Mathematics holds a vital place in a wide variety of fields, including the sciences and finance. Number calculations have proved the viability of countless scientific phenomenon. Money lenders generally need statistical data to evaluate a consumer’s financial situation before granting them a loan (although installment loans are easier to come by). Whatever the field, math leads to results.

According to David Landes of the Swedish news publication The Local, a 16-year-old student named Mohamed Altoumaimi from Falu Frigymnasium high school has achieved a significant accomplishment in the field of mathematics. He has derived a formula with Bernoulli numbers that is normally the territory for only seasoned professional mathematicians. Professors at prestigious Uppsala University have recognized the young man’s accomplishment, and hope to see more from him.

What are Bernoulli numbers?

Bernoulli numbers are “a sequence of rational numbers with deep connections to number theory,” according to Wikipedia. They’re named for the 17th century Swiss mathematician Jacob Bernoulli. There a number of practical applications to number theory, which is sometimes referred to as “pure” math. Such applications include cryptography, cryptanalysis, computer science and numerous uses in physics, such as (reference here):

• Analytic regularizations in quantum theories
• Selberg Trace formula, is very similar to Gutzwiller formula for the trace of resolvent (E-H+i\epsilon)^{-1}
• Negative values of Zeta function \zeta (-m) or Bernoulli Numbers (related to negative value of Zeta) can be used to compute divergent series and integrals
• Combinatorial problems of Number theory has application to Bose-Einstein or Fermi-Dirac statistics

… in case you were wondering and weren’t familiar…

Go over their heads if they won’t help you

Mohamed Altoumaimi, a Swedish citizen originally from Iraq, has long been interested in math. His efforts to write a formula to explain the relationships between Bernoulli numbers took about four months for him to complete. Once he announced to his high school instructors that he’d derived a formula on his own, they were understandably skeptical.

“When I first presented it to my teachers, none of them believed that the formula I had written down really worked,” Altoumaimi told the newspaper Falu Kuriren.

But the boy was undeterred. He contacted a professor at Uppsala University so that his work could be validated.

“Right away, he wanted to take a look at all my calculations and the documents where I show that the formula really works,” said Altoumaimi.

“A very clever guy”

While this isn’t the first time a person has established Bernoulli numbers relationships, the fact that a 16-year-old high school student has done it is impressive, said Uppsala University senior mathematics lecturer Lars-Åke Lindahl. The calculations are difficult, to say the least.

“He’s a very clever guy,” Lindahl told Landes. “What he did isn’t necessarily new, but it is quite remarkable for a first year high school student to take on these types of problems all on his own. It’s certainly an achievement.”

Beyond the help of high school

Lindahl verified Mohamed Altoumaimi’s formula and proof, which led to the student’s increased recognition.

“We’re going to keep our eye on him,” said Lindahl. He also encouraged Altoumaimi to attend Uppsala University after high school. In the meantime, he’s offered books and tutoring to help the young man in his continued quest to develop his math skills.

“I think he’s likely beyond being able to get the kind of help he needs from high school math teachers,” said Lindahl.

So make him a teacher

Jacob Bernoulli

Since Mohamed Altoumaimi’s math skills are beyond those of his high school instructors, Falu Frigymnasium plans to use the young man in a teaching capacity – to teach the teachers. In the fall, Altoumaimi will serve as an instructor for a number of the math teachers. He’ll explain his Bernoulli numbers work to them with the hope that they’ll be able to pick up on his computations and pass them on to other students who aren’t quite as advanced.

“It’s really exciting, now all the teachers have come and congratulated me,” said Altoumaimi.

School is not out for the summer

This summer, Altoumaimi has plans to continue his studies of  advanced mathematics and physics. School is never out, and the exciting opportunities mathematics like Bernoulli numbers have opened for the high school student are yet another motivation to continue on the path of discovery.

“I wanted to be a researcher in physics or mathematics; I really like those subjects. But I have to get better at English and social science,” he told Falu-Kuriren.

Depending upon his religion, Mohamed Altoumaimi may not be allowed to go to money lenders for a loan once he graduates school and enters the working world. But with his number skill, he might not even need the service.

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