About

Matthew Tambiah

Matthew Tambiah

Matthew Tambiah

FastMath Creator

  • Former McKinsey Consultant
  • Bachelor’s from Harvard with Highest Honors in Electrical & Computer Engineering
  • MBA from MIT Sloan

Hello! My name is Matthew Tambiah, and I’m the creator of FastMath — a unique mental calculation system.

Math has always come naturally to me. I excelled in math and science subjects beginning in elementary school (I skipped 1st grade math), and continuing through high school, college at Harvard, and graduate school at MIT. In both high school and college, I frequently helped friends with math and science subjects — and this showed me first-hand that what came naturally to me didn’t come so naturally to numerous other people. Many people have told me they always found math challenging, frustrating, unintuitive, and/or difficult to understand. I have met many people who think they are “just not a math person” and believe understanding quantitative concepts is beyond their “innate ability.”

Harvard_RowingWhile I didn’t realize it when I was younger, my approach to math was always very different from the approach of my classmates in high school and college. Most people, especially those who struggle with math, have told me they learned math primarily through memorization —whereas my approach to math was to develop a thorough understanding of the underlying mathematical principles and concepts, and how to apply these principles to perform calculations and solve problems. While this approach initially took more time, it eventually simplified things, as I didn’t have to memorize lots of math facts and equations. Instead, I would naturally remember the equations as intuitive expressions of the relevant mathematical principles, and could calculate basic facts as needed.

For example, I never memorized the single-digit multiplication tables; instead, I learned the single-digit multiplication table by learning how to calculate the answers, and then repeatedly calculating the individual entries as needed. A benefit of this approach is that you can error-check any specific answer, which you can’t do if you rely on memory alone — e.g., how do you know your memory is correct?

When learning a math subject, most people memorize solution methods for specific problem types. Unfortunately, this means they have trouble solving problem types they haven’t encountered before — or even minor variations of previous problems. My approach (solving problems by understanding and using the underlying math principles, what is often called “first principles”) allowed me to solve not only variations of problems I had previously encountered but also completely new problems.

Harvard Widener LibraryWhereas most of my classmates solved problems exactly the way their instructor or textbook had specified, I always looked for the simplest and easiest way to solve a problem. I saw that I could find methods that required less work, but required a deeper understanding of the mathematics concepts involved — an understanding my peers hadn’t developed because they relied on memorization. For example, most people can multiply two-digit numbers with pen and paper. Go ahead and do the following calculation on a piece of scratch paper: 43 × 87.

Now, could you explain to a 12-year-old why the method you are using gives the correct answer? If you can’t, you don’t truly understand multiplication.

Results
My approach to math has always led to success in quantitative academic courses and standardized tests.

My academic accomplishments include:
Graduating from Harvard with Highest Honors with a Bachelor’s in Electrical and Computer Engineering
Graduate coursework at MIT in EECS with a 4.0/4.0 GPA (5.0/5.0 on the MIT Scale)
MBA from MIT

I have received the following scores on standardized tests:
Math SAT: 800/800
GMAT: 99th percentile
SAT Math II Achievement: 800/800 (currently called SAT Mathematics Level 2 Subject Test)
Advanced Placement Physics C Mechanics: 5/5

Harvard AnnenburgOrigin of FastMath Ace the Case

I developed the initial concept for the FastMath Ace the Case material when I was in business school at MIT Sloan. I was enrolled in the two-year full-time MBA program at MIT, and I spent the summer between academic years working in the technology practice at McKinsey in New York. When I returned to school for my second year, many classmates asked me to help them prepare for their Case Interviews because I had successfully navigated the interview process and received an offer to return to McKinsey. I began giving classmates mock interviews based on the Case Interview questions I had received and noticed that many people struggled with the quant problems — even people with strong math and science backgrounds.

While there were many existing Case Interview preparation books and resources, I didn’t think they did an adequate job helping people prepare for the quantitative component of Case Interviews. So I volunteered to host a workshop focused on quantitative skills for Case Interviews through MIT Sloan Management Consulting Club. My MIT classmates liked the material and thought it was very helpful in preparing for Case Interviews.

MIT DomeAfter business school, I returned to work in the tech industry for a few years and then developed the desire to start my own company. Since I had previously seen that many people struggle with math, I believed creating high-quality online math and science courses would be extremely helpful to many people. After all, if I could help my MIT classmates prepare for the quantitative component of Case Interviews, then I could most likely also help many other people prepare.

I contacted the Consulting Clubs at numerous MBA programs and offered to host a workshop focused on quant skills for Case Interviews based on my initial quant Case Interview prep Workshop at MIT Sloan. A number of schools expressed interest, and my first workshop was for for MBA students at Wharton. Then, over the course of a few months, I hosted additional workshops at Harvard, MIT, Columbia, London Business School, INSEAD, Georgetown, and other schools. I refined my material after each workshop, and then created an online course to make this material accessible to candidates around the world — and the FastMath Ace the Case Online Course was born.

The response to the FastMath Ace the Case Online Course has been overwhelmingly positive. Thousands of students — from many of the world’s top universities such as Harvard, Stanford, MIT, Wharton, Columbia, Oxford, Cambridge, INSEAD, LBS, Chicago, and Northwestern — have used the FastMath Ace the Case Online Course to prepare for Case Interviews. My students have joined McKinsey, Bain, BCG, PwC, Accenture, Deloitte, Booz Allen, and many other leading consulting firms.

More importantly, many people have said that, after taking the FastMath Ace the Case Online Course, the way they understand and approach numbers and quantitative problems is completely different.

About FastMath

In a literal sense, FastMath is a set of methods for simplifying and improving the efficiency of mathematical calculations — especially mental calculations. Collectively, these methods form a calculation system that is effective for a wide variety of calculation types and is, therefore, useful in many different scenarios.

Harvard Seaver HallHowever, this is just a surface-level description of FastMath. A deeper answer is that FastMath is an approach (or mindset) to solve math problems in the simplest way and with the least amount of effort. You can think of FastMath as the mathematical equivalent of “Lean Manufacturing,” which is derived from the Toyota Production System (TPS) and which seeks to minimize waste (“Muda”) without sacrificing productivity — i.e., achieve the desired result while expending fewer resources (both labor and material). In this sense, FastMath is a philosophy to perform math calculations and solve math problems in the simplest and easiest way possible. This is accomplished through a set of FastMath calculation methods and an understanding of when to apply each method — together these form the FastMath system.

In contrast, many other mental calculation books and resources simply provide a list of calculation methods where each method can be used only in very specific circumstances, and don’t provide a framework for handling general calculations. The methods covered often require memorizing procedures and don’t develop an intuitive understanding of math.

FastMath Examples

The best way to communicate the FastMath philosophy is through examples. Therefore, try doing the following examples purely mentally, without using a calculator, spreadsheet, or pen and paper.

FastMath Example 1

What is 16 × 35?

Example 1 Solution Method  (Expand on click)

Most people would solve this by doing longhand multiplication or decomposing 16 into 10 + 6 and calculating:
10 × 35
+ 6 × 35

This will work, but some people find this challenging to do mentally.

FastMath Method
Below is the FastMath method for this problem. It’s a different set of steps, but each step is very simple.

What is 16 ÷ 2?
Answer: 16 ÷ 2 = 8

What is 35 × 2?
Answer: 35 × 2 = 70

What is 8 × 70?
Answer: 8 × 70 = 560

Well, 16 × 35 = 560 (check with pen and paper or a calculator). You basically cut 16 in half (which is 8), double 35 (which is 70), and multiply those results (8 × 70 = 560) — and that’s the answer to the original problem (16 × 35 = 560).

This FastMath method is called the “Halve & Double” method (for obvious reasons). When multiplying numbers, you halve one number, double the other number and multiply those results.

Applying the Halve & Double method to 16 × 35 leaves us with 8 × 70, which requires only one multiplication operation of single non-zero digits, whereas the traditional longhand method for calculating 16 × 35 requires four single-digit multiplication operations as well as addition.

The Halve & Double method will work when multiplying any numbers, but is most effective when one digit ends in a “5” (so doubling it results in a number ending in “0”) and the other number is even (so halving it gives a whole number that is smaller and, hopefully, has fewer digits). Since “35” ends in “5” and “16” is even, using the Halve & Double method will simplify this calculation.

You can also use variations of the Halve & Double method in scenarios where these conditions don’t apply.

FastMath Example 2

What is 16% of 25?

Example 2 Solution Method  (Expand on click)

This problem is difficult because 16% is not a round number. Most people would calculate 10% of 15, then perhaps add 6% of 25. Again, this is challenging to do mentally.

FastMath Method
Let’s first solve a related calculation, which should be simpler: what is 25% of 16?

That should be easier:
25% = ¼
25% of 16 = ¼ × 16 = 4

Well, guess what — that’s the answer to the original problem of 16% of 25.

That is: 16% × 25 = 25% × 16 = 4. You can check this with a calculator.
More generally, X% of Y = Y% of X.

This FastMath method is called a Percentage Swap.

For a more detailed explanation of why these methods work — and to challenge your mental math skills — watch this video:

FastMath Example 3

What is the average of 183, 187, 182, 183, and 185?

Example 3 Solution Method (Expand on click)

If your approach for solving this problem is adding up all the numbers and divide by 5 (which is the how the average of a set of numbers is defined), you may find this calculation difficult to do mentally.

FastMath Method

The FastMath method for this problem is to recognize that all the numbers are close to 180. Therefore, for each element, we will calculate the difference between that element and 180 by subtracting 180 from each element. For 183, the difference from 180 is 183 − 180 = 3. Subtracting 180 from each number gives the sequence: 3, 7, 2, 3, 5. For these numbers, this can easily be done by simply removing the first two digits of each number, and looking only at the last digit.

Now, we add up all these numbers, which is 20 (3 + 7 + 2 + 3 + 5 = 20). For easier addition, you may want to group these numbers into two sets of 10 (3 + 7 = 10; 2 + 3 + 5 = 10).

Now, we divide this result (20) by the number of elements (5): 20 ÷ 5 = 4.

The average is then 4 more than 180, which is 184 (180 + 4 = 184).

This method may seem complicated, but, with a little practice, it becomes easy to calculate the average of a set of numbers if the numbers are somewhat close together.

Process:
Pick an Anchor value
Subtract the Anchor from each value in the set
Sum the elements from Step 2
Divide the result of Step 3 by the number of elements
Add the result of Step 4 to the Anchor

Notes
The result is independent of the choice of the Anchor
Values in the initial set that are less than the Anchor become negative values in Step 2. For example, if the initial sequence included the value 178 — and we used an Anchor of 180 — this would become a value of −2 (178 − 180 = −2) after Step 2. Step 2 therefore calculates the signed difference between each element in the set and the Anchor, which is defined as subtracting the Anchor from each element.

Goals

My goal in creating FastMath is to teach you how I think about math and how I approach solving mathematical problems. Simultaneously, I want to make math more intuitive and easier to understand and apply. I try to do this by teaching an understanding of the underlying math principles instead of teaching math through memorization and repetition (i.e., “drill and kill”).

After learning FastMath, many people have said they see math in a completely different light, and aren’t intimidated by math or quantitative topics anymore — in a sense they feel mathematically “enlightened.” It is my goal to help as many people as I can achieve a similar understanding of math.

I also believe that the FastMath methods and approach to problem solving would be useful to a wide variety of people, and not just people preparing for Case Interviews. Therefore, I am working on creating a new online course designed for a broader audience, called FastMath Foundations, which will teach general mental calculation skills that can be used in a wide variety of scenarios. FastMath Foundations is intended to be useful for people who work with numbers in a professional environment such as finance, marketing, or accounting; people studying for standardized tests such as the SAT, ACT, GRE, or GMAT; students in math or quantitative academic subjects such as algebra or economics; and people planning a large financial purchase such as furniture, a car, a house, or investment in a company. FastMath Foundations will also have methods for unit conversions — such as Fahrenheit to Celsius, kilograms to pounds, and miles to kilometers — and currency conversions, which will be useful for people who travel internationally.

WordPress Lightbox Plugin