface of a profoundly creative discipline. Mathematics is much more than mere numerical manipulation. It is a rich and intricate realm that influences everything from art and science to philosophy and technology.

Just as Jill was stunned by the beauty of nature, you too can be amazed by the beauty of math! The golden ratio is one math concept that garners a reputation for being particularly beautiful, perhaps due to its presence in different parts of nature. You can explore it through some Maple Learn documents.

Check out the Fibonacci sequence and golden ratio document to better understand the golden ratio and its relationships. Perhaps, once you have a good grasp on the basics, you would like to check out the golden spiral document. Notice how the spiral that results resembles the outline of a nautilus shell and the arms of a spiral galaxy!

Nautilus shell image: https://en.wikipedia.org/wiki/File:NautilusCutawayLogarithmicSpiral.jpg -- Spiral galaxy image: https://www.cnet.com/pictures/natures-patterns-golden-spirals-and-branching-fractals/

Next, you may want to understand why the golden ratio is considered the most irrational number. You can do that by checking out the most irrational number document. Or you could explore this golden angle document to see how the irrationality of the number can be used to reproduce structures found in nature, such as the arrangement of seeds in a sunflower's centre!

Sunflower image: https://commons.wikimedia.org/wiki/File:Helianthus_whorl.jpg
 

That's all for this post! No worries, though. Maple Learn has hundreds of documents that can aid you in exploring the abundant beauty of math. Enjoy!

It’s finally here. The mystical treasure that has long been rumoured to lie deep within the labyrinthine halls of Maple Learn is within your grasp at last. The ordeals ahead are treacherous, and most who have ventured in have never returned… but, armed with nothing but your wits and your curiosity, you know you’re prepared to conquer the trials that await you. Can you be the first to uncover the secrets of Maple Learn?

Surprise! We here at Maplesoft have decided to become game developers. Okay, maybe not really, but we do have one game that we’re excited to be sharing with you all. Introducing: The Treasure of Maple Learn. This series of documents mimics the style of a text-based adventure game, and takes you through a series of puzzles that challenge you to discover for yourself all of what Maple Learn has to offer. It was originally created by myself and a team of other co-op students during the 2021 Maplesoft Hackathon, and I’m very excited to be releasing this updated and polished version of the game. Finally, it’s time to set out on your quest to discover the legendary treasure that lurks within Maple Learn… if you dare.

If you don’t dare, don’t worry, we have other options. You can also check out our new video on Getting Started with Maple Learn, which takes you through everything you need to know to become a Maple Learn expert. And if that’s not enough learning Maple Learn for you, we also have an extensive collection of How-To documents. Want an in-depth look at how to use the plot window? How about an exploration of how to work with linear algebra? Or maybe you want to unleash your artistic side? We’ve got you covered.

So if you’re just getting started with Maple Learn and are looking for a tutorial, you’ve got options—we’ve got a quick video overview, tons of collections of in-depth documentation, and a quest through the treacherous depths of Maple Learn to uncover the secrets that lie within. Pick your poison! (But maybe watch out for literal poison in that labyrinth.)

The concept of “Maple Learn art” debuted on the MaplePrimes blog in December 2021.  Since then, we’ve come a long way with new Maple Learn features and ever-growing creative minds.  Creating art using mathematical expressions and shapes is a great way to hone both your mathematical skills and your creativity, and is the perfect break from a bout of studying or the like.

I started my own Maple Learn art journey over one year ago.  Let’s see how one’s art can improve over time using new and advanced features!

Art with Shapes, March 2022

This pi-themed pie is simple and cute, but could use some additional features:

Adding Shaded() around Maple Learn shape commands colors them in!

Fun fact: I hand-picked all of the coordinates for that pi symbol.  It was an arduous but rewarding process.  Nowadays, I recommend a new method.  When you create a table in Maple Learn with two number columns, the values are plotted as points.  These points can be clicked and dragged across the plot window, and the table updates automatically to display the new coordinates.  How can you use this to make art?

1. Create a table as described above.
2. Move the points with your mouse to create an outline of the desired shape.
3. Use the coordinates from your table in your geometry command.

Let’s apply these techniques in a newer piece: a full recreation of the spaghetti emoji!

Art with Shapes, August 2023

Would you look at that?!  Fully-shaded colors, a background, and lines of spaghetti noodles that weren’t painstakingly guesstimated combine to create a wonderfully improved piece of art.

Art with Animation, March 2022

Visit the document to see its animation.  Animation is an invaluable feature in Maple Learn, frequently utilized to observe how changing variables affect functions or model a concept.  We’ve harnessed its power for animated artwork!  This animation is cute, using parametric functions and more to change the image as the animation variable changes.  Like the previous piece, it’s missing a background, and the leaves overlap the stem awkwardly in some places.

Art with Animation, August 2023

This piece has a simple background made with a large black square, but it enhances the overall effect.

The animation here comes from piecewise functions, which display different values based on a given criterion.  In this case, the criterion is the current value of the animation variable.

There are 32 individual polygons in this image (including 8 really tiny ones along the edges!) and 8 rainbow colors.  Each color is associated with a different piecewise function, and displays four random squares in that color in each frame of the animation.

This image isn’t that much more advanced than the animated flower, but I think the execution has vastly improved.

Whether you’ve been following these blog posts since December 2021 or are new to Maple Learn, we hope you give Maple Learn art a try.

And don’t forget that Maple is also a goldmine of artistic potential.  Maple’s bountiful collection of packages such as Fractals, ColorTools, plottools and more are great places to start for math that is as aesthetically pleasing as it is informative.

This week, our staff participated in a series of art challenges using either Maple Learn or Maple itself, each featuring a suggested theme and suggested mathematical content.  Check out the challenges and some of our employees’ entries below, and try out a challenge for yourself!

Tuesday’s Art Theme: Pasta

Mathematical Content: Shapes

Example: Lazar Paroski’s spiraling take on spaghetti

Wednesday’s Art Theme: Nature

Mathematical Content: Fractals

Example: John May’s Penrose tiling landscape (in Maple!)

Thursday’s Art Theme: Disco

Mathematical Content: Animation

Example: Paulina Chin’s disco ball (in Maple!)

Friday’s Art Theme: Space

Mathematical Content: Color

Example: that’s today!  Who knows what our staff will create…?

We hope these prompts have inspired you! If you create some art you’re really proud of, consider submitting it to be featured in the 2023 Maple Conference’s Creative Works Showcase.

Space. The final frontier. A frontier we wouldn’t stand a chance of exploring if it weren’t for the work of one Albert Einstein and his theories of special relativity. After all, how are we supposed to determine at what speed an alien spaceship is traveling towards Earth if we can’t understand how Newtonian physics break down at high velocities? That is precisely the question that this Maple MathApp asks. Using the interactive tool, you can see how the relative velocities change depending on your reference point. Just what you need for the next time you see a UFO rocketing through the sky!

But what if you don’t have the MathApp on hand when the aliens visit? (So rare to travel anywhere without a copy of Maple on you, I know, but it could happen.) You’ll have to just learn more about special relativity so that you can make those calculations on the fly. And luckily, we have just what you need to do that: our new Maple Learn collection on modern physics, created by Lazar Paroski. Still not quite sure how to wrap your head around the whole thing? Check out this document on the postulates of special relativity, which explains and demonstrates some of the fundamentals of special relativity with lively animations.

Once you’ve gotten familiar with the basics, it’s time to get funky. This document on time dilation shows how two observers looking at the same event from different frames of reference can measure different times for that event. And of course once you start messing with time, everything gets weird. For an example, check out this document on length contraction, which explains how observers in different frames of reference can measure different lengths for the same moving object. Pretty wild stuff.

So now, armed with this collection of documents, we’ll all be ready for the next time the aliens come down to Earth—ready to calculate the relative speed of their UFOs from the perspectives of various observers. That’ll show ‘em!

Disability Pride Month happens every July to celebrate people with disabilities, combat the stigma surrounding disability, and to fight to create a world that is accessible to everyone. Celebrating disability pride isn’t necessarily about being happy about the additional difficulties caused by being disabled in an ableist society: as disabled blogger Ardra Shephard puts it, “Being proud to be disabled isn’t about liking my disability… [It] is a rejection of the notion that I should feel ashamed of my body or my disability. It’s a rejection of the idea that I am less able to contribute and participate in the world, that I take more than I give, that I have less inherent value and potential than the able-bodied Becky next to me.” The celebration started in the US to commemorate the passing of the Americans with Disabilities Act, which prohibits discrimination based on disability, and since then it has spread around the world.

So what does any of this have to do with us here in the math community? Well, while it’s easy to think of mathematics as an objective field of study that contains no barriers, the institutions and tools used to teach math are not always so friendly. For an obvious example, if there's a few steps leading up to your math classroom and you use a wheelchair, that's going to be a challenge. And that's just scratching the surface—there are countless ways to be disabled, many of which are invisible, and many of which make a typical classroom environment very challenging to learn in for a variety of different reasons. As well, it can be difficult for prospective mathematicians to ask for accommodations, because of both the stigma against disability and the systemic barriers to receiving the proper accommodations. Just ask Daniel Reinholz, a disabled math professor at San Diego State University, whose health forced them to drop out of several engineering courses during their undergraduate degree: “Throughout it all, I never had a notion that I could receive accommodation or support, or that I deserved it. (Even though I’ve never really fit into the “right” category of disabled to be accommodated, so who knows what difference it really would have made.)” While Daniel was lucky enough to find a path to mathematics that worked for them, not all disabled people currently have that path available to them. As math professor Allison Miller puts it in her AMS blog post about disability in math, “Success in mathematics should not depend on whether someone’s needs happen to mesh sufficiently well with institutional structures and spaces that have been designed to serve only certain kinds of minds and bodies.”

While we can’t make systemic changes on our own, we here at Maplesoft can still do our part to make tools for math that are something everyone can use and enjoy. As such, we’re excited to share that Maple Learn is now compatible with the screen reader NVDA. By using this screen reader, and with our extensive keyboard shortcuts that negate the need for a mouse, individuals with low or no vision can now use Maple Learn to help them explore mathematics. All you need to do is select “Enable Accessibility” from the hamburger menu, and you’ll be ready to go! Maple Learn also includes the colour palette CVD, which is designed to be accessible to colourblind users. To learn how to access the colour palettes, check out this How-To document.

There is still more work for us to be done to ensure that we’re doing our part to make math accessible to everyone. Not only are there still ways in which we’re working to improve the accessibility of our products, but we all as a math community need to strive towards recognizing the barriers we may have previously overlooked and finding ways to provide accommodation for all mathematicians. One organization, called Sines of Disability, is already working towards that very goal. They are a community of disabled mathematicians dedicated to dismantling the systemic ableism present in mathematics. For this Disability Pride Month, consider taking the time to check out these resources and learn more about this issue.

Can’t seem to find the mistake in your math? Instead of painfully combing through each line, let the new “Check my work” operation in Maple Learn help! Now in Maple Learn, you can type out a solution to a variety of math problems, and let Maple Learn check your work! Additionally, by signing on to Maple Learn and the Maple Calculator app, you can take a photo of your handwritten math, import it into Maple Learn, and check your work with the click of a button.

Whether you’re solving a system of linear equations or an algebra problem, computing an integral or a partial derivative, “Check my work” can help. Maple Learn will tell you which steps are “Ok” and which steps to double-check. If you get a step wrong, Maple Learn will point out which line has an error, then proceed to check whether the rest of your work followed the right procedure.

Here’s an example of a solution to a system of linear equations written out by hand. All I had to do was snap a picture in the Maple Calculator app, and Maple Learn instantly had my equation set ready to go in the Cloud Expressions menu. Then, I just clicked “Check my work” in the Context Panel.

Maple Learn identified that I was trying to solve a system with 3 equations, checked my steps, and concluded my solution set was correct.

What happens if you make a mistake? Here’s an example of evaluating an improper integral with a u-substitution that involves a limit. This time, I directly typed my steps into Maple Learn and pressed “Check my work” in the Context Panel. Check my work recognized the substitution step and noted what step was incorrect; can’t forget to change the limits of integration! After pointing out where my mistake was, Maple Learn continued to evaluate the rest of my steps while taking my error into account. It confirmed that the rest of the process was correct, even though the answer wasn’t.

After making my change in Maple Learn and checking again, I’ve found the correct value.

Checking your work has never been easier with Maple Learn. Whether you want to type your solution directly in Maple Learn or import math with Maple Calculator, the new “Check my work” feature has you covered. Visit the how-to document for more examples using this new feature and let us know what you think!

What was established in 1788 in Prussia, is derived from the Latin word for “someone who is going to leave”, and can be prepared for using the many capabilities of Maple Learn? Why, it’s the Abitur exam! The Abitur is a qualification obtained by German high school students that serves as both a graduation certificate and a college entrance exam. The exam covers a variety of topics, including, of course, mathematics.

So how can students prepare for this exam? Well, like any exam, writing a previous year’s exam is always helpful. That’s exactly what Tom Rocks Math does in his latest video—although, with him being a math professor at Oxford University, I’d wager a guess that he’s not doing it as practice for taking the exam! Instead, with his video, you can follow along with how he tackles the problems, and see how the content of this particular exam differs from what is taught in other countries around the world.

Oh, but what’s this? On question 1 of the geometry section, Tom comes across a problem that leaves him stumped. It happens to the best of us, even university professors writing high school level exams. So what’s the next step?  Well, you could use the strategy Tom uses, which is to turn to Maple Learn. With this Maple Learn document, you can see how Maple Learn allows you to easily add a visualization of the problem right next to your work, making the problem much easier to wrap your head around. What’s more, you don’t have to worry about any arithmetic errors throwing your whole solution off—Maple Learn can take care of that part for you, so you can focus on understanding the solution! And that’s just what Tom does. In his video, after he leaves his attempt at the problem behind, he turns to this document to go over the full solution, making it easy for the viewer (and any potential test-takers!) to understand where he went wrong and how to better approach problems like that in the future.

So to all you Abitur takers out there—that’s just one problem that can be transformed with the power of Maple Learn. The next time you find yourself getting stuck on a practice problem, why not try your hand at using Maple Learn to solve it? After that, you’ll be able to fly through your next practice exam—and that’ll put you one step ahead of an Oxford math professor, so it’s a win all around!

We have just released updates to Maple and MapleSim.

Maple 2023.1 includes improvements to the math engine, Plot Builder, import/export, and more.  We recommend that all Maple 2023 users install this update.

This update is available through Tools>Check for Updates in Maple, and is also available from the Maple 2023.1 download page, where you can find more details.

In particular, please note that this update includes fixes to problems with Quantifier Elimination and Group  Theory, and improves performance after a period of inactivity, all of which were reported on MaplePrimes. Thanks for the feedback!

At the same time, we have also released an update to MapleSim, which contains a variety of improvements to MapleSim and its add-ons. You can find more information on the MapleSim 2023.1 download page.

Sometimes, it’s the little things. Those little improvements that make a good tool even better. Sometimes, it’s as simple as an easy shorthand notation that allows you to create and label points on a graph with a single command. Just to pick a totally random example.

Okay, maybe it’s not totally random. Maybe this new point notation is one of our newest features in Maple Learn, and maybe it’s now easy and quick for you to create labeled points to your heart’s content. Maybe you could learn more about all the ins and outs of this new feature by checking out the how-to document.

But I can’t make any guarantees, of course.

That said, if this hypothetical scenario were true, you would also be able to see it in action in our new document on the proof of the triangle inequality.

With this document, you can explore a detailed (and interactive!) visualization of the proof using Euclidean geometry. You can adjust the triangles to see for yourself that the sum of the lengths of any two sides must be greater than the third side, read through the explanation to see the mathematical proof, and challenge yourself with the questions it leaves you to answer. And those points on those triangles? Labeled. Smoothly and easily. I wonder how they might have done it?

We hope you enjoy the new update! Let us know what other features you want to see in Maple Learn, and we’ll do our best to turn those dreams into reality.

This is a reminder that we are seeking presentation proposals for the Maple Conference.

Details on how to submit your proposal can be found on the Call for Participation page. Applications are due July 11, 2023.

We would love to hear about your work and experiences with Maple! Presentations about your work with Maple Learn are also welcome.

We’re now coming to the end of Pride Month, but that doesn’t mean it’s time to stop celebrating! In keeping with our celebration of queer mathematicians this month, we wanted to take some time to highlight the works of LGBT+ mathematicians throughout history. While it’s impossible to say how some of these individuals would have identified according to our modern labels, it’s still important to recognize that queer people have always existed, and have made and continue to make valuable contributions to the field of mathematics. It’s challenging to find records of LGBT+ people who lived in times when they would have been persecuted for being themselves, and because of that many contributions made by queer individuals have slipped through the cracks of history. So let’s take the time to highlight the works we can find, acknowledge the ones we can’t, and celebrate what the LGBT+ community has brought to the world of mathematics.

If you ask anyone to name a queer mathematician, chances are—well, chances are they won’t have an answer, because unfortunately the LGBT+ community is largely underrepresented in mathematics. But if they do have an answer, they’ll likely say Alan Turing. Turing (1912-1954) is widely considered the father of theoretical computer science, largely due to his invention of the Turing machine, which is a mathematical model that can implement any computer algorithm. So if you’re looking for an example of his work, look no further than the very device you’re using to read this! He also played a crucial role in decoding the Enigma machine in World War II, which was instrumental in the Allies’ victory. If you want to learn more about cryptography and how the field has evolved since Turing’s vital contributions, check out these Maple MathApps on Vigenère ciphers, password security, and RSA encryption. And as if that wasn’t enough, Turing also made important advances in the field of mathematical biology, and his work on morphogenesis remains a key theory in the field to this day. His mathematical model was confirmed using living vegetation just this year!

In 1952, Turing’s house was burgled, and in the course of the investigation he acknowledged having a relationship with another man. This led to both men being charged with “gross indecency”, and Turing was forced to undergo chemical castration. He was also barred from continuing his work in cryptography with the British government, and denied entry to the United States. He died in 1954, from what was at the time deemed a suicide by cyanide poisoning, although there is also evidence to suggest his death may have been accidental. Either way, it’s clear that Turing was treated unjustly. It’s an undeniable tragedy that a man whose work had such a significant impact on the modern era was treated as a criminal in his own time just because of who he loved.

Antonia J. Jones (1943-2010) was a mathematician and computer scientist. She worked at a variety of universities, including as a Professor of Evolutionary and Neural Computing at Cardiff University, and lived in a farmhouse with her partner Barbara Quinn. Along with her work with computers and number theory, she also wrote the textbook Game Theory: Mathematical Models of Conflict. If you want to learn more about that field, check out this collection of Maple Learn documents on game theory. As a child, Jones contracted polio and lost the use of both of her legs. This created a barrier to her work with computers, as early computers were inaccessible to individuals with physical disabilities. Luckily, as the technology developed and became more accessible, she was able to make more contributions to the field of computing. And that’s especially lucky for banks who like having their money be secure—she then exposed several significant security flaws at HSBC! That just goes to show you the importance of making mathematics accessible to everyone—who knows how many banks’ security flaws aren’t being exposed because the people who could find them are being stopped by barriers to accessibility?

James Stewart (1941-2014) was a gay Canadian mathematician best known for his series of calculus textbooks—yes, those calculus textbooks, the Stewart Calculus series. I’m a 7th edition alumni myself, but I have to admit the 8th edition has the cooler cover. To give you a sense of his work, here’s an example of an optimization problem that could have come straight from the pages of Stewart Calculus. Questions just like this have occupied the evenings of high school and university students for over 25 years. I suspect not all of those students really appreciate that achievement, but nonetheless his works have certainly made an impact! Stewart was also a violinist in the Hamilton Philharmonic Orchestra, and got involved in LGBT+ activism. In the early 1970s, a time where acceptance for LGBT+ people was not particularly widespread (to put it lightly), he brought gay rights activist George Hislop to speak at McMaster University. Stewart is also known for the Integral House, which he commissioned and had built in Toronto. Some may find the interior of the house a little familiar—it was used to film the home of Vulcan ambassador Sarek in Star Trek: Discovery!

Agnes E. Wells (1876-1959) was a professor of mathematics and astronomy at Indiana University. She wrote her dissertation on the relative proper motions and radial velocities of stars, which you can learn more about from this document on the speed of orbiting bodies and this document on linear and angular speed conversions. Wells was also a woman’s rights activist, and served as the chair of the National Woman’s Party. In her activism, she argued that the idea of women “belonging in the home” overlooked unmarried women who needed to earn a living—and women like her who lived with another woman as their partner, although she didn’t mention that part. There is a long-standing prejudice against women in mathematics, and it’s the work of women like Wells that has helped our gradual progress towards eliminating that prejudice. To be a queer woman on top of that only added more barriers to Wells’ career, and by overcoming them, she helped pave the way for all queer women in math.

Now, there is a fair amount of debate as to whether or not our next mathematician really was LGBT+, but there is sufficient possibility that it’s worth giving Sir Isaac Newton a mention. Newton (1642-1727) is most known for his formulation of the laws of gravity, his invention of calculus (contended as it is), his work on optics and colour, the binomial theorem, his law of temperature change… I could keep going; the list goes on and on. It’s unquestionable that he had a significant impact on the field of mathematics, and on several other fields of study to boot. While we can’t know how Newton may have identified with any of our modern labels, we do know that he never married, nor “had any commerce with women”^[a], leading some to believe he may have been asexual. He also had a close relationship with mathematician Nicolas Fatio de Duillier, which some believe may have been romantic in nature. In the end, we can never say for sure, but it’s worth acknowledging the possibility. After all, now that more and more members of the LGBT+ community are feeling safe enough to tell the world who they are, we’re getting a better sense of just how many people throughout history were forced to hide. Maybe Newton was one of them. Or maybe he wasn’t, but maybe there’s a dozen other mathematicians who were and hid it so well we’ll never find out. In the end, what matters more is that queer mathematicians can see themselves in someone like Newton, and we don’t need historical certainty for that.

So there you have it! Of course, this is by no means a comprehensive list, and it’s important to recognize who’s missing from it—for example, this list doesn’t include any people of colour, or any transgender people. Sadly, because of the historical prejudices and modern biases against these groups, they often face greater barriers to entry into the field of mathematics, and their contributions are frequently buried. It’s up to us in the math community to recognize these contributions and, by doing so, ensure that everyone feels like they can be included in the study of mathematics.