Last week, DeepMind announced their new AlphaEvolve software along with a number of new results improving optimization problems in a number of areas. One of those results is a new, smaller, tensor decomposition for multiplying two 4 × 4 matrices in 48 scalar multiplications, improving on the previous best decomposition which needed 49 multiplications (Strassen 1969). While the DeepMind paper was mostly careful about stating this, when writing the introduction, the authors mistakenly/confusingly wrote:

For 56 years, designing an algorithm with rank less than 49 over any field with characteristic 0 was an open problem. AlphaEvolve is the first method to find a rank-48 algorithm to multiply two 4 × 4 complex-valued matrices

This gives the impression that this new result is the way to multiply 4 × 4 matrices over a field with the fewest number of field multiplications. However, it's not even the case that Strassen's 1969 paper gave a faster way to multiply 4 × 4 matrices. In fact, Winograd's 1968 paper on computing inner products faster could be applied to 4 × 4 matrix multiplication to get a formula using only 48 multiplications. Winograd uses a trick 

which changes two multiplications of ab's into one multiplication of ab's and two multiplications involving only a's or only b's. The latter multiplications can be pre-computed and saved when calculating all the innerproducts in a matrix multiplication

    # i=1..4, 4*2 = 8 multiplications
    p[i] := -A[i, 1]*A[i, 2] - A[i, 3]*A[i, 4];
    # 4*2 = 8 multiplications
    q[i] := -B[1, i]*B[2, i] - B[3, i]*B[4, i];

    # i=1..4, j=1..4, 4*4*2 = 32 multiplications
    C[i,j] = p[i] + q[j] 
            + (A[i,1]+B[2,j])*(A[i,2]+B[1,j])
            + (A[i,3]+B[4,j])*(A[i,4]+B[3,j])

It is simple to verify that C[i,j] = A[i,..] . B[..,j] and that the above formula calculates all of the entries of C=A.B with 8+8+32=48 multiplications.

So, if Winograd achieved a formula of 48 multiplications in 1968, why is the DeepMind result still interesting? Well, the relative shortcoming of Winograd's method is that it only works if the entries of A and B commute, while tensor decomposition formulas for matrix multiplication work even over noncommutative rings. That seems very esoteric, but everyone's favorite noncommutative ring is the ring of n × n matrices. So if a formula applies to a matrix of matrices, that means it gives a recursive formula for matrix multiplication - an tensor decomposition formulas do just that.

The original 1969 Strassen result gave a tensor decomposition of 2 × 2 matrix multiplication using only 7 scalar multiplications (rather than the 8 required by the inner product method) and leads to a recursive matrix multiplication algorithm using O(N^log[2](7)) scalar multiplications. Since then, it has been proved that 7 is the smallest rank tensor decompostion for the 2 × 2 case and so researchers have been interested in the 3x3 and larger cases. Alexandre Sedoglavic at the University of Lille catalogs the best tensor decompositions at https://fmm.univ-lille.fr/ with links to a Maple file with an evaluation formula for each.

The previous best 4 × 4 tensor decomposition was based on using the 2 × 2 Strassen decomposition recursively (2 × 2 matrix of 2 × 2 matrices) which led to 7 2 × 2 matrix multiplications each requiring 7 scalar multiplications, for a total of 49. The new DeepMind result reduces that to 48 scalar multiplications, which leads to a recursive algorithm using O(N^log[4](48)) scalar multiplications: O(N^2.7925) vs. O(N^2.8074) for Strassen. This is a theoretical improvment over Strassen but in 2024 the best known multiplication algorithm has much lower complexity: O(N^2.3713) (see https://arxiv.org/abs/2404.16349). Now, there might be some chance that the DeepMind result could be used in practical implementations, but its reduction in the number of multiplications comes at the cost of many more additions. Before doing any optimizations I counted 1264 additions in the DeepMind tensor, compared to 318 in the unoptimized 4×4 Strassen tensor (which can be optimized to 12*7+4*12=132). Finally, the DeepMind tensor decomposition involves 1/2 and sqrt(-1), so it cannot be used for fields of characteristic 2, or fields without sqrt(-1). Of course, the restriction on characteristic 2 is not a big deal, since the DeepMind team found a 4 × 4 tensor decomposition of rank 47 over GF2 in 2023 (see https://github.com/google-deepmind/alphatensor).

Now if one is only interested in 4 × 4 matrices over a commutative ring, the Winograd result isn't even the best possible. In 1970, Waksman https://ieeexplore.ieee.org/document/1671519 demonstrated an improvement of Winograd's method that used only 46 multiplications as long as the ring allowed division by 2. Waksman's method has since been improved by Rosowski to remove the divisions see https://arxiv.org/abs/1904.07683. Here's that nice compact straight-line program that computes C = A · B in 46 multiplications.

And, here attached are five Maple worksheets that create the explicit formulas for the 4 × 4 matrix methods mentioned in this post, and verify their operation count, and that they are correct.

Strassen_444.mw  Winograd.mw  DM_444.mw Waksman.mw Rosowski.mw

If you are interested in some of the 2022 results, I posted some code to my GitHub account for creating formulas from tensor decompositions, and verifying them on symbolic matrix multiplications: https://github.com/johnpmay/MapleSnippets/tree/main/FastMatrixMultiplication

The clear followup question to all of this is:  does Maple use any of these fast multiplication schemes?  And the answer to that is mostly hidden in low level BLAS code, but generally the answer is: No, the straightforward inner-product scheme for multiplying matrices optimized memory access thus usually ends up being the fastest choice in most cases.

Maplesoft’s CEO, Dr. Laurent Bernardin, has written an opinion piece on Fostering Student Retention through Success in Mathematics. In it, he discusses ways to reduce university dropout rates by turning the technology shortcuts students are already using in their math courses into data-driven insights and interventions that promote student success.

You can read the whole article here:  Fostering Student Retention through Success in Mathematics

You will not be shocked to learn that Maplesoft plays a role in the strategy he proposes. 😊 (But this is a serious problem for a lot of schools, and we really would like to help!)

As a university-level math student, I am constantly working through practice problems. An issue I constantly face is that when I get a problem wrong, it can be challenging to find out which line I did wrong. Even if I use Maple Calculator or Maple Learn to get the full steps for a solution, it can be tedious to compare my answer to the steps to see where I went wrong.

This is why Check My Work is one of the most popular features in Maple Learn. Check My Work will check all the lines in your solution and give you feedback showing you exactly where you went wrong. I honestly didn’t know that something like this existed until I started here at Maplesoft, and it is now easy to see why this has been one of our most successful features in Maple Learn.

Students have been loving it, but the only real complaint is that it’s only available in Maple Learn. So, if you were working on paper, you'd either have to retype your work into Maple Learn or take a picture of your steps using Maple Calculator and then access it in Maple Learn. Something I immediately thought was, if I’m already on my phone to take a picture, I’d much rather be able to stay on my phone.

And now you can! Check My Work is now fully available within Maple Calculator!

To use Check My Work, all you need to do is take a picture of your solution to a math problem.

Check My Work will recognize poor handwriting, so there is no need to worry about getting it perfect. After taking the picture, select the Check My Work dropdown in the results screen to see if your solution is correct or where you made a mistake.

Check My Work will go through your solution line-by-line giving you valuable feedback along the way! Additionally, if you make a mistake, Maple Calculator will point out the line with the error and then proceed with checking the remainder of the solution given this context.  

For students, Check My Work is the perfect tool to help you understand and master concepts from class. As a student myself, I’ll for sure be using this feature in my future courses to double-check my work.

What makes Check My Work great for learning a technique is that it doesn’t tell you what mistake you made, but rather where the mistake has been made. This is helpful since as a student you don’t have to worry about the time-consuming task of finding the step with an error, but rather you can focus on the learning aspect of actually figuring out what you did wrong.

Once you have made corrections to your work on paper, take a new picture and repeat the process. You can also make changes to your solution in-app by clicking the “Check my work in editor” button in the bottom right, which runs Check My Work in the editor where you can modify your solution.

No other math tool has a Check My Work feature, and we are very proud to bring this very useful tool to students. By bringing it fully into Maple Calculator, we continue working towards our goal of helping students learn and understand math.

View the GIF below for a brief demonstration of how to use Check My Work!

We hope you enjoy Check My Work in Maple Calculator and let us know what you think!

Maplesoft now has a new approach to providing customer support for Maple users! The Maple Customer Support Updates allows Maplesoft to provide important updates to our customers as fast as possible. These updates contain a series of improvements and fixes to any area of the Maple library, enabling a rapid response for customer reports and requests. When a Maple user reports a bug or weakness, or requests some missing functionality that can be addressed with an update to the Maple library, such an update can now be provided immediately after the fix or improvement is developed. Furthermore, the update will not just be available to that customer who reported it, but also to any other Maple users who wishes to use them. Of course, not all reports will be able to be addressed quickly, and for those that are, it will be up to the developer's discretion whether to make the fix or improvement available via these new Maple Customer Support Updates. Please note that these Updates may contain experimental elements that could change in subsequent official releases.

The updates are available as a workbook containing a Maple library file that can be downloaded and installed from the Maple Cloud. To install the Maple Customer Support Updates from the Maple Cloud,

• Click the MapleCloud icon in the upper-right corner of the Maple GUI window and select Packages.
• Find the Maple Customer Support Updates package and click the Install button, the last one under Actions.
• To check for new versions of Maple Customer Support Updates, click the MapleCloud icon and select Updates. If the cloud icon in the Actions column of Maple Customer Support Updates has the word Update beside it, then you can click on it to download a new update.

To make the process of installing and maintaining the Maple Customer Support Updates as smooth as possible, we've also introduced a new Maple library package, SupportTools, with 3 commands, Update, Version, and RemoveUpdates.

Download SupportTools.mw

In Maple 2025.0, the SupportTools package is not installed by default. For the first installation, you can also run the command
PackageTools:-Install(4797495082876928); instead of installing it from the Maple Cloud.

The Maple Customer Support Updates were inspired by and modelled after the existing Physics Updates which many Maple users may be famiilar with already. Going forward, Physics Updates will only contain changes to the Physics package itself. All other library updates will be available via the Maple Customer Support Updates. For compatibility with the pre-existing Physics:-Version command, calling SupportTools:-Version(n) is equivalent to calling SupportTools:-Update(n), and similarly SupportTools:-Version(latest) and SupportTools:-Update(latest) are both equivalent to the single call SupportTools:-Update().

I’m absolutely delighted to announce the launch of Maple 2025!

Although you see a new release every year, new features take anything from a few fast-paced weeks to develop, to months of careful cultivation.

Working on so many features in parallel, each with varying time scales, isn't easy! We have to fastidiously manage and track our work.

So it's easy to lose ourselves in the daily minutiae of software development. To help us maintain perspective, we constantly ask ourselves questions like:

• What user problem are we solving and how often does this problem occur?
• Can we validate our proposed solution with preliminary user feedback?
• Is this a solution to a problem that doesn't exist and will never exist, or are we pre-empting a future need?
• Are we offering value to our users?

Given the answers, we course-correct to make sure we stay on track for our central mission - to make you happy, and to keep you coming back year-after-year.

With Maple 2025, I think we've smashed that goal. We have many new features that'll appeal to many different types of users - from students, educators and mathematicians, to engineers, scientists and technical professionals

Let me walk you through some of my personal highlights.

It’ll be difficult for anyone to miss this - Maple 2025 has a new interface! It’s a ribbon-based UI that look clean and contemporary, and helps you find and discover tools more quickly than before.

You have large, meaningful icons.

Items are logically grouped.

The ribbons is contextual. If you click on a plot, you get new tabs for interacting with and drawing on the plot.

A new Education tab collects pedagogical resources that were scattered around the interface in prior releases.

This is the biggest visual overhaul to Maple in many years. We hope you like it! 

We also appreciate that changes in look and feel can be divisive. Please rest assured that we will refine and finesse the interface with each successive release; your comments and suggestions are most welcome.

The new interface is available on Windows and Linux, and as a technology preview on Mac.

The right arrow key on my keyboard is wearing out…and it’s all because of Maple. I’m knee deep in Maple nearly every day entering equations, and I’m always using right-arrow to move the cursor. It gets kind of tedious!

This anecdote reflects some investigative work we did. We comprehensively examined our internal library of thousands of Maple worksheets and discovered that these three input patterns are extremely common.

Previously, you’d use the right-arrow key to move the cursor out of the exponential, division or subscript.

Now, in Maple 2025, when you

• type ^, /, or enter a literal subscript with a double-underscore,
• followed by a number or symbol
• and then input another operator (such as +)

the operator is automatically inserted on the baseline (except when y = 1).

Of course, you can also make the cursor return to or stay in the exponent or denominator with a simple keystroke, when that is what is needed.

This is one of those little quality of life refinements that I’m very fond of - it’s a little visual and usability dopamine hit.

The sum command (and its typeset form) now indexes into vectors without you needing to spam unevaluation quotes all over your expression.

We’ve been integrating units deeper into the Maple system, release after release. Much of this is driven by our engineering users.

A few releases ago, we made int(numeric) compatible with units. With Maple 2025, you can now numerically differentiate  expressions and procedures that have units.

I’m a grizzled thermodynamics hack, so here’s an example in which I calculate the specific heat capacity of water by differentiating enthalpy with respect to temperature (and then confirm the result with the built-in value):

This is in addition to many other improvements to the units experience.

Although this is a part of Maple that I don’t touch often (my colleague Karishma takes point on the education side), I REALLY wish I’d had this when I was struggling with math.

You can now automatically generate unlimited variants of the same problem for students to solve with the Try Another feature, which has been added to Maple’s Check My Work tools (another feature I really could have used!). This is available for many common math principles, including factorization, simplification, integration and more.

This is just one of the improvements in Maple 2025 for teaching and learning.

 If you’ve ever found yourself going back and forth (and back and forth) between two large, almost identical-looking Maple expressions, trying to figure out how they are different, you’re going to love this one.  ExpressionTools is a new package that lets you compare the differences between two expressions.

I really like the use of color to highlight differences. Less squinting at the screen!

You can now run Maple Flow worksheets from Maple (you don’t need Maple Flow installed to do this). You can send parameters into the Flow worksheet and extract your desired results.

This means you can use the entire flexibility of Maple to analysis and manipulate your Flow worksheet. You could, for example:

• Attach a Flow worksheet to a Maple workbook and create an interactive application
• Carry out parameter studies of a Flow worksheet by evaluating it over many parameter sets in Maple
• Create an Excel interface for a Flow worksheet using the Maple add-in for Excel

Simplify is one of those functions that literally tens of thousands of people use each day. Every time we make an incremental improvement, the cumulative benefits across our entire user base are significant.

We’ve refined simplify in a number of critical ways. For example, simplify now recognizes when exponentials can be profitably converted to hyperbolic trig functions:

The analysis of many scientific phenomena result in Laplace transforms that do not have a symbolic inverse which can be expressed in terms of elementary functions. This includes applications in heat transfer, fluid mechanics, fractional diffusion processes, control systems and electrical transmission.

For example, this monster Laplace transform results from an analysis of voltage on a transmission line:

You can now numerically invert this transform courtesy of an enhancement to inttrans:-invlaplace - a fast quadrature method.

I’ve saved what I think has the most future potential for last.

I’m sure nearly all of you have experimented with the various AI tools. They’re an inevitable part of our present and future, whether we're comfortable with it or not.

This is something we've been mulling over for some time.

• In Maple 2019, the DeepLearning package made its debut. This package provides tools for machine learning, supporting operations such as classification and regression using neural networks.
• In Maple 2024, we introduced an AI-powered formula lookup feature.

In Maple 2025, we’re giving you an early-stage technology preview of AI-powered document generation.

You can automatically generate worksheet content by prompting an AI, and then gradually refine the content

If you’re an educator, you might want some content that describes applications of calculus. So you might ask the AI “How do I derive the formula for the area of a circle” by entering your prompt into this text box:

This is the worksheet content that may be returned:

If you’re structural engineer who wants to know how to calculate the hardness of concrete, you might ask the AI: “How do I calculate the compressive strength of slow hardening concrete as a function of time? Use the CEB-FIP Model Code 90. Include a worked example with Maple code”.

This worksheet content that could be generated (note the live Maple code):

We’re labelling AI-generated worksheet content as a technology preview. You might see

• text that might be misleading (but sounds plausible)
• code that doesn’t work (but looks plausible)
• or different results each time you click “Generate Document”

For the moment, I would not rely on AI-generated worksheet content without realistic expectations, a healthy dose of scepticism and a modicum of detached analysis. But AI models are rapidly growing in robustness, and we want to position ourselves to best exploit their future potential. The next few years will be VERY exciting.

We can never cover everything in a short blog post like this. So if you want to know more, head on over to the What’s New pages for Maple 2025!

As some of you may have noticed, MaplePrimes was down for a few days, and some customers may have encountered a few problems with our web site, as well.

As you can see, MaplePrimes is up and running again. We are still experiencing a few lingering issues on our main web site, but we expect these will be resolved shortly.

Apologies to those who were inconvenienced by the outage. We appreciate your patience.

I'm happy to announce the publication of Volume 5, Issue #1 of Maple Transactions.  You can find it at

mapletransactions.org
 

We have a survey paper by Veselin Jungic and Naomi Borwein on teaching Experimental Mathematics courses as our Featured Contribution.  Many of you will find it interesting and useful.

In the refereed paper section we have a paper on Metaprogramming with Maple and C by Ilias Kotsireas; a paper on fast transposed Vandermonde solving by Hyukho Kwon & Michael Monagan; a paper by David Ulgenes (an honours student in Oslo) on Gamma, Pseudogamma, and Inverse Gamma functions; and a paper by John Campbell on applications of Gosper's nonlocal derangement identity (which, if you don't know that the word "derangement" has a technical mathematical meaning, may give you the wrong impression!).

As usual I've also written something, and I hope you like it: it's about Chladni figures and standing modes in an elliptical drum, and visualizing such in Maple.  It uses Mathieu functions in Maple and noodles a bit about zerofinding (but winds up using fsolve because that's so convenient).
 

Keep the papers coming.  This is the 12th issue of Maple Transactions, and I remind you that it has a "Diamond Class" designation, which means there are no page charges to authors, and the articles are free to read for everyone.  This means that there's some volunteer labour needed, of course: you have to write the articles, and what we want is that you write articles that people in the Maple community actually want to read.

I'd also like to thank the copyeditor, Michelle Hatzel, for her very hard work on this issue.  She's really made a difference, and I think you will be able to see it.   

Download blogpost-algebra.mw

With Maple Flow, we’re regularly rolling out exciting updates. Each offers new features, as well as resolving many user-reported issues.

Flow 2024.2 lives up to that track record. Two major new features - drop-down menus and phasors - make their debut. We've also made many other quality-of-life enhancements.

Drop-down list boxes make your worksheets more tactile and interactive. The menu items can be defined in a matrix or vector, or in a table. You can return the index of the selected item, or return an entire row or column of a matrix.

An important use case is populating the contents of a drop-down menu with data from an external file. In movie below, we

• import a database of steel shapes and their associated properties
• populate the drop-down menu with the steel shapes in the first column of the imported data
• based upon the selected shape, use ArrayTools:-Lookup to return a property
• and finally perform a design analysis.

If you look carefully, you'll see that you can hide commands on a per-container basis to make your worksheets cleaner.

We have a large number of power system engineers who want to model electrical systems in phasor notation.

Entering a phasor is easy - just enter the magnitude, the angle character and then the angle. Phasors evaluate to rectangular complex numbers but can be recast to phasor format with the Context Panel.

You can also associate a unit with the magnitude and angle. On output, you can change units inline or via the Context Panel.

You can also prevent floating point approximation of phasors using the symbolic toggle on each container.

We've also made a raft of other improvements. Extracting slices of matrices is faster, and you can now enter units in 2d notation in the Context Panel (particularly useful when you want to change the units of everything inside a matrix).

As ever, the new features are driven by you. The only way you can point us the right direction is by telling us what you want. Don't be shy!

We’re thrilled to announce the launch of our new Student Success Platform! Over the past several months, our academic team has dedicated itself to understanding how we can better support institutions in addressing their concerns around student retention rates. The numbers tell a concerning story: In the U.S., nearly 25% of first-year undergraduates don’t complete their studies, and in STEM fields, the numbers are even higher. In both STEM programs and non-STEM programs with math gateway courses, struggles with math are often a key reason students do not, or cannot, continue their studies. This has a profound impact on both the students’ futures and the institution’s revenue and funding.

From what we’re hearing from institutions and instructors, one of the most pressing issues is the lack of readiness among first-year students, particularly in math courses. With larger class sizes and students arriving with varying levels of preparedness, instructors face challenges in providing the personalized support that is essential. Additionally, many students don’t fully utilize existing resources, such as office hours or TA sessions, which increases their risk of falling behind and ultimately dropping out.

Our new Student Success Platform is designed to tackle these issues head-on. It combines all of our existing tools with exciting new features to help students succeed on their own terms—without adding to instructors' already busy workloads. The early feedback has been fantastic, and we can’t wait for you to see the impact it can make.

You can read more about the Student Success Platform here: https://www.maplesoft.com/student-success-platform/

Maple Transactions has just published the Autumn 2024 issue at mapletransactions.org

From the header:

This Autumn Issue contains a "Puzzles" section, with some recherché questions, which we hope you will find to be fun to think about.  The Borwein integral (not the Borwein integral of XKCD fame, another one) set out in that section is, so far as we know, open: we "know" the value of the integral because how could the identity be true for thousands of digits but yet not be really true? Even if there is no proof.  But, Jon and Peter Borwein had this wonderful paper on Strange Series and High Precision Fraud showing examples of just that kind of trickery.  So, we don't know.  Maybe you will be the one to prove it! (Or prove it false.)

We also have some historical papers (one by a student, discussing the work of his great grandfather), and another paper describing what I think is a fun use of Maple not only to compute integrals (and to compute them very rapidly) but which actually required us to make an improvement to a well-known tool in asymptotic evaluation of integrals, namely Watson's Lemma, just to explain why Maple is so successful here.

Finally, we have an important paper on rational interpolation, which tells you how to deal well with interpolation points that are not so well distributed.

Enjoy the issue, and keep your contributions coming.

With the 2024 Maple Conference coming up this week, I imagine one of two of you have noticed something missing. We chose not to have a Conference Art Gallery this year, because we have been working to launch new section of MaplePrimes:  The MaplePrimes Art Gallery. This new section of MaplePrimes is designed for showing off your Maple related images, in a gallery format that puts the images up front, like Instagram but for Math.

To get the ball rolling on the gallery, I have populated it with many of the works from past years' Maple Art Galleries, so you can now browse them all in one place, and maybe give "Thumbs Ups" to art pieces that you felt should have won the coveted "People's Choice Award".

Once you are inspired by past entries, we welcome you to submit your new artwork!  Just like the conference galleries, we are looking for all sorts of mathematical art ranging from computer graphics and animations, to photos of needlework, geometrical sculptures, or almost anything!  Art Gallery posts are very similar to regular MaplePrimes posts except that you are asked to supply an Image File and a Caption that will displayed on the main Gallery Page, the post itself can include a longer description, Maple commands, additional images, and whatever else you like.  See for example this Art Gallery post describing Paul DeMarco's sculpture from the 2021 Maple Conference Gallery - it includes an embedded worksheet as well as additional images.

I can't wait to see what new works of art our MaplePrimes community creates!

The complete Maple Conference 2024 program is now available online. You can view it HERE.
Thank you to all those who voted for the "Audience Choice" sessions. The winning topics are listed in the program.

Registration is still open and free of charge.  

We hope to see you there!

VerifyTools is a package that has been available in Maple for roughly 24 years, but until now it has never been documented, as it was originally intended for internal use only. Documentation for it will be included in the next release of Maple. Here is a preview:

VerifyTools is similar to the TypeTools package. A type is essentially a predicate that a single expression can either satisfy or not. Analogously, a verification is a predicate that applies to a pair of expressions, comparing them. Just as types can be combined to produce compound types, verifications can also be combined to produce compund verifications. New types can be created, retrieved, queried, or deleted using the commands AddType, GetType (or GetTypes), Exists, and RemoveType, respectively. Similarly in the VerifyTools package we can create, retrieve, query or delete verifications using AddVerification, GetVerification (or GetVerifications), Exists, and RemoveVerification.

The package command VerifyTools:-Verify is also available as the top-level Maple command verify which should already be familiar to expert Maple users. Similarly, the command VerifyTools:-IsVerification is also available as a type, that is,

VerifyTools:-IsVerification(ver);

will return the same as

type(ver, 'verification');

The following examples show what can be done with these commands. Note that in each example where the Verify command is used, it is equivalent to the top-level Maple command verify. (Also note that VerifyTools commands shown below will be slightly different compared to the Maple2024 version):

Download VerificationTools_blogpost.mw

Austin Roche
Software Architect
Mathematical Software
Maplesoft

As AI becomes increasingly relevant in the tech world, Maplesoft has taken steps to integrate AI into our products. We recently launched two new features: Ask AI in Maple Learn and Word Problem Solver in Maple Calculator. 

Ask AI - Maple Learn

As a Math Content Creator at Maplesoft, sometimes I find myself in a creative rut. What documents would be engaging for students? How can I address certain math topics in a fun and interactive way?

I've had the pleasure of creating several collections during my time, including Extreme Value Theorem, Intermediate Value Theorem, and Polynomial Long Division. Nonetheless, each collection took a lot of storyboarding and creativity before I even began drafting them, and I've missed out on creating so many more collections because of this long idea generation process. Having a tool in my back pocket to reignite those creative juices would make it so much easier and faster to create new and exciting Maple Learn documents. 

Luckily, our new Ask AI feature in Maple Learn can help with that! 

Whenever you enter text into a Maple Learn document, a new Context Panel operation called "Ask AI" will pop up. Simply click that button to receive an AI response related to your prompt.

One of my favourite uses of Ask AI is to pick a random subject or phrase and see what the AI responds with. The Ask AI feature is designed to respond with a mathematics-centric answer so it will twist even the least mathematical of concepts into a math problem! The prompt "tacos" resulted in some formulas about sharing tacos with friends, and a prompt of "celebrity gossip" introduced statistical functions to compute the number of celebrity mentions per day. 

I also found that completing part of a tongue twister will result in some funny AI responses!

Here are a couple of my favorites below:

"She sells sea shells..."

Ask AI completes this tongue twister, then offers some formulas to compute the profit of selling S shells!

"How much wood..."

After relating that this tongue twister is not a mathematical problem, Ask AI then builds a simple formula for computing how much wood a woodchuck would (hypothetically) chuck.

There are many more applications of this feature, and I hope you all enjoy exploring them as you create documents on Maple Learn. If you're having trouble inputting text into your documents, or looking for a quick introduction to Maple Learn, check out the Walkthrough Tutorial. Beginner Tutorial (slide 8) addresses adding text to your document. Check out this blog post if you aren't sure how to access the Walkthrough Tutorial. 

Word Problem Solver - Maple Calculator

Maple Calculator now offers support for word problems by leveraging AI. Simply take a picture of your word problem and Maple Calculator will provide a solution generated by AI.

Here is a quick example:

I wrote on paper, “Alice and Bob have 17 apples total. Alice has double the number of apples as Bob plus two. How many apples does Bob have?”. Then I took a picture of this in Maple Calculator, and it gave me a breakdown of the problem using linear equations. See screenshots of my Maple Calculator below.

AI can be an amazing tool, but it can also make mistakes. We ensure that all our tools that incorporate AI clearly indicate its use, so that our users can know when AI is used and choose whether to use it. We're committed to remaining transparent about AI as our journey continues and we are always open to feedback. 

For our community of educators, a valuable exercise for students might be to show examples where AI makes mistakes and encourage students to find and explain the errors.

As an example, here is an algebra problem answered by Ask AI in Maple Learn – but it made a mistake! See if your students can spot where it went wrong and explain what should happen instead.

Building these skills will translate into good critical thinking skills that will benefit students inside and outside the classroom. For example, these exercises aim to help students identify their own mistakes in math and critically evaluate online sources. We would love to hear feedback about these exercises if you try them.

We hope these features will come in handy next time you use Maple Learn and Maple Calculator!