The Center for Data Innovation spoke with Conrad Wolfram, strategic director and European cofounder of Wolfram Research, a computational software company with headquarters in Champaign, Illinois and Oxfordshire, UK. Wolfram described how computation can be beneficial for quantitative problem solving, as well as the problems with the current state of math education around the world.

**Joshua New: **Most people are probably familiar with the Wolfram name thanks to Wolfram Alpha, the “computational knowledge engine” run by Wolfram Research. What exactly is a computational knowledge engine? Why might somebody need this over a traditional search engine?

**Conrad Wolfram:** Essentially, we’re trying to come up with the answers to questions, not search what other people’s answers are. A search engine is a bit like a librarian, and we’re more like your personal research assistant. The objective is the same—to answer a question—but the technology is there to actually compute a solution based on curated data. This works really well when your question is more quantitative, or when nobody has put out much information that could help answer your question.

When you type in your question to Wolfram Alpha, the software breaks it down to symbolic representation and tries to understand what you’re actually asking. With this understanding, and our data, it builds an answer to your question “on the fly.” Traditional search is useful for a lot of questions, but this approach is particularly beneficial for certain cases like medical diagnostics. When you plug in unique patient data, a unique answer is much more valuable than general information that other people may have published. For example, you want to know what an individual patient’s heart attack risk would be for a certain procedure, not heart attack risk associated with the procedure as a whole.

**New: **Wolfram’s computational software is used in a wide variety of industries. What use case do you think is the most valuable, or stands out the most?

**Wolfram:** Our software stack has been growing since its launch in the 1980s, and there are a lot of different layers and facets. One key underlying piece of the Wolfram language—which is in a sense a modern programming language—is that computation is built in. This means you can immediately act on data with the language, since algorithms are built in to its function. This language is a building block to allow people to do huge amount of work and computation much quicker than they could before. Typically, people need to find other languages and tailor them to accomplish specific computations—there are a lot of moving parts that can slow the process down. Other times, there is software that can accomplish niche computations, such as for finance or engineering, but it’s difficult to combine these with other tools to build a robust platform. So what we have is a complete, end-to-end solution to compute things—even new things that you maybe hadn’t planned on or things that have never been computed before.

We’re trying to push the boundaries of computation, and our software stack is designed to do this at every level. One part of this stack in particular is our computable documents. Traditionally, the method of communicating information from one person to another, particularly in government, is via text reports. This is ok, but reports are “dead”—they’ve been pretty much the same thing for the last 300 years. Our computable documents allow us to mix interactivity with narrative.

We try to think about which areas are best for computational knowledge, rather than just search. Take transportation for example. We already have apps out there that compute the best route to a user’s destination. Educational assessment and social security also benefit from this approach. But I think the area with the highest potential for gain is in healthcare. Regardless of a country’s healthcare system, there are always huge inefficiencies. Better data science and technology has so much to offer here. System-wide, this enables massive process improvements, such as by applying advanced analytics to medical imaging rather than relying on humans to examine this data. And on a more individual level, patient-generated data is hugely valuable for diagnostics. Around the world, the rate of success for diagnostics hovers around or below 50 percent. Computation-aided diagnostics, like I mentioned in the previous question, could add so much here.

**New: **Wolfram’s software has been around for 30 years. How has the program changed over the years in response to the needs of your customers and what they want to do with their data?

**Wolfram:** When we launched Mathematica, one of our flagship products, people thought we just did math, and that math was a specialized thing. They even said, “it’s weird you guys think you can launch a company around math.” What’s happened over the last 30 years is that math has turned into computation, and the world has become far more quantitative. This has been an iterative process, partly because of people pushing the boundaries of what computers can do with math and applying it to areas that didn’t focus heavily on math before. Take biology for example. When we started Mathematica, very little biology was done with math. Biologists performed standard data analysis, but it was very basic and they didn’t really rely on image processing. Biology today is almost an entirely new field compared to a couple decades ago, thanks to sophisticated computation. We’ve tried to drive this change. We started out as a math company—and we still are—but now we focus on computation meeting knowledge. That’s what inspired Wolfram Alpha, which we launched six years ago.

In practical terms, this means we can automate so much more. Before, if someone was trying to solve an equation, they took the time to plug in formulas and tools until they got their answer. But now we can just give them the answer automatically. Over time, automation has become much better than human capability, and we try to put this tool in as many peoples’ hands as possible. This means two things. First, people who already use high level math can become much more effective and efficient. And second, many more people can start using this behind the scenes to supplement what they’re already doing. Computable documents, as I mentioned, lets users make informed decisions without having to expose themselves to all the math going on underneath.

In virtually every walk of live, computation is a critical feature. But, like the early days of computers, the solutions at the enterprise level are piecemeal. We’ve been trying to answer the question of how to put enterprise-level computation everywhere to make everyone more effective at what they do.

**New: **It’s pretty apparent that you’re passionate about math, and one of your main projects is a campaign called Computer Based Math, in which you advocate for math education reform. Could you explain the problem with the current state of math education a little more in depth?

**Wolfram:** Current math education is based on the idea that humans do the calculating about 80 percent of the time. In real life though, computers are the ones doing the calculating. My gripe is that today, math is so important to life in ways it wasn’t even just 30 years ago due to the fact that computers have mechanized the process of solving problems. In education we have insisted that humans have to be the calculators. This used to be essential, but now it’s holding us back because computers are so much better at this than humans ever can be.

What we need to do is rethink the subject of math in education to accommodate for its new role in the outside world. If we start thinking that computers can solve all these basic problems that human are educated to solve, we can focus our attention on much harder problems. We educate people for 10 years to solve problems so they can graduate and use a machine to do the same task, and we find that they haven’t actually learned much about how to apply mathematics to solve problems—just to solve math problems themselves. In my view, math is a four-step problem solving process. First, you have to ask a specific question. How much bandwidth do I need to give a phone call good audio quality, for example. Then, you have to turn to abstract math, or code, to figure out how you want to solve the problem. Next, you must compute this to get an answer. Finally, you must go back and ensure that your answer is the one you were looking for in your original question. So much of math education focuses on step three—computing by hand—not steps one, two, and four. People aren’t learning how to set up a problem or abstract it to find answers. And importantly, we’re boring the pants off most of them because this isn’t applicable to their lives. We need to teach math in a manner that assumes computers exist so we can focus on relevant and conceptual problems.

**New: **What are some of the key obstacles to changing how math education works?

**Wolfram:** I think most people would agree that we need to fix math, but the problem is that they haven’t thought enough about how. Most people assume math is just this static “thing” that doesn’t change, despite the fact that math fundamentally has changed in the outside world. Most government administrators I’ve talked to around the world simply haven’t thought about how math relates to the world, even if they think it’s important.

Additionally, writing a curriculum based on this theory is really tricky. The people who really know math were trained traditionally, and it’s hard for them—myself included—to step back and say “do others really need to learn this?” instead of “I learned this, so other people should too.” There was a historical way of doing things, but now there’s a better way.

Building off that, a new problem arises from the fact that it’s mathematicians that set the math curriculum. Obviously they should be involved. But over 96 percent of Mathematica buyers would not classify themselves as mathematicians—they’re engineers, in finance, government workers, and so on—because math is used in practical applications, not just for itself. When you don’t get this whole range of people involved, you’re going to get people who set the curriculum who like math and think it’s interesting to teach math just for the sake of math.

Finally, assessment is a huge obstacle. Assessment drives what people teach, for better or for worse. People want good test scores so they can go to college, and these tests all examine hand calculating ability. If you can do great computer-based problem solving, but not by hand, you’ll still fail. Teaching this calculation takes up so much time in the curriculum as a result that people can’t learn anything else.

So, it’s somewhat of a chicken-and-egg problem, but we’ve actually had our first country adopt this new approach. Estonia has begun to pilot some of our curriculum so we’re very excited to see how that turns out.