Good at Math
What are computers good for? Many things, of course, and thanks to advances in natural language interaction, user interfaces and connectivity today’s computers can be used for an ever-growing range of specialist and everyday tasks.
But back at the dawn of the digital age the only thing that computers were really any good at was number crunching—performing calculations faster than human or mechanical machines could.
In 1953, IBM developed its first commercial scientific computer, the 701 and put it to work crunching data to produce weather predictions. Sixty years on it, the number crunching capabilities of a smartphone far exceed the capabilities of the 701 and, it goes without saying, the smartphone costs a lot less – the 701 cost $12,000 a month to rent.
So you would expect today’s computers to be good at math and have no trouble passing the math test of a university entrance exam, for example.
But you’d be wrong.
Japan’s National Institute of Informatics (NII) believes it will take until 2021 for an artificial brain to pass the math-test threshold required to gain admission to the University of Tokyo.
So why do computers fail math tests which many Japanese high-school students pass?
For a computer to solve the typical math problems posed in entrance exams, it must first understand the question. That’s more difficult than it might at first appear, as the problem is expressed using natural language and formulas that are easily understandable by math students – but not by computers.
Natural-language processing technology can be used to produce a semantic representation of the problem text. But unlike when you speak instructions to your TV or mobile phone – increasingly common tasks in today’s NLI-enabled world – understanding the text of a math problem is not simply a matter of analyzing the words.
It also involves skillfully integrating mathematical terminology and a high-school level understanding of math.
Computers do not know that, for example, “a/c” when used in the context of a math problem represents a fraction, not an abbreviation for “air conditioning” – which is the top result if you type “a/c” into Google.
Similarly, the artificial brain needs to be told that Greek letters like “Σ” are not misspellings but have special meanings in mathematical formulae.
Assuming it can decipher the question the computer then needs to translate the problem into a form a program can execute. Then it must find the best way to solve the problem.
Currently, only approximately 50-60% of entrance-exam problems can be solved by computer so the calculation algorithm “needs improvement,” admits the NII researchers.
Over the next eight years, they hope to drive improvements in the three key areas of semantic analysis, problem formulation and calculation.
Each of these steps poses major theoretical and practical problems, and for each one the solution will involve an appropriate combination of various technologies.
The hope is that the technologies developed as part of this project will enable anyone to easily use sophisticated mathematical analysis tools, which will lead to solutions for a wide range of real-world problems, and even the automation of mathematical analysis and optimization.
That will benefit not just tomorrow’s students– imaging being able to dictate math problems into your smartphone– but also businesses and consumers facing a broad range of more mundane challenges, such as optimizing fleet delivery schedules, calculating body fat percentages or understanding those complex formula used in mortgage applications.
There’s little doubt that the number-crunching power of computer technology will continue to increase with Moore’s Law.
But for that power to be accessible to laypeople and available on non-traditional consumer devices will increasingly hinge on advances in natural language technology from vendors such as Artificial Solutions.