###### Photo Credit: Regeneron Science Talent Search

Homeschool student Gopal Goel, 17, of Portland, Oregon, placed fourth in this year’s Regeneron Science Talent Search. Founded and produced by Society for Science, the prestigious science competition recognizes and empowers the most promising young scientists in the U.S. who are creating the ideas and solutions that will address our world’s most urgent challenges.

Gopal Goel received a $100,000 award for his math research on “Discrete Derivative Asymptotics of the Beta-Hermite Eigenvalues,” which made connections between two subjects regarding randomness and probability. Goel believes his work can be useful to researchers in the fields of nuclear physics, quantum field theory and meteorology. Gopal hopes that his research will aid in the search for the true nature of quantum gravity, more commonly known as “the theory of everything.”

Gopal Goel joins the ranks of other Science Talent Search alumni, many of whom have gone on to have world-changing careers in STEM fields, and some of whom have earned the most esteemed honors in science and math, including the Nobel Prize, National Medal of Science, Fields Medal, and MacArthur Foundation Fellowships.

We had the pleasure of interviewing Gopal Goel for this article. Here are our questions along with his answers…

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**1: What is your favorite “fun” math website or app?**

The Art of Problem Solving website (aops.com), but also http://www.cut-the-knot.org is very good.

**2: What is your favorite “serious” math website or app?**

https://mathworld.wolfram.com is a very useful reference. https://www.wolframalpha.com/input is also very useful.

**3: What unsolved problem in mathematics would you really like to see solved?**

Probably the P vs NP conjecture, as it would have very serious implications for the future of computing.

**4: Few people do long division today; they use a calculator. Comparably, do you think it’s worthwhile to work out integral solutions by hand (learning all the tricks required) or just let computers produce the numerical answers we need?**

Learning new techniques and methods is very important, since it builds intuition and knowledge in the field. In particular, the “tricks” learnt to do arithmetic calculations more efficiently actually contain important ideas that are useful in their own right, so trying to avoid learning these and just use computers would make one miss out on this learning opportunity. As an example, say I asked you to compute 49*51. Obviously this is very easy with a calculator, but it turns out you can say 49*51 = (50-1)*(50+1) = 50^2-1 = 2499, which demonstrates the really powerful idea of difference of squares!

**5: What is your favorite computer game?**

I enjoy playing games with my friends online such as *Among Us* and *Spyfall*. I also enjoy playing chess online.

**6: Do you find it surprising how useful mathematics is at making models of physical reality? Were you surprised when you first saw that abstract numbers have real world applications?**

I don’t find it that surprising, but that’s probably because I’ve been thinking about physics since I was really young. I remember learning calculus when I was very young (using the wonderful book “Calculus Made Easy” by Silvanius Thompson, highly recommended!), and I was fascinated by how it could be used to describe continuous physical phenomenon.

**7: How would you describe the relationship between math and physics?**

I would say that physics is more or less applied math. At very high levels of physics research, a good part of the work becomes indistinguishable from mathematics, especially theoretical physics. Experimental work has a bit more of a pure science aspect to it, which has a different feel than pure mathematics.

**8: What do you think of teaching kids a conceptual understanding of mathematics, rather than hammering math skills like times tables? Should the goal be quick calculations in their head by practice, practice, and more practice or is there a place for using math manipulatives and other visual methods over rote memorization of arithmetic?**

I think for sure there needs to be more focus on understanding concepts and applying math in interesting ways. For example, an example of an interesting concept to study is the Fibonacci numbers, and their many interesting properties (ratio converging to golden ratio, cool identities, etc), or Pascal’s triangle. Adding in things like these could show students how mathematics is more than just memorization, and in fact has many beautiful concepts.

**9: Do you think it is advisable to discuss (not rigorously but intuitively) how division by zero can lead to infinity with students who were told it is “not defined”?**

It is important to discuss topics such as division by 0 as to why they are intuitively rather than simply shelving them away in the blackbox of “undefined”. I always stay curious and eager to learn more than what is presented to me. The kind of discussions which are led by my curiosity are what increased by interest in mathematics. In particular, division by 0, though undefined, can be understood by dividing by numbers that get progressively closer to 0. If we divide by say 0.01, then we are multiplying by 100, and if we divide by 0.001, then we are multiplying by 1000. Extrapolating to dividing by 0, we can see that it is basically multiplying by a number larger than any other, which we call “infinity”.

**10: Can you name some top universities for mathematics? (And where do you plan to go?)**

Some of the top universities for mathematics are MIT, Harvard, Princeton, Stanford, etc. I’m still waiting for all my admissions decisions to come in to make my final decision.

**11: If a theoretical mathematician is serious about advancing human understanding in mathematics, what are some good places for them to work besides the obvious (academia)?**

Research in mathematics is most often done at a high level in academia, but it is not necessary to wait till then to start researching and making real contributions to fields of knowledge in mathematics till then. It requires much previous study in a specific field to be able to then advance knowledge, which is why most researchers are also in academia. Theoretical computer science research, which is very much related to certain fields of mathematics, is also done at big tech companies.

**12: What will your prize money be used for?**

Paying for college.

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Congratulations to Gopal Goel on winning fourth place in the Regeneron Science Talent Search! Thank you for answering our questions, and best of luck in your future career!