Steven Finch received his B.A. in Mathematics from Oberlin College in 1982 and his M.S. in Applied Mathematics from the University of Illinois (Urbana-Champaign) in 1985. He initially worked in statistical weather forecasting, first at The Analytic Sciences Corporation (TASC) and then at MIT Lincoln Laboratory. He subsequently was a technical writer at MathSoft Inc., held biostatistics programming positions at the Boston University School of Public Health and at Tufts-New England Medical Center, and served as Statistical Computing Scientist/Preceptor at the Harvard University Department of Statistics for nearly ten years. He is grateful to the MIT Sloan School of Management for his current role as Research Computing Specialist. Finch is also honored to have received a Book Fellowship from the Clay Mathematics Institute beginning in 2004, and a Ford award for expository excellence in 2005. In his other life, he is a piano accompanist and composer, and appears frequently as a classical recitalist and choral singer. A compact disc recording, entitled An Apple Gathering, of entirely original vocal music is available for purchase; it features the extraordinary choral group Boston Secession and acclaimed concert soprano Nancy Armstrong.

Pure Mathematics publications

• S. R. Finch, Mathematical Constants II, Cambridge Univ. Press, 2019; MR3887550; more info.
• S. R. Finch, Mathematical Constants, Cambridge Univ. Press, 2003; MR2003519.
  
  
• L. Mutafchiev and S. Finch, On the deepest cycle of a random mapping, J. Combin. Theory Ser. A. 206 (2024) 105875; MR4708575; arXiv:2301.13829.
• S. Finch, G. Latouche, G. Louchard and B. Meini, Traffic lights, clumping and QBDs, Stochastic Models 37 (2021) 102-126; arXiv:1911.01134; MR4224026.
• Z.-Q. Bai and S. R. Finch, Precise calculation of Hausdorff dimension of Apollonian gasket, Fractals 26 (2018) 1850050; RG preprint; MR3858491.
• Z.-Q. Bai and S. R. Finch, Fibonacci and Lucas representations, Fibonacci Quart. 54 (2016) 319--326; RG preprint; MR3584000.
• S. Finch, G. Martin and P. Sebah, Roots of unity and nullity modulo n, Proc. Amer. Math. Soc. 138 (2010) 2729-2743; UBC preprint; MR 2011h:11105.
• S. Finch and P. Sebah, Comment on "Volumes spanned by random points in the hypercube", Random Structures Algorithms 35 (2009) 390-392; MR 2010i:52008.
• N. J. Calkin, S. R. Finch and T. B. Flowers, Difference density and aperiodic sum-free sets, Integers 5 (2005) A3; MR 2006i:11024.
• S. R. Finch and I. Hueter, Random convex hulls: A variance revisited, Adv. Appl. Probab. 36 (2004) 981-986; MR 2005m:60015.
• S. R. Finch and J. E. Wetzel, Lost in a forest, Amer. Math. Monthly 11 (2004) 645-654 [winner of the Ford award]; RG reprint; MR 2006d:51016.
• P. E. Manne and S. R. Finch, A solution to the bent wire problem, Amer. Math. Monthly 109 (2002) 750-752; MR1927626.
• S. Finch, Several constants arising in statistical mechanics, Annals of Combin. 3 (1999) 323-335; arXiv:math/9810155; MR 2001h:82035.
• S. Finch, The average value of the Smarandache function, Smarandache Notions J. 10 (1999) 95-96; 11 (2000) 140-141; MR 2000a:11129.
• N. Calkin and S. Finch, Conditions on periodicity for sum-free sets, Experim. Math. 5 (1996) 131-137; MR 98c:11010.
• J. Cassaigne and S. Finch, A class of 1-additive sequences and quadratic recurrences, Experim. Math. 4 (1995) 49-60; MR 96g:11007.
• S. Finch, Patterns in 1-additive sequences, Experim. Math. 1 (1992) 57-63; MR 93h:11014.
• S. Finch, Are 0-additive sequences always regular?, Amer. Math. Monthly 99 (1992) 671-673; MR1542165.
• S. Finch, On the regularity of certain 1-additive sequences, J. Combin. Theory Ser. A. 60 (1992) 123-130; MR 93c:11009.
• S. Finch, Conjectures about s-additive sequences, Fibonacci Quart. 29 (1991) 209-214; MR 92j:11009.

Pure Mathematics preprints

• S. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578.
  
  
• S. Finch, An exceptional convolutional recurrence, arXiv:2408.12440.
• S. Finch, A deceptively simple quadratic recurrence, arXiv:2409.03510.
• S. Finch, Generalized logistic maps and convergence, arXiv:2409.15175.
• S. Finch, Iterated radical expansions and convergence, arXiv:2410.02114.
• S. Finch, What do sin(x) and arcsinh(x) have in common?, arXiv:2411.01591.
• S. Finch, Exercises in iterational asymptotics, arXiv:2411.16062.
• S. Finch, Popa's "Recurrent sequences" and reciprocity, arXiv:2412.11806.
• S. Finch, Exercises in iterational asymptotics II, arXiv:2501.06065.
• S. Finch, Abel's functional equation and interrelations, arXiv:2503.00579.
• S. Finch, Exercises in iterational asymptotics III, forthcoming.
  
  
• S. Finch, M/G/1-FIFO queue with uniform service times, arXiv:2206.11108.
• S. Finch, M/D/1 queues with LIFO and SIRO policies, arXiv:2208.09980.
• S. Finch, D/M/1 queue: Policies and control, arXiv:2210.08545.
• S. Finch, Stochastic reservoir calculations, arXiv:2301.03111.
  
  
• S. Finch, Resolving conflicts and electing leaders, arXiv:1912.06545.
• S. Finch, Recursive PGFs for BSTs and DSTs, arXiv:2002.02809.
• S. Finch, Cantor-solus and Cantor-multus distributions, arXiv:2003.09458.
• S. Finch, Variance of longest run duration in a random bitstring, arXiv:2005.12185.
• S. Finch, Covariance within random integer compositions, arXiv:2010.06643.
• S. Finch, Permute, Graph, Map, Derange, arXiv:2111.05720.
• S. Finch, Rounds, Color, Parity, Squares, arXiv:2111.14487.
• S. Finch, Second best, Third worst, Fourth in line, arXiv:2202.07621.
• S. Finch, Joint probabilities within random permutations, arXiv:2203.10826.
• S. Finch, Components and cycles of random mappings, arXiv:2205.05579.
  
  
• S. Finch, Moments of maximum: Segment of AR(1), arXiv:1908.04179.
• S. Finch, Number of sign changes: Segment of AR(1), arXiv:1909.02556.
  
  
• S. Finch, How far might we walk at random?, arXiv:1802.04615.
• S. Finch, Maximum queue length for traffic light with Bernoulli arrivals, arXiv:1802.04621.
• S. Finch, The maximum of an asymmetric simple random walk with reflection, arXiv:1808.01830.
• S. Finch and G. Louchard, Conjectures about traffic light queues, arXiv:1810.03906.
• S. Finch and G. Louchard, Traffic light queues and the Poisson clumping heuristic, arXiv:1810.12058.
• S. Finch, Geo/Geo/2 queues and the Poisson clumping heuristic, arXiv:1902.09272.
• S. Finch, M/M/c queues and the Poisson clumping heuristic, arXiv:1904.04054.
• S. Finch, How long might we wait at random?, arXiv:1906.07021.
  
  
• S. Finch, Ptolemy constants as described by eccentricity, arXiv:1608.04299.
• S. Finch, Random cyclic quadrilaterals, arXiv:1610.00510.
• S. Finch, Triangles formed via Poisson nearest neighbors, arXiv:1712.08481.
• S. Finch, Three random intercepts of a segment, arXiv:1802.02466.
• S. Finch, 0-pierced triangles within a Poisson overlay, arXiv:1804.01353.
• S. Finch, Median area for broken sticks, arXiv:1804.09602.
• S. Finch, Four vignettes on apparent size, arXiv:1811.10593.
  
  
• S. Finch, Union of n disks: Remote centers, common origin, arXiv:1511.04968.
• S. Finch, Expected n-step product for Gaussian tours, arXiv:1512.05592.
• S. Finch, Capturing, ordering and Gaussianity in 2D, arXiv:1601.04937.
  
  
• S. Finch, Pins, stakes, anchors and Gaussian triangles, arXiv:1410.6742.
• S. Finch, Uniform triangles with equality constraints, arXiv:1411.5216.
• S. Finch, Lognormality and triangles of unit area, arXiv:1412.5860.
  
  
• S. Finch, In limbo: Three triangle centers, arXiv:1406.0836.
• S. Finch, Least capacity point of triangles, arXiv:1407.4105.
• S. Finch, Appell F1 and conformal mapping, arXiv:1408.1074.
  
  
• S. Finch, Convex hull of two orthogonal disks, arXiv:1211.4514.
• S. Finch, Oblique circular cones and cylinders, arXiv:1212.5946.
• S. Finch, Mutually equidistant spheres that intersect, arXiv:1301.5515.
  
  
• S. Finch, Width distributions for convex regular polyhedra, arXiv:1110.0671.
• S. Finch, Mean width of a regular simplex, arXiv:1111.4976.
• S. Finch, Mean width of a regular cross-polytope, arXiv:1112.0499.
• S. Finch, Planar projections and second intrinsic volume, arXiv:1203.2464.
• S. Finch, Rank-3 projections of a 4-cube, arXiv:1204.3468.
  
  
• S. Finch, Random Gaussian tetrahedra, arXiv:1005.1033.
• S. Finch, Two sample covariances from a trivariate normal distribution, arXiv:1005.1183.
• S. Finch, Perimeter variance of uniform random triangles, arXiv:1007.0261.
• S. Finch and A. Jones, Random spherical triangles, arXiv:1009.5329.
• S. Finch, Correlation between angle and side, arXiv:1012.0781.
• S. Finch, Three random tangents to a circle, arXiv:1101.3931.
• S. Finch, Covering a sphere with four random circular caps, arXiv:1502.06931.
  
  
• S. Finch and P. Sebah, Squares and cubes modulo n, arXiv:math/0604465.
• S. Finch, Idempotents and nilpotents modulo n, arXiv:math/0605019.
• S. Finch, Powers of Euler's q-Series, arXiv:math/0701251.
• S. Finch, Quartic and octic characters modulo n, arXiv:0907.4894.
• S. Finch and P. Sebah, Residue of a mod 5 Euler product, arXiv:0912.3677.
  
  
• S. Finch, Another look at AR(1), arXiv:0710.5419.
• S. Finch, CLT variance associated with Baxendale's SDE, arXiv:0809.5274.
  
  
• S. Finch, P. Sebah and Z.-Q. Bai, Odd entries in Pascal's trinomial triangle, arXiv:0802.2654.
• S. Finch, Z.-Q. Bai and P. Sebah, Typical dispersion and generalized Lyapunov exponents, arXiv:0803.2611.
  
  
• S. Finch and J. Shonder, Lost at sea, arXiv:math/0411518.
• S. Finch and L.-Y. Zhu, Searching for a shoreline, arXiv:math/0501123.
• S. Finch, The logarithmic spiral conjecture, arXiv:math/0501133.
  
  
• S. Finch, A convex maximization problem: Discrete case, arXiv:math/9912035.
• S. Finch, A convex maximization problem: Continuous case, arXiv:math/9912036.
  
  
• M. Schweitzer and S. Finch, Zero divisors in associative algebras over infinite fields, arXiv:math/9903182.

Problems seeking solutions

• S. Finch, Problem 1302 (Oblique circular cones, randomly inscribed), Pi Mu Epsilon J. v. 14 (2015) n. 2, reprint; v. 14 (2019) n. 10, reprint.
• S. Finch, Problem 11687 (Slicing a doughnut at random), Amer. Math. Monthly 120 (2013) 77; 122 (2015) 177-178.
• S. Finch, Computer algebra and elliptic functions, incomplete work (2013).
• S. Finch, Problem 1305 (Well-centered tetrahedra, randomly inscribed), Elem. Math. 67 (2012) 151; 68 (2013) 128-131.
• S. Finch, Problem 979 (Acute chordal triangles, randomly inscribed), College Math. J. 43 (2012) 258; 44 (2013) 237-238.
• S. Finch, Problem 1895 (Three random intercepts of a segment), Math. Mag. 85 (2012) 151; 86 (2013) 152-153.
• S. Finch and B. Harder, Periodicity in sequences mod 3, incomplete work (2002).
• S. Finch, A convex maximization problem, J. Global Optim. 2 (1992) 419; follow-on research.

Translations and other

• Henri Joris' "Le chasseur perdu dans la forêt" (1980), arXiv:1910.00615.
• V. A. Zalgaller's "On a problem of the shortest space curve of unit width" (1994), arXiv:1910.02729.
• Jonathan Sondow's "Irrationality and transcendence of alternating series via continued fractions" (2017), arXiv:2009.14644.
• J. H. Schmerl's theorem & proof of regularity, communicated via a letter (1994), occupies a significant portion of "Multisum sets", arXiv:2407.05065.
• Review of On-Line Encyclopedia of Integer Sequences, founded by N. J. A. Sloane, Math. Intelligencer, J. H. Conway memorial issue, v. 43 (2021) n. 2, 146-147; Springer reprint; MR4278491.
• Composite of two earlier preprints, entitled "Iterational asymptotics of sine and cosine" (2025), as an interactive computational notebook on a Wolfram community board.

Applied Mathematics/Statistics publications

• R. Ziff, S. Finch and V. Adamchik, Universality of finite-size corrections to the number of critical percolation clusters, Phys. Rev. Lett. 79 (1997) 3447-3450; arXiv:cond-mat/9707168.
• S. Finch, R. Cole, G. Rasmussen, W. Wilson and S. Kim, Summer 1992 Terminal area-Local Analysis and Prediction System (T-LAPS) evaluation, MIT/LL Project Report ATC-218 (1994).
• K. MacNichol and S. Finch, CFLOS4D accuracy assessment using Whole Sky Imager data, Proc. 1991 Conf. Cloud Impacts on DoD Operations and Systems (July 1991); also AF Phillips Laboratory Report PL-TR-91-2098 (1991).
• S. Finch and K. MacNichol, Preliminary data requirements analysis for CFLOS4D/CFARC model validation, Proc. 1989/90 Conf. Cloud Impacts on DoD Operations and Systems (Jan. 1990).
• C. Medler and S. Finch, Semi-Markov models for cloudy and cloud-free intervals, Proc. 1988/89 Conf. Cloud Impacts on DoD Operations and Systems (Oct. 1988).
• S. Finch, S. Koenig and F. K. Sun, Modeling strategic weapon system error due to reentry weather, Proc. Military Operations Research Society 56th Symp. (June 1988).

Contact information

steven_finch_mathoutlook.com

ORCID listing