No, the OP mostly fails to 'get it'. First, beating up on Lisp is next to irrelevant to the role, potential or current, of math in business or computing. Seco

No, the OP mostly fails to 'get it'. First, beating up on Lisp is next to irrelevant to the role, potential or current, of math in business or computing. Second, the OP fails to make a solid case for the power of math to make a powerful, valuable contribution to the solution of real problems for which we do believe we need software. In particular, in spite of the claim of the OP, I doubt that linear programming did much if anything to defeat Germany in WWII; why? Because both the Kantorovich Nobel prize for his work on the 'transhipment' problem and Dantzig's work on his simplex algorithm came after WWII was over. Third, the OPs recommendation for math for applications is too meager; what he listed is all good, but we need more to be as successful as we should wish. Here's a simple description of the potential of math for 'information technology' (IT) business, i.e., the money making kind: We have a lot of input data and want to process it, that is, manipulate it, with software to generate output data that is valuable in business, the money making kind. So, a question is how to process the data? We want powerful means that will convert the input data to valuable output data; did I mention valuable in the sense of business, the money making kind? Well, the traditional means in business IT has been to take some work that is well understood just as manual work, that is, in principle could be done manually. Then take those means and write software to do the corresponding data manipulations. There nearly always the means were just intuitive, obvious. So, what IT did with the input data was nearly always just intuitive, i.e., what was well understood from manual efforts. Some of the big examples were bookkeeping, accounting, payroll, order entry, inventory control, materials requirements planning (MRP), customer relationship management (CRM), airline and hotel reservations. Here, again, we have means well understood manually, and IT wrote software to do essentially the same thing. So, we are taking input data and manipulating it to get valuable output data. So, for more valuable output data, we want more powerful means of manipulating the data. So, where do we find the more powerful means? E.g., we are flying airplanes and want to get the work done, that is, meet the published schedule, but at minimum cost. Turns out, can do much better, save maybe 15% of direct operating costs, where just the fuel savings alone are finger lick'n good, with integer linear programming set partitioning, i.e., quite a lot of applied math, including one of the early and main leads to the question of P versus NP. Another example? Okay, how to climb, cruise, and descend an airplane for minimum cost within a given time window. There are various approaches, but a start is deterministic optimal control theory, which is some quite good and advanced applied math. E.g., once the FedEx Board wanted some revenue projections. A mess up had the representatives of crucial Board Member General Dynamics (GD) pack their bags and get plane reservations back to TX, which would have killed FedEx. Here's what pleased the GD guys and saved FedEx: We know the present revenue, and we know the revenue at our planned target market. So, the question is how to interpolate between these two. So, let t denote time, say, in days, y(t) the revenue at time t, and b the revenue per day when are serving all the planned market. Then make a 'virality' assumption, that is, that the rate of growth in revenue is directly proportional to (a) the number of current customers talking and (b) the number of potential customers listening (or the corresponding revenue). With y'(t) the calculus first derivative of y(t), that is, y'(t) is the rate of growth in revenue, in dollars per day, we have that there exists some constant k so that y'(t) = k y(t) ( b - y(t) ) There is a closed form solution via freshman calculus, and the result is a lazy S curve that rises asymptotically to the full market revenue b. So, with this bit of math, there is only one guesstimate, k. So, draw some curves for various values of k and from other considerations pick a reasonable value of k. Or estimate k from the data on the growth so far. Done. The GD guys stayed, and FedEx was saved. True story. There are many more examples, and many more to be found and executed. Net, the role of the math is to find more powerful means of processing the input data and, thus, yield more valuable output data, valuable in the sense of business, the money making kind. For the relevant math, there is nearly no limit. Fortran, Lisp, C, recursion, etc. have essentially nothing to do with the value or role of the math. The math is before the software development, leads to telling the programmers what to program, that is, what data manipulations to do. The data manipulations can be programmed in nearly any programming language although some languages are much easier for the programmer than others.