What do you do if you need to simplify complex mathematical concepts in an interview?

Analogies allow you to draw comparisons between the unfamiliar mathematical concept and something familiar to the interviewer. For example, if you want to explain non-linear dynamics or instability in fluid flow through mathematical concept (i.e Navier Stokes equation) you can use analogy for behavior of human which is extremely non linear in nature and if given certain perturbations to the human how does human respond to that perturbations. This approach makes the abstract more concrete and can make a lasting impression on your interviewer.

I’m a personal fan of analogies. The ability to use analogies is an indication of a comprehensive understanding of the mathematical principles you’re being questioned about. Do not try to force a comparison but let it be a second nature to explain concepts on your with analogies on your own even when you’re not preparing for an interview.

Try explaining the context where the mathematical concept was first discovered. Mathematical concepts usually have a very simple core problem they're trying to solve. They only become complex under very specific circumstances

In some sense, mathematics is a means of formalizing analogies. A lot of the time when you make an analogy between something familiar and some abstract mathematical concept, you're in effect just providing a concrete example of the mathematics in an indirect way. Thus, rather than make an analogy, I'd rather select a tangible and commonplace example of the mathematics I'm trying to describe and explain that example and how it demonstrates the broader theory.

With analogies you can give examples of certain edge cases as well. This will depict your ability to go beyond the norm. For example, in promotional modeling & optimization of a new item without any history, you can explain how its closest matching or clone can be used to predict the discount that will maximize the profit. This clone is identified using certain characteristics of the new item such as its category, market size, brand, audience etc that is used to calculate a similarity score between 0 & 1. Once a clone is identified you can use its optimised results as reference to your new item until the new item accommodates enough history for model training.

Analogies are like bridges that connect complex mathematical concepts to more familiar ideas. Once, during an interview, I was asked to explain the concept of derivatives. I compared it to driving a car: just as speed tells you how fast you're going, the derivative tells you how fast a function is changing at a specific point. By likening derivatives to speedometers, I helped the interviewer grasp the concept easily. Analogies create a shared understanding, making complex topics more accessible and memorable.

Make assumptions. Simplify your problem by reducing the factors that will affect your answer. Make clear to your employer the assumptions you are making and the effects they will have on your calculation. For many fields, you can still produce a surprisingly accurate result within the correct order of magnitude by understanding your problem and reducing its complexity.

I find it's best to use real world examples and tailor them to fit either your interviewer's personal interests or the company itself. This way, when you are using analogies to explain, you have established a commonality between the material (complex mathematical concept) and the viewer (your interviewer).

Mathematics, among other things, is a language. And like most languages, it can be translated using analogies. Furthermore, the laws of the universe are built on mathematics. So while you may not realise it, you can see, hear and feel mathematics just by observing the world around you.

People cannot understand everything with text or formulas. I cannot fathom trying to understand concepts without some use of visual aids. By providing visual aids, like graphs, tables, pictures, etc., the gap can be closed in terms of understanding a lot of mathematical concepts.

Utilising graphical visualisations whilst explaining difficult concepts is a technique I have used with great success in interviews. It firstly demonstrates a desire to prepare some materials for the interview, providing a good first impression. It also enables clearer engagement from interviewers - I found that having visuals prepared enabled interviewers to ask targeted questions, and make the subject matter approachable, as often the interviewers hadn’t previously encountered the mathematical concepts I was explaining. It allows both interviewer and interviewee to keep conversation concentrated, rather than trying to keep up with memorising a concept that someone had orally explained.

Visual aids are powerful allies in simplifying mathematical concepts. Once, I used a simple graph to explain the concept of slope-intercept form in algebra. I drew a line on a graph and showed how its slope represented the rate of change, while the intercept showed where it intersected the y-axis. This visual representation helped the person I was explaining it to understand the relationship between the equation of a line and its graphical representation. Visual aids like graphs, diagrams, or even simple drawings can make abstract concepts more tangible and easier to grasp for everyone.

Start with the core makeup of the concept you are being asked to break down. This way the problem may become more accessible to the 'learner'. Then build to reach the desired outcome of the task.

Technical terms aid precision and conciseness when constructing the rules that make up mathematics. But behind every technical term and complex theory, there is usually a simple concept (or a collection of them) that can be explained using everyday language.

Simplifying terms without diluting their meaning is crucial when discussing complex mathematical concepts. During one discussion, I explained the concept of integration using the term "accumulation." Instead of diving into technical jargon, I emphasized that integration is like adding up small pieces to find the total accumulation, which resonated well with the audience. Simplifying terms helps build understanding without sacrificing accuracy, ensuring that everyone can follow along and grasp the essence of the concept.

Start with the simplest modelling representation that conceptualises the problem. Once you understand that and can explain it, add further modelling complexity to gain better insight into the intricacies of the problem. With this understanding, you can communicate a good narrative for the intended outcome.

When simplifying complex mathematical concepts in interview, consider -utilizing appropriate visual representation (diagrams, graphs or illustrations) and explain using real-life scenarios that can be easily understood by the interviewers.

When attempting to simplify a complex mathematical concept in an interview, it's crucial to know your audience. Real Life examples only work when the person receiving them understands that perspective or experience. Take what you've learned from them during or before the interview and use that to narrow down what kind of examples work best. Rather than having a generic, "catch-all" example, you'll stand out with something that's tailored to the person you're speaking to; it's a great way of showing that you're a good listener as well.

Relating complex mathematical concepts to real-life situations can significantly aid understanding. For instance, when explaining the concept of probability, I likened it to weather forecasting. Just as meteorologists predict the likelihood of rain based on various factors, probability calculates the likelihood of certain outcomes in events. By connecting abstract mathematical ideas to everyday experiences like weather predictions, I helped others see the relevance and practical applications of these concepts, making them more relatable and easier to comprehend.

This is perhaps the most important point. In most business settings, core decision-makers are not mathematicians, and decisions are made with profitability in mind. The math behind operations research (e.g. finding an objective minima using Simplex algorithm) will not be enough to convince/influence decisions. Rather, show that your model incorporated business constraints (e.g. xx workers available, yy raw materials/month) (NOT IN MATH FORM), as well as the objective (e.g. how profit is calculated, and if your maximizing profits/minimizing costs), and present the decision variables + expected profit improvements. They see your qualitative framing of the problem, and see quantitative outputs from your math, that's what convinces them.

You can't plan a journey if you don't know where you're going in the first place. Likewise, outcomes help focus the mind on what is important, and guide people towards the most practical and efficient solutions to a problem.

Most people don't really care about the nuts and bolts: they are concerned with what they need to do to make things run well and want to know what comes out that's useful. Focusing on costs and inputs as well as impacts and ROI are going to be far more understandable. If they ask questions, you can always go deeper.

When simplifying mathematical concepts, it's essential to focus on the outcomes rather than getting bogged down in intricate details. For example, when explaining the concept of multiplication, I emphasized its practical application in situations like calculating the total cost of items when shopping. Instead of delving into the mechanics of multiplication, I highlighted how it helps in quickly determining the total quantity or price, which resonated well with the audience. By prioritizing the end result and showcasing the usefulness of the concept, understanding becomes more intuitive and engaging for learners.

Teachers are made, not born. What works as an explanation for one person, won't necessarily be useful for someone else whose brain works differently. Only through practice and experience can someone develop the skill of explaining things to others.

This comes with practice and more experience interacting with non-technical stakeholders through collaboration. Not an easy task but being able to explain very technical concepts in lay terms is a special skill that every OR professional needs to excel.

Integrating storytelling to discuss complex mathematical concepts during interviews is essential for effective communication, ensuring you develop a shared understanding with interviewers. The use of analogies, visual aids, and real-world examples helps to bridge the gap between technical complexity and audience comprehension. Use simple language and engage directly with interactive and personal elements to enhance understanding. Such an approach ensures that the audience grasps the technical content and appreciates its relevance and application in real-world scenarios. Applying these ideas fosters a shared understanding that extends beyond technical knowledge to a deeper appreciation of how these concepts deliver business value.