The Society of Actuaries (SOA) has officially named The Ohio State University’s Actuarial Science Program a Center of Actuarial Excellence (CAE) — a distinction reserved for the world’s top programs in actuarial education.
Since launching the CAE designation in 2009, the SOA has recognized universities that go above and beyond in preparing future actuaries through outstanding teaching, research and student support. Ohio State now joins this elite group, affirming its commitment to shaping the next generation of analytical thinkers and problem-solvers.
Actuarial science is the art and science of measuring risk. Using math and data, actuaries help design insurance policies, pension plans, and employee benefits that keep people financially secure.
To celebrate, the Department of Mathematics is challenging you to put your skills to the test with four fun (and tricky!) word problems. Think you’ve got what it takes? Flex those math muscles and see how you stack up — answers will be revealed on Instagram on July 1, 2026.
Columbus, Ohio, sits at around 40° north. If we draw a circle around the earth at this latitude, is it true that there must be two points on this circle, diametrically opposed to each other, which are the same temperature at the same time?
Solution hint: Requires continuous functions.
Choose two nonnegative integers N and M (at random), and I write them on two separate sheets of paper. The distributions of these choices are unknown to you, but you do know that the numbers are different. You choose one of the sheets at random and observe the number on it. The other number is still unknown to you. Your task is to guess whether the number you observed is larger or smaller than the number still unobserved. You have access to a random number generator (ie you can generate numbers on [0,1] uniformly at will). Devise a strategy which guesses which number is larger with greater than 1/2 probability.
Solution hint: This is a playful puzzle for curious minds — jump in and see where your thinking takes you!
Choose at random 3 points on the unit circle x^2 +y^2 =1. Interpret them as cuts that divide the circle into three arcs. Compute the expected length of the arc that contains the point (1,0).
Remark: Here is a “solution”. Let L1, L2, L3 be the lengths of the three arcs. Then L1 + L2 + L2 = 2π and by symmetry E(L1) = E(L2) = E(L3), so the answer is E(L1) = 2π/3. Explain why this is wrong.
Solution hint: Change the problem to three points on the line segment [0,1].
Intuitively the average (mean) of a random variable is somewhere in the middle of the possible values it takes. This is not true. Give an example of a random variable whose average is infinity, though the random variable takes finite values with probability 1.
Solution hint: This is related to the St. Petersburg paradox.