**A natural math interface comes from the most unlikely source: Apple. **

*A ping pong ball is hit at 10 m/s at an angle of 30° 0.3m off the tabletop. How high will it rise? Time to dust off your Physics 101 textbook. *

Apple’s June 2024 Worldwide Developer Conference was well received by Apple fanboys and girls, but if any of them were engineers, they would surely have been startled by the company's introduction of Math Notes, a feature in the calculator app that is able to understand numbers and formulae, make graphs and do calculations — all from your handwritten input!

It was stunning. Here was Apple — a company never associated with math or engineering software — leapfrogging PTC’s Mathcad with handwriting recognition for math. PTC had just gone on record to say that trying to interpret handwriting as math would be inadvisable. Numbers should not be subject to interpretation. Too many things can go wrong. PTC would not be going there. And here goes Apple showing off the ability to recognize handwritten numbers and formulae -- and solving them!

**How Does it Work?**

Math Notes is a feature found in the Calculator app which will make its debut on the iPad with iPadOS 18.

In a demo 47 minutes in to the WWDC24 keynotes, we see how simply drawing a line under a column of numbers will total them. Math Notes solves equations and can graph them. Of course, any graphing scientific calculator can do all that — but this is being done by writing on an iPad with the Apple Pencil. It is simply the most natural way to get math into a computer to date.

I have to rub my eyes and check… Yes, was this really an *Apple* production?

Math Notes understands numbers and mathematical operations. Write an equal sign and it calculates a result. It understands a numerator over a denominator as division. Changes to an equation will update the results. And your writing style may be preserved. In the demo, the results are shown in a style similar to the user’s handwriting -- though I seriously doubt if Apple could duplicate mine.

Skeptical of Apple’s understanding of physics? You might be since the example shown has obvious shortcomings. The trajectory shown is not parabolic and variables are oddly named (x for velocity, acceleration due to gravity should be negative, for example), but the formula is valid and the maximum height the ping pong ball reaches above the table is correct.

Furthermore, we see that if the input is changed, so is the result. This is not just a math formatter such as the one found in MS Word. Replacing the equals sign with “y=” and up pops a XY graph. It gets better: you can adjust the value with a slider bar and see the graph change in real time – just like Mathcad, except Mathcad is $779 per year and Math Notes is no extra cost, it's part of iPad OS. More on cost later.

We need to temper our excitement, however. This was only a demo of future product. Will the final release live up to its billing, a calculator with handwriting superpower? Will it handle units conversions as gracefully as Mathcad, for example. Will it have as many advanced functions, be able to solve as many integrals, do partial differential equations, etc.? That all remains to be seen. And it may be unfair to ask so much from a first release by a company that does not have mathematics or engineering at its core. But Math Notes had me with its ability to do calculations from ordinary handwriting. I will now be free of the keyboard and cryptic keyboard shortcuts.

Efficient use of Mathcad relies on memorizing keystrokes for mathematical notation. For example, you have to use the left bracket key, [, to make a subscript and a colon to define a variable because the equal key (=) is reserved for solution. You can’t use the equals key to define a variable as is routinely done everywhere else. Want to use pi in Mathcad. You can find it on the menu or type the letter “p” followed by Ctrl g. Does that make sense to anyone?

PTC is big on keystroke shortcuts. It has hundreds of them. Granted, those who use Mathcad everyday have memorized many of them and can fly through a worksheet. It is an example of software that is easy to use if you know how to use it and for everyone else, frustratingly difficult.

Apple's Math Notes may finally give us a scratch pad that understands what we write on it. Will we finally be able to do away with the engineering triumvirate, the notepad, computer and calculator, and let us do it all on one device?

**How to Hide a Super Power?**

Math Notes will be delivered with iPadOS 18 — so some time this Fall. Good luck finding it, though. Apple has hidden it Russian-doll style in the calculator button in the Calculator app. Why not integrate it into Apple Notes? Or make it an app available on the home screen? Or even make it the default in Calculator rather than an option? As it is, the Calculator on an iPad is useless. It's too big for one-handed operation even on the iPad Mini. The big screen will have you using both hands with one moving around to access the buttons whereas on the iPhone you can use a calculator app with in one hand and just move your thumb. It's not a big deal if you are doing one or two calculations but engineers use their calculators a lot. The iPad attempts to make use of the extra space around the calculator keys by show a history and for unit conversion but really can't get over the fact that it is just to big to be useful.

Apple calls Math Notes the Calculator’s “super power.” Oh, I get it. Apple is hiding it’s superpower under a drab cover like Superman is hidden under Clark Kent.

**How Much?**

We don't expect engineers worldwide to drop their notebooks and calculators in favor of a iPad for price reasons alone. The cheapest iPad is currently selling for a minimum of $329. The most expensive, the iPad Pro, can be configured for well over $2K. You can’t use your finger to draw or write. You may have to get the Apple Pencil Pro, which costs $129. You don't pay anything for Math Notes per se, as it is part of iPados 18, but if you don't have the most recent versions of an the iPad and Apple pencil, you will have to spend at least $458 to have Math Notes.

Still, that's a one time cost. Compare that to subscription pricing for math software. Mathcad has a free version but the Pro version without the embarrassing I'm-using-the-free-version watermark costs a whopping $779 per year.

Also, writing on a glass surface using a stylus takes a little getting used to. It’s feels at first like ice skating. There is no friction. It had the effect of make my messy writing even messier. You can, however, buy aftermarket films that increase the friction a little –without noticeably reducing brightness or the touchscreen function.

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