Carlos Gustavo Moreira – more popularly known as ‘Gugu’ – delivered a plenary lecture on Fractal Geometry, Dynamical Systems and Diophantine Approximations on the third day of ICM 2018.  But, before he got into the academic dynamics of his research, he dipped into politics and expressed his hope for a more robust democracy in the future.

 

Gugu, one of the bright stars of Brazilian mathematics, and an avid Brazilian Communist Party (PCB) supporter, could be found running around with a Marx pin on his shirt at age 11, and a year later won the Rio de Janeiro city Chess Championship.

 

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Having developed an early interest in mathematics, Gugu completed his high school degree and master’s degree simultaneously: from the age of 14, after attending high school in the mornings, he would rush off to the prestigious Institute of Pure and Applied Mathematics (IMPA). He graduated from high school and his masters just after his 17th birthday.

 

Gugu’s research relates diophantine approximations to other areas of math. There is a fundamental problem which encompasses fractions and real numbers. Irrational numbers, or fractions, can approximate all real numbers. For example, Pi is an irrational number that can be approximated by a real number through decimals: 3.14. But, as the decimals would go on forever, it will never have a perfect real number representation.  However, it is possible to get close using specific fractions. Some fractions are better than others at finding these approximations, and part of Gugu’s work shows how to reach these better approximations and relate them to seemingly unrelated areas of mathematics, such as dynamical systems, chaos theory, and fractal geometry.

 

Luckily, his trajectory in mathematics has been more successful than his retired political career, which started and ended with a mere 133 votes for his city council candidacy. “I’m not a very effective candidate,” he joked.