MSU’s spring semester kicked off with mathematics professor David Ayala receiving a National Science Foundation CAREER grant for his research in quantum physics. Ayala works in a mathematical field called higher category theory. The intent of his research is to use patterns to address the behavior of intricate quantum systems.Due to the complexity, Ayala provided the following metaphor to gain a better understanding of his research:

Assume one comes across an infinite amount of data. The Fibonacci sequence can be used as an example. This sequence is the series of numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. . .. One seeks to reduce this seemingly infinite amount to a finite amount of data. This is where one searches for a pattern within the data. In this case, the next number in the Fibonacci sequence is found such that each number is the sum of the two preceding ones. This rule determines the entire set of data. In this way, the infinite data set can be expressed as a structural rule with a few data points.

Ayala will use this $400,000 grant to fund two mathematical and physics conferences in Bozeman, help fund MSU graduate students in the Department of Mathematical Sciences and continue his research while traveling. 

He is currently on a semester-long appointment at the Mathematical Sciences Research Institute in Berkeley, California. While there, he is serving as a leader for a four-month conference in which a total of 200 mathematicians from around the globe are attending. 

From the get-go, Ayala enjoyed reading mathematics and physics books. He grew up in the small town of Rockville, Utah and became engrossed in these subjects, eventually attending the University of Utah. While attending the university, he earned two bachelor’s degrees in mathematics and physics and later a master’s degree in mathematics. He then went on to earn his doctorate in mathematics from Stanford University. Afterward, he engaged in postdoctoral work at the University of Southern California, Harvard University and the University of Copenhagen before moving his career to MSU in 2014. 

His excellence does not just stop in mathematics and physics. Ayala is also a devoted runner. He commented on Bozeman saying, “What’s better than to wake up and decide which mountain range to run across today?” He has competed in multiple races, one being the local Bridger Ridge Run, where he finished first overall, not just once, but twice. This 19.90 miles of rough terrain is known to be one of most technical trail runs in the country. Ayala says that exercise prevents him from becoming somber. 

 “Good things come from the support of specific individuals and the institution of MSU.” Ayala shares he would not be where he is today without his loving mom and proud partner inspiring him to take risks. 

For more information on David Ayala and to look into his previous research, visit

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