Limits, a mathematical function that has represented so many sleepless nights for some university students in their first semester and that always seemed to have a difficult solution, can now be easily solved thanks to the inventiveness of two Antioquia teachers.

The Cadavid-Vélez algorithm, the result of three years of research, is the answer that many were looking for to solve the limit of functions of two variables. "We realized that the existing teaching methods, which have always been used were somewhat complex and rudimentary. In addition, there was not an algorithm that could solve a classic and most common problem of limits, functions of two variables, and that is why we decided to think and do research about it," said Carlos Cadavid Alberto Moreno, professor of the Department of Mathematical Sciences at EAFIT.

After getting the right answer, the researchers published an article in the Journal of Symbolic Computation, one of the most recognized journals in the field, which attracted the attention of programmers at Maple, the world’s leading software solution in mathematical algorithms, who immediately spotted this creation and decided to implement it in their latest version of the package.

"Finding a solution with sophisticated mathematics seemed very magical to us. We take pride in the fact that a large world corporation like Maple has taken the Cadavid-Vélez algorithm into account to compute a routine that appears in many situations and for which no solution was known," says Juan Diego Vélez, professor of graduate studies in mathematics at Universidad Nacional in Medellín.

These teachers and researchers agree that the algorithm can be used by anyone. Users only need to have the Maple license in their 18 or 2015 version, enter the ‘limit’ command, type the formula and click. The result will appear instantly. "It's simple because our idea was to find a unique, easy and scientific way of solving the problem," says professor Cadavid.

The teacher at Universidad Nacional acknowledges that it is a complicated topic and, precisely for that reason, his main goal was to find a mathematical solution to, somehow, bring people closer to exact sciences.

"A person who uses a cell phone does not realize that it is built using solid-state physics, which is based on other complex concepts. After all, it is a level of mathematics available to engineering students. Therefore, we must make them understand that abstract concepts seen in class are not a luxury or issues that only serve for the purpose of passing a midterm exam," adds professor Cadavid.

## The future of Cadavid-Vélez

Now the challenge is to expand the algorithm to more variables and patent it because it has not been patented yet and, for that reason, it can be used by anybody as Maple did. "We did not patent it from the beginning because it is usually expensive and difficult to process and we did not have the experience or advice to do it. In addition, among university professors there is a kind of rush to publish the results of their research before others do," said professor Vélez.

This pair of teachers from Universidad EAFIT and Universidad Nacional at Medellín started working jointly many years ago, and together they have written several publications.

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Alejandro Gómez Valencia

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