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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!

This post is written by a mathematics teacher who usually views Maple’s new initiatives from an educational perspective, and I’m well aware that others may see things differently. A single user might be delighted by a new feature that fits their personal workflow. An advanced user might not care if something requires a workaround.

There are also many preferences when it comes to how the interface should look. I often consider whether something will work well for our high school as a whole. We have students who are not very mathematically or scientifically inclined, and others who are. That’s why user-friendliness is essential. Some packages have been developed to make things easier for students. We try to avoid too many workarounds, since these often create problems for them.

Now, on to Maple 2025’s new interface:

When Microsoft introduced tabs and ribbons instead of menus and toolbars in Word many years ago, I personally thought it was a good idea. I can imagine it working well in Maple too — especially if the different elements are placed logically on the tabs, and frequently used functions are easy to access.

However, I just returned from summer vacation, ready for a new school year, only to discover something surprising: the Windows version comes with the new ribbon interface, while the Mac version still has the old one! For any teacher, this is a nightmare scenario: teaching a class where the Windows and Mac interfaces look completely different. Has Maplesoft ended up caught between two chairs here?

I’ve heard that a Mac version with tabs and ribbons is under development. But since it’s not ready yet, we can’t use it. On Windows, I also noticed a strange extra application called “Maple 2025 Screen Readers”. If you open it directly, you get an odd mix of modern 2D notation and old 1D Maple notation, which is simply unacceptable. If you instead click “Screen Reader Mode” in the top-right corner, it looks more normal. But does that mean it’s fully functional? If so, we might be able to combine this with the Mac version that still uses the old interface — and then switch next year to both Windows and Mac with tabs and ribbons. Still, I must say that Maplesoft is providing far too little information on this! Around 75% of our students use Macs, while only 25% use Windows.

Another issue: When saving a Maple file on a Windows computer, you’re forced into Maple’s own “Save As” window. I’ve previously suggested that it should instead open directly in Windows’ native File Explorer, which is far more powerful. In File Explorer, you can quickly use Quick Access shortcuts to save the file in the right folder. In Maple’s “Save As” window, however, it often takes 6–7 extra clicks to reach the desired location. For students who aren’t very tech-savvy, navigating through a deep folder tree can be a real challenge. Why doesn’t Maplesoft just use Windows’ own File Explorer, which students are already familiar with? Most other programs do. Perhaps someone can explain why Maplesoft insists on keeping their own limited “Save As” dialog.

Finally: I do believe that tabs and ribbons can be a good solution, but there’s still work to be done in placing items on appropriate tabs. For example, although I personally use the F5 keyboard shortcut to switch between Text, Non-executable Math, and Math mode, I know many students prefer to click on these options in Maple 2024. In the new interface, it now takes two or three clicks to do so. Since this is a function used very frequently, that’s a drawback. Couldn’t users be allowed to customize the Quick Access toolbar — via the Options menu — so these items can be placed there if needed?

With the launch of ChatGPT 5.0, many people are testing it out and circulating their results. In our “random” Slack channel, where we share anything interesting that crosses our path, Filipe from IT posted one that stood out. He’d come across a simple math problem, double-checked it himself, and confirmed it was real:

As you can see, the AI-generated solution walked through clean, logical-looking steps and somehow concluded:

x = –0.21

I have two engineering degrees, and if I hadn’t known there was an error, I might not have spotted it. If I’d been tired, distracted, or rushing, I would have almost certainly missed it because I would have assumed AI could handle something this simple.

Most of us in the MaplePrimes community already understand that AI needs to be used with care. But our students may not always remember, especially at the start of the school year if they’ve already grown used to relying on AI without question. 

And if we’re honest, trusting without double-checking isn’t new. Before AI, plenty of us took shortcuts: splitting up the work, swapping answers, and just assuming they were right. I remember doing it myself in university, sometimes without even thinking twice. The tools might be different now, but that habit of skipping the “are we sure?” step has been around for a long time.

The difference now is that general-purpose AI tools such as ChatGPT have become the first place we turn for almost anything we do. They respond confidently and are often correct, which can lead us to become complacent. We trust them without question. If students develop the habit of doing this, especially while they are still learning, the stakes can be much higher as they carry those habits into work, research, and other areas of their lives.

The example above is making its rounds on social media because it’s memorable. It’s a basic problem, yet the AI still got it wrong and in a way that’s easy to miss if you’re not paying attention.

Using it in the classroom can be a great way to help students remember that AI’s answers need to be checked. It’s not about discouraging them from using AI, but about reinforcing the habit of verifying results and thinking critically about what they see.

So here’s my suggestion:

• Show this example in your class, no matter the subject. If your students are using AI, they’ll benefit from seeing it.
• Spend 10 minutes discussing it.
• Use it as a jumping-off point to talk about what’s OK and not OK when using AI for your course.
• Share other examples like this throughout the year as small reminders, so “critical thinking” becomes second nature.

This isn’t just about catching an AI’s bad subtraction. It’s about building a culture of verification and reasoning in our students. The tools will keep improving, but so will the temptation to turn off our own thinking.

If we can help students get into the habit of checking, AI can be a powerful partner without putting them on autopilot.

To the MaplePrimes community: How do you talk to your students to help them build strong habits when working with AI? Do you bring in examples like this one, or use other strategies? I’d love it if you could share your thoughts, tips, and ideas.

I was wondering whether MapleSoft has opted for an outdated concept. Here is Gemini's answer:

A "better" GUI for Word is subjective, as different users have different needs. The current ribbon interface is great for discovering features, but it can also feel cluttered.

With the former GUI (having a larger quick acess bar) and a tool bar (in red)

only one click was required with substantially less mouse movement.

Personally I would switch to the new GUI with the following improvements

• a quick access bar that is customizable
• a smart ribbon that switches to the edit mode tab when the cursor is placed on editable text or a new text/input/document block is inserted

Having the functions that I use most frequently available in the quick access tool bar (highlighted in yellow) would allow me to minimize the ribbon with the same productivity and even more screen space as before.

Keyboard shortcuts that differ from standard OS shortcuts are not a viable alternative for me.

Overall, the direction with the new ribbon seems to be right to get new users productive faster. It seems to be a good choice without clear alternatives, and its graphical design aligns much better with the core values Maple provides.

However, becoming productive fast does not mean that the productivity is high. From this perspective the former GUI is not outdated yet. The workflow with it is much faster and more focussed on math and code.

Perhaps MapleSoft has solutions that will make the new GUI even more productive than the former GUI. This would be great!

In Maple 2025, there are many strange issues, such as plot errors in math apps under Computer Science > Boolean Algebra, which did not occur in Maple 2024. Furthermore, in the 2025 version, when you open load package, some packages are blocked, and you must hide the taskbar to see the blocked packages. Finally, the Ribbon interface in Maple 2025 is really not suitable. Restart and startup code should not be placed in Home; some interfaces should be removed, or an option to retain the 2024 interface should be provided. I sincerely hope my suggestions are taken into consideration. Thank you.

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.

We are pleased to announce that the registration for the Maple Conference 2025 is now open!

Like the last few years, this year’s conference will be a free virtual event. Please visit the conference page for more information on how to register.

This year we are offering a number of new sessions, including more product training options, and an Audience Choice session.
Also included in this year's registration is access to an in-depth Maple workshop day presented by Maplesoft's R&D members following the conference.  You can find an overview of the program on the Sessions page. Those who register before September 14th, 2025 will have a chance to vote for the topics they want to learn more about during the Audience Choice session.

We hope to see you there!

Hi,

look at this Maple code.

short_list_prime_factorization_fun.mw

short_list_prime_factorization_fun.pdf

Have a good day

Matthew

Hi,

check out this maple code

positive_odd_integer_factorization_data.pdf

positive_odd_integer_factorization_data.mw

that is all

Regards,

Matthew

Hi,

have some Maple code to share.

prime_triplet_0_4_6.mw

prime_triplet_0_4_6.pdf

Enjoy

Matthew

ps Prime numbers are fun

see https://t5k.org/

We are a week away from the submission deadline for the Maple Conference!  
Presentation proposal applications are due July 25, 2025.

We are inviting submissions of presentation proposals on a range of topics related to Maple, including Maple in education, algorithms and software, and applications. We also encourage submission of proposals related to Maple Learn. You can find more information about the themes of the conference and how to submit a presentation proposal at the Call for Participation page.

We hope to see there.

Hi,

Don't laugh.

Some of you are not familair with Wagstaff Prime Numbers

see Wolfram Math World

also, this Maple code is esentially, a loop and the isprime() function

for your edification

b

have a look

just wanted to contribute my two cents to the Maple community

good day

Thank you for your patience and understanding during the recent outage of MaplePrimes. The outage was caused by a server issue. We have obtained and configured a replacement to prevent disruptions moving forward. We are sorry for any inconvenience this may have caused.

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.

We are excited to announce that the Maple Conference will be held Novemeber 5-7, 2025!

Please join us at this free virtual event as it will be an excellent opportunity to meet other members of the Maple community, get the latest news about our products, and hear from the experts about the challenges and opportunities that our technology brings to teaching, learning, and research. More importantly, it's a chance for you to share the work you've been doing with Maple and Maple Learn. 

The Call for Participation is now open. We are inviting submissions of presentation proposals on a range of topics related to Maple, including Maple in education, algorithms and software, and applications. We also encourage submission of proposals related to Maple Learn. 

You can find more information about the themes of the conference and how to submit a presentation proposal at the Call for Participation page. Applications are due July 25, 2025.

After the conference, all accepted presenters and invited speakers will be invited to submit related content to the Maple Transactions journal for consideration.

Registration for attending the conference will open in July.  Watch for further announcements in the coming weeks.

We hope all of you in the Maple Primes community will join us for this event!

Kaska Kowalska
Contributed Program Co-Chair