In late July, the International Congress on Mathematical Software (ICMS 2026) came to the University of Waterloo and Wilfrid Laurier University. Maplesoft had the privilege of sponsoring this year's event, and on the first evening of the conference we opened our Waterloo office for a reception, welcoming around 140 researchers, professors, students, and developers from around the world for an evening of food, demos, and good conversation. Among the many brilliant guests were the ICMS General Chair Bernard Mourrain and Local Organization Chairs Stephen M. Watt and Ilias S. Kotsireas.

About 30 of us pitched in to organize, demo, and host, turning our office into a packed social hub for the evening. Our CEO, Dr. Laurent Bernardin, opened the evening with some welcome remarks and a talk on math education in the age of AI, tying into the recent launch of the Math Success Platform - a new tool built on Maple to help educators understand where students are struggling and provide more targeted support.

I, alongside the other co-op students for this term, got the opportunity to volunteer at one of the demo booths, where we showed off the new AI Assistant and Document Import features in Maple 2026, as well as the Maple MCP Server. Two live examples in particular seemed to resonate quite well with our guests...

The first was a demonstration of the Document Import tool. We brought messy handwritten multivariable calculus notes, outlining limit definitions and squeeze theorem example problems, and scanned them directly into Maple. Within seconds, the handwriting was converted into a functional Maple worksheet, math and all, right down to preserving the hand-drawn graphs. The worksheet was ready to be edited and executed just like anything typed in natively. A skeptical guest even asked us to scan their research papers - written completely in German - just to see the import work in this case as well, and it did, intelligently creating a worksheet with collapsible sections for each individual topic. For a room full of people who spend their careers working with mathematical software, this feature got a reaction every single time.

The second was Maple's AI assistant, specifically its ability to generate and debug Maple code within the context of your workspace. We loaded a worksheet with a spherical coordinates problem - calculating the volume of the upper half of a sphere with radius 4 - and simply prompted the AI Assistant to create a 3D diagram with interactive sliders to help visualize the problem. Moments later, it had analyzed the sheet and written a working code block for generating a fully interactive 3D visualization, letting guests drag each slider and watch the diagram update in real time across the sphere. It turned an abstract triple integral into something you could physically manipulate and understand, which for a lot of students really helps make these topics click.

Working the demo booth was a rewarding experience for all of us co-op students, as researchers asked some tough, thought-provoking questions that pushed us to think on our feet and imagine new ways to use the very tools we were demonstrating.
Beyond the demos, it was also just a great chance to talk with inspiring figures in the world of mathematics - hearing what ambassadors are building with Maple day-to-day, swapping stories with both students and professors on their academic experiences, and getting a glimpse into just how wide and varied the math software community really is. It's not every day that I get to spend time chatting with the people actually shaping the field I'm studying.

Thank you to the ICMS for bringing the international math software community to our door. It made for one of the most memorable evenings of our time as Maplesoft co-op students!

Today is Pi approximation day (22/7) and I will use that as an excuse to share my new favourite expression for Pi:

And this isn't even an approximation! Recently, continuous mathematics has found its own equivalent to the digital hardware NAND gate. In his paper “All elementary functions from a single binary operator”, Andrzej Odrzywołek demonstrated that a single functional primitive can generate the entire standard continuous spectrum of operations. In other words, every single button on a scientific calculator, from addition and subtraction to sines, cosines, and logarithms, can be built using just this one function.

This Maple Worksheet explores how the 'Exp-Minus-Log' ("EML") operator, when paired solely with the constant 1, can be systematically nested to construct basic arithmetic, constants, and complex transcendental functions within Maple.

In essence, he discovered that the binary operator EML, along with the constant 1, forms a basis for the set of standard scientific-calculator operations.

This means that functions like ,  and operations like  or  can be creating by composing EML with itself in clever ways. Some constants and functions are trivial to represent, such as EML(1,1) = e or EML(x, 1) = exp(x), others however, are not...

With a quick one-command tweak, you can get Maple to use the property of the extended reals that

And then with a simple argument about standard branches, you can construct the natural logarithm for real numbers, which immediately leads the constant zero:

You can then expand the tools in your toolbox by creating subtraction with EML, ln(x), and exp(x)

Which then expands the toolbox further by allowing for the construction unary minus from the constant 0 (since -x = 0 - x), and then addition (since a+b=a-(-b))

Since we've constructed addition, subtraction, zero and one, we can technically construct every integer! It would not be very pleasant, and by no means optimal... but you could! Here's 7 for example:

The next step to building all the standard functions is multiplication and inversion. And these use the classic trick by using the fact that x=exp(ln(x)) can help simplify:

These are compositions of exp, addition, ln, and unary minus (all functions constructed previously), which means they can be made with only EML:

It's at this point that I will leave the derivation of division (a/b) and exponentiation (a^b) as exercises for the reader, so I can skip to something a little more complex...

To go beyond the basic operators, you'll need to step into the complex domain by constructing the imaginary constant i. To do this, take ln(-1) = -i*Pi (by using the standard branch) and combine it with Euler's formula

And once again the expression on the left-hand side is made up of operations that were all previously defined, so you can compose EML to get a new constant:

And finally, it's possible to break down the expression for Pi from the start, since it's the product i*ln(-1)

By successfully extracting the mathematical constants i and Pi, I think this demonstrates the complete constructive capability of the EML operator in the complex domain. While the resulting syntax trees become exponentially deep and unoptimized for human readability, they prove that continuous operations do not require a massive, distinct toolbox. Future applications of this uniform binary structure could dramatically simplify symbolic regression and machine learning optimization models. 
Ultimately, the EML operator reveals the remarkable truth that the vast complexity of scientific mathematics can be distilled down to a single, beautiful building block.

Isn't math awesome?

I am very pleased to announce the publication of my new book written together with Nic Fillion, "Perturbation Methods Using Backward Error", which uses Maple heavily throughout.

You can find it at

the SIAM bookstore

and I hope that you find it useful and interesting.

You can also find a paper in Maple Transactions, written with Michelle Hatzel, that explains how we generated the image that was chosen for the cover.  Exploring Cover Designs for an Upcoming Book  In the end, the SIAM design people chose a different one than we had thought, but they did pick one of the ones we generated!  

This was fun to do.

my second Question was deleted by a "moderator" !!!!!!!!! what is this censorship????????? (spam i was told)

Download geodesics.mw

it contained only the file geodesics.mw

Jean-Michel 

I have contacted Maplesoft support with the intend to send them corrupted Maple.ini files (that caused Maple 2026 installation to malfunction) for further analysis.

Before sending I asked whether they were interested. In the email response support replied that they were happy that my problem has been solved. I replied that they apparently did not understand my first mail. Then I got this back.

Hello,

Thank you for clarifying! I apologize for not being more clear in my response.

The issue with the preferences file (Maple.ini) was summarized in the MaplePrimes links that you provided which have been shared with our R&D team. They will be able to investigate the problem further.

Please let us know if you have any questions or concerns.

Best Regards,

XXX(Name removed, Case - 00191471 )
Technical Support Analyst

Apparently I have shared the files already. Not to my knowledge. Without my ini files no one can investigate the case.

For me this answer sounds like an automated AI generated reply. That is not what I expect as a long-time customer and EPM participant (paying full price). Premium products should come with premium support!

In this case I solved the installation problem myself with the help of this forum and wanted to support Maplesoft to make better products. Now I really feel like an idiot. Spending my free time with debugging, offering assistance, talking to a bot(?!?).

Dear upper management and owners:

If you have replaced support staff with bots that do not identify themselves as such, please reconsider what you are doing. Don't squeeze Maple for maximum profit and hide this. Think about your loyal customer base if you have a long-term growth strategy. The value of most companies lies in the people who work for them not in dumb, sloppy working bots. Humans want to deal with competent humans.
And: Do not let AI code Maple. This will lead to sloppy untrustworthy code with definitly more support requests.

I am very pleased to announce that Volume 6 Number 1 of Maple Transactions has been published.  This is a Special Issue on Matrices and Polynomials in Computer Algebra, and the Guest Editors (our first ever!) were Marc Moreno Maza and Tomas Recio.  There are still some papers that are expected to be added to the issue when they come in, but at this moment there are 8 papers there for you to read (and a description of the issue in the Front Matter section, by the Guest Editors).

A link to this Special Issue

While conducting a workshop for business calculus students one day, I was reminded of a familiar challenge. Many students approach calculus with hesitation, especially those in business programs who may not see themselves as “math people.” Even when they are following the steps, it is not always clear that real understanding is happening.

During the workshop, we were discussing inflation as an example of exponential growth. I wrote the model on the board and explained how prices increase over time. Students were taking notes, but their expressions suggested they were still trying to connect the formula to its meaning.

So I opened Maple Learn.

I entered the equation, and the graph appeared right beside it. Almost immediately, the mood in the room shifted. One student leaned forward and said, “Oh… that’s what inflation looks like over time.”

That simple moment captured why visualization matters so much in calculus.

One of the strengths of Maple Learn is how naturally it combines symbolic work and graphical representation in a single space. Students can write equations, perform calculations, and see the corresponding graphs without switching tools. This makes abstract ideas feel more concrete and easier to interpret.

Maple Learn also works well as a note-taking tool. During the workshop, students kept their formulas, graphs, and written explanations together in one organized document. Instead of passively copying, they were actively building understanding as they worked through the example.

What stood out most was how easily students began sharing their work. They compared graphs, discussed small differences in their models, and asked one another questions. The technology supported conversation and collaboration, helping create a sense of community rather than isolated problem-solving.

By the end of the workshop, students seemed more confident and engaged. The combination of visualization, structured note-taking, and peer sharing helped transform a challenging topic into something accessible and meaningful.

Experiences like this remind me that when students can see mathematics, talk about it, and learn together, calculus becomes far less intimidating and far more powerful.

As I have stated "a few times" here on Maple Primes, I've written a new book with Nic Fillion on perturbation methods.  The book will be published by SIAM early next year.  To help market the book, I sent several images to my editor who asked her team to make a desk calendar out of them.  The PDF for that is

here at this link to my web page at github

I had fun making the images, in Maple, and the QR code on the calendar links to a Maple Transactions paper that describes each of the images.  To save you struggling with your QR code reader, here is a link to that paper.

Best wishes for the season and for 2026.

The Autumn Issue is now up, at mapletransactions.org

This issue contains two Featured Contributions; a short but very interesting one by Gilbert Labelle on a topic very dear to my own heart, and a longer and also very interesting one by Wadim Zudilin.  I asked Doron Zeilberger about Wadim's paper, and he said "this is a true gem with lots of insight and making connections between different approaches."

The "Editor's Corner" paper is a little different, this time.  This paper is largely the work of my co-author, Michelle Hatzel, extracted and revised from her Masters' thesis which she defended successfully this past August.  I hope that you find it as interesting as I did.

We have three refereed contributions, a contribution on the use of Maple Learn in teaching, and a little note on my design of the 2026 Calendar for my upcoming SIAM book with Nic Fillion, as well.  All the images for the calendar were generated in Maple (as were most of the images in the book).

It's been fun to put this issue together (with an enormous amount of help from Michelle) and I hope that you enjoy reading it.

I would also like to thank the Associate Editors who handled the refereeing: Dhavide Aruliah, David Jeffrey, and Viktor Levandovskyy.

I was honored to give a talk about the MRB constant at the INTERNATIONAL 10th USBILIM APPLIED SCIENCES.

If you're unfamiliar with the MRB constant, this is a solid introduction to it.

(28) INTRODUCING THE MRB CONSTANT: CONVERGENCE, GEOMETRY, AND OPEN PROBLEMS

The need to solve quadratic equations never seems to disappear. Whether it is completing a physics problem, solving a differential equation, or performing equilibrium calculations in chemistry, quadratic equations are an integral part of all STEM-based disciplines.

Depending on the complexity of the quadratic equation, the typical 'guess-and-check' method taught in most high school classes can often be frustrating and time-consuming. Professor of mathematics Dr. Po-Shen Loh, in his new method shown here, recognizes some important properties of solutions to quadratic equations and integrates them into a more intuitive approach that students are much more likely to feel motivated by.

For example, consider the equation x^2 - 14x + 45 = 0. Most students are taught to first factor this equation by thinking of two numbers that multiply to 45 and add to -14. After trying multiple values, we would discover that those values are -5 and -9. We would use these values to factor the equation into the form (x-5)*(x-9) = 0. Setting each factor equal to zero, we would get x = 5 or x = 9. Equivalently, to solve for x more directly, we need two numbers that multiply to 45 and add to 14 (again, x = 5 and x = 9).

The only way to speed up this process of guess-and-check is to do enough similar problems until the guesses become second nature. Not to mention, this becomes exponentially more difficult as the coefficient on x^2 increases (for example, solving the equation 6x^2 + 7x - 20 = 0).

For the example above, Dr. Loh's method builds on a simple starting point:

(i) We know that the numbers (call them R and S) add to 14

(ii) We know that since the numbers add to 14, they must have a mean value of 14/2 = 7

(iii) If the two numbers have an average of 7, they must be an equal 'distance' (call this distance z) from 7

(iv) We can write the two numbers as R = 7+z and S = 7-z

(v) Since the numbers R and S multiply to 45, then (7+z)*(7-z) = 45 ⇒ 49 - z^2 = 45. In other words, z^2 = 4, so z = +2 or z = -2

(vi) The solution to the equation is then R = 7+2 = 9 and S = 7-2 = 5 (as we predicted)

We can generalize this idea for any complex coefficients a, b and c in the equation ax^2 + bx + c = 0 to actually prove the quadratic formula. However, using Dr. Loh's method on specific examples (as above) helps build intuition for why the quadratic formula works in the first place. Other proof methods such as completing the square are just as mathematically sound, but they do not utilize the mathematical instinct that makes solving a problem in mathematics so gratifying.

Although I am currently a student working for Maplesoft, I had not used Maple Learn extensively beforehand. Dr. Loh's idea of creating a more intuitive way to solve such a conventional problem inspired me to create a document in Maple Learn, linked here, outlining the steps above.

Learning new ways to solve a problem in mathematics is exciting, but it is often difficult to present in a way that is clear, visually-appealing and easy to create. Most online mathematical environments are difficult to navigate and typically lack visualizations to accompany an idea. With Maple Learn, it felt comforting to open a clean canvas where I was able to easily build a document in just a few hours that not only summarized the main ideas of this new method, but also showed the user why the method works using live animations and colour schemes (see some examples below).

I surprised myself (as well as my managers) by how quickly I was able to transfer all of my ideas into the document. I could also split related content into groups and use collapsible sections to keep the document uncluttered and easy to read.

I also took advantage of the freedom to explore other documents and directly reference them through hyperlinks.

Sometimes it can be difficult to follow a new concept without having some background information. Adding these references makes it simple for the reader to access supporting documents and ensure there are no knowledge gaps to be filled along the way. Once you make a document, you also have the option to publish it to your own gallery and make it public for others to use and learn from.

Maple Learn has been incredibly helpful for sharing the things that interest me the most. If you have something related to mathematics that excites you, try not to keep it to yourself. Consider using Maple Learn to share your ideas with the world and see your vision come to life!

The Summer Issue of Maple Transactions has been published.  There are articles from a range of interests: research, education, and personal stories.

Have a look, and I hope you find something of value in the issue.

Back in 2017, when the concept of Maple Flow was first proposed at Maplesoft, we developed an aspirational brochure to ignite our creative energy. I still have a printed few copies – here’s one that’s sat behind my monitor.

At that time, the product that did not yet exist was called “Maple Whiteboard” and the brochure described what we had gradually come to appreciate that engineers wanted from a calculation tool:

• simplicity at its beating heart – just learn a few basic game mechanics, and then everything else “flows” (ahem). 
• units support from the get-go
• documentation features to describe the analysis
• connectivity with other software
• engineering-focused math functions

The first working version of Maple Whiteboard was crude…but the basic building blocks were in place and the concept worked. This image dates from 2019.

We unveiled Maple Flow to the public in 2021 (coming up with the name was a trial in of itself). Here’s what it looked like.

The target audience loved the new product—they liked what it could do now and were excited about its future potential. Our initial assumptions had been validated!

Maple Flow has evolved dramatically since the fever dream of the initial brochure and early prototypes. Even though it's much more powerful now, we've made sure it’s still simple to use.

Today, I’m delighted to announce the launch of Maple Flow 2025. This release is a major turning point for the product. You'll see a clean, new interface, faster performance, and more tools for documentation and moving your work from other programs.

Let me touch on my personal highlights.

A new interface headlines the release! It’s clean and simple, with logically ordered buttons in organized groups.

The ribbon is contextual; for example, click on an image, and you’ll see tools for adding shapes and text.

There's always room for improvement and refinement. Let me know what you think!.

You can now insert a table of contents into your document. The page numbers automatically update, and headings are hyperlinked – just click and you jump to that part of the worksheet.

Hyperlinks in the table of contents are preserved when you export the worksheet to PDF – that’s an awesome navigation feature when you distribute your work.

This feature gives me a visual dopamine hit every time I use it. Look how easy it is to use!

We've decided to release a tool we’ve been using internally for some time. The Maple Flow Migration Assistant is a free addon that helps you convert your Mathcad 13, 14 and 15 worksheets to Maple Flow. 

You can convert single Mathcad worksheets or point to a folder for bulk conversion. You also get many function translations.

Automatically converting executable code between two different high-level math tools is difficult; some manual reworking is probably needed for anything that’s not simple arithmetic (we documented what the Migration Assistant does here). But if you’ve already decided to make the switch from Mathcad 13, 14 or 15, then the Migration Assistant is a great time saver.

Large worksheets now evaluate faster! These are benchmarks from our internal testing suite.

You can now run Maple Flow worksheets through Excel via a simple function call. You can change parameters and get updated results.

To help you set up that function call, an interface walks you through the process.

You can use this feature to develop a simple spreadsheet reporting dashboard or perform parameter sweeps on your Flow analyses.

Large analysis projects can be difficult to manage. 

• The results of one worksheet might need to be used in another,
• there may be equations that are reused everywhere, 
• or you might need to split your project into small chunks that different people can work on separately

Well, now we’ve made that whole process easier! You can now treat Flow worksheets as “black box” functions that you can call from other Flow worksheets. You can even change parameter values, and return updated results

The AI Formula Assistant made its debut in Maple 2025 and it sparked a lot of interest (and some interesting conversations about the future of AI in math software). 

By popular demand, we've brought this feature into Flow. You can now look up an engineering formula with a simple natural language query,

That's enough of my personal highlights. If you want to know more, visit the What's New pages for a complete rundown and grab a trial.

If you haven’t tried Maple Flow yet, now is the right time to jump in. We have several time-limited launch offers to make the transition to Flow as frictionless as possible; these include offers for users who are

• deploying a small suite of licenses
• switching from other tools
• in large organizations that need a full implementation plan.

As ever, we can only keep Maple Flow on track if you let me know what you want - send all your feedback my way.

claude.ai can write and explain many facits in the feild of prime number theory. Look what was created.

https://claude.ai/public/artifacts/b5b0697c-01a2-4e42-843b-7ddecc63c568

The link below goes to the Proceedings of the Maple 2024 Conference, which includes several articles that will be of interest to the readers of Maple Primes.

There may be one more paper coming in to the proceedings later as per policy; since most things are ready, away we go!

Proceedings of the Maple 2024 Conferenc