ESP Biography



BENJAMIN KRAFT, MIT graduate, math major, software engineer




Major: Math

College/Employer: MIT

Year of Graduation: 2015

Picture of Benjamin Kraft

Brief Biographical Sketch:

I'm a crazy math person. I grew up in Bethlehem, PA, did lots of math competitions and summer math programs, and then went to MIT and loved it! I majored in math with a sprinkling of physics, CS, and political science. In my spare time I organized and taught for ESP programs, and ran the Association of Student Activities. Now I'm a software engineer at Khan Academy.



Past Classes

  (Look at the class archive for more.)


How to Run A Splash in Splash 2018 (Nov. 17 - 18, 2018)
Ever thought about what happens behind-the-scenes when you sign up for Splash classes? Or how all of our teachers and classes fit into MIT's classrooms? Splash takes months to plan, and for good reason. Come learn how we make Splash happen every year!


Gerrymandering: Theory and Practice in Splash 2018 (Nov. 17 - 18, 2018)
Gerrymandering: America's favorite political power play since 1812. We'll learn how and why parties draw congressional districts with nicknames like "The Pinwheel of Death", "The Mistake by the Lake", and "The 8 Mile Mess", and why it's hard to outlaw such madness. Then you'll get to try your hand at gerrymandering, to see if you can do better than your classmates at getting more seats for your party.


How to Run A Splash in Splash 2017 (Nov. 18 - 19, 2017)
Ever thought about what happens behind-the-scenes when you sign up for Splash classes? Or how all of our teachers and classes fit into MIT's classrooms? Splash takes months to plan, and for good reason. Come learn how we make Splash happen every year!


Gerrymandering: Theory and Practice in Splash 2017 (Nov. 18 - 19, 2017)
Gerrymandering: America's favorite political power play since 1812. We'll learn how and why parties draw congressional districts with nicknames like "The Pinwheel of Death", "The Mistake by the Lake", and "The 8 Mile Mess", and why it's hard to outlaw such madness. Then you'll get to try your hand at gerrymandering, to see if you can do better than your classmates at getting more seats for your party.


Between the Lines: Crosswords and Coloring! in Splash 2017 (Nov. 18 - 19, 2017)
We've got coloring books, Crayola crayons, and crosswords. Shade within the lines of your drawings or write letters inside the lines of a grid. It's like kindergarten all over again!


Gerrymandering: Theory and Practice in Splash 2016 (Nov. 19 - 20, 2016)
Gerrymandering: America's favorite political power play since 1812. We'll learn how and why parties draw congressional districts with nicknames like "The Pinwheel of Death", "The Mistake by the Lake", and "The 8 Mile Mess", and why it's hard to outlaw such madness. Then you'll get to try your hand at gerrymandering, to see if you can do better than your classmates at getting more seats for your party.


Elections: Theory and Practice in Splash 2016 (Nov. 19 - 20, 2016)
Congratulations to ???, the 45th President of the United States! By the time you take this class, we'll know how to fill in that blank, along with who will control the House and Senate, whether Massachusetts has legalized marijuana, and the results of thousands of other state and local races across the country. So we'll talk about all of that! Topics will probably include who won, which pundits, forecasters, and politicians were wrong, what it means for the government and the country, and why it happened. Sore winners and sore losers not welcome; leave your gloating and moaning at the door.


Preference and Policy in Spark 2016 (Mar. 12 - 13, 2016)
Do legislators vote for what they want, what their constituents want, what they think their constituents want, what their constituents should want, what will be best for the country, what will be best for their constituents, or for something else entirely? What should they vote for? How should they know what to vote for? In this class, we'll talk about possible answers to these questions, about research on what the members of the American congress actually do. We'll also talk about how we can use the methods of political science to make these questions precise and answer them in a scientific way.


Gerrymandering: Theory and Practice in Splash 2015 (Nov. 21 - 22, 2015)
Gerrymandering: America's favorite political power play since 1812. We'll learn how and why parties draw congressional districts with nicknames like "The Pinwheel of Death", "The Mistake by the Lake", and "The 8 Mile Mess", and why it's hard to outlaw such madness. Then you'll get to try your hand at gerrymandering, to see if you can do better than your classmates at getting more seats for your party.


How to run a Splash! in Splash 2015 (Nov. 21 - 22, 2015)
Step 1: Get teachers. Step 2: Get students. Step 3: ??? Step 4: SPLASH! Want to know what the ”???” is? Come find out how we make Splash happen! Presented by the directors of several past Splashes.


Lie Groups: Theory and Practice in Splash 2015 (Nov. 21 - 22, 2015)
Ever wonder what geometry, differential equations, and subatomic particles have in common? Ever find yourself with a matrix $$A$$ and wonder how to compute $$e^A$? Probably not. But now you will! Welcome to the world of Lie groups, where matrices, differential equations, and symmetry come together to solve differential equations, understand the symmetry of geometric objects, and describe the most fundamental structure of our universe. We'll talk about how the study of Lie groups came about, what they are, and how they've been used in physics and math ever since. Oh, and we'll come out with some cool tricks like taking the exponential of a matrix.


Giant Modular Origami in Spark 2015 (Mar. 14 - 15, 2015)
Make giant modular origami using old ESP flyers!


Preference and Policy in Spark 2015 (Mar. 14 - 15, 2015)
Do legislators vote for what they want, what their constituents want, what they think their constituents want, what their constituents should want, what will be best for the country, what will be best for their constituents, or for something else entirely? What should they vote for? How should they know what to vote for? In this class, we'll talk about possible answers to these questions, about research on what the members of the American congress actually do. We'll also talk about how we can use the methods of political science to make these questions precise so that we can apply data to them.


Gerrymandering: Theory and Practice in Splash 2014 (Nov. 22 - 23, 2014)
Gerrymandering: America's favorite political power play since 1812. We'll learn how and why parties draw congressional districts with nicknames like "The Pinwheel of Death", "The Mistake by the Lake", and "The 8 Mile Mess", and why it's hard to outlaw such madness. Then you'll get to try your hand at gerrymandering, to see if you can do better than your classmates at getting more seats for your party.


Learning Programming Through Elm in Splash 2014 (Nov. 22 - 23, 2014)
Let's say you're in math class, and you're supposed to be solving an equation, but rather than find out how old Bill is who will be twice as old as Mary in seven years you'd prefer to think about how in seven years you'll have taken over the entire world and surely equations won't get you any closer to world domination... Enter computer programming, also known as writing equations for world domination. This course will be a fast-paced introduction to programming. We'll be using Elm, a functional reactive programming language for web graphics with nice properties that let us reason about our programs as if they were mathematical equations. We'll learn how these properties make it a great programming language and how we can write programs in Elm that do cool things. This is intended to serve as a first course in programming; no programming experience is necessary.


Giant Modular Origami in Splash 2014 (Nov. 22 - 23, 2014)
Make giant modular origami using old ESP flyers!


Giant Modular Origami in Spark 2014 (Mar. 15 - 16, 2014)
Make giant modular origami using old ESP flyers!


Learning Programming Through Haskell in HSSP Spring 2014 (Mar. 01, 2014)
Let's say you're in math class, and you're supposed to be solving an equation, but rather than find out how old Bill is who will be twice as old as Mary in seven years you'd prefer to think about how in seven years you'll have taken over the entire world and surely equations won't get you any closer to world domination... Enter computer programming, also known as writing equations for world domination. This course will be a fast-paced introduction to programming. We'll be using Haskell, a purely functional programming language with nice properties that let us reason about our programs as if they were mathematical equations. We'll learn how these properties make it a great programming language and how we can write programs in Haskell that solve real problems. This is intended to serve as a first course in programming; no programming experience is necessary.


INTEGARLS in Splash! 2013 (Nov. 23 - 24, 2013)
Come learn about INTEGARLS like those found in the MIT Integration Bee! We'll be teaching a number of cool integration tricks, like crazy tangents and swingy-swingy.


Infinitely Many Proofs of Infinitely Many Primes! in Splash! 2013 (Nov. 23 - 24, 2013)
How many primes are there? INFINITELY MANY! How many different ways can you prove that? INFINITELY MANY! Unfortunately, Splash isn’t infinitely long, so we’ll only have time to cover $$\infty - 1$$ ways.


Ninjas in Splash! 2013 (Nov. 23 - 24, 2013)
Play Ninjas, a game of "one smooth motion".


Learn You A Haskell: Functional Programming in Splash! 2013 (Nov. 23 - 24, 2013)
FUNCTIONS ARE DATA LISTS ARE INFINITE HASKELL IS FUN Haskell is a purely functional, strongly typed programming language with non-strict evaluation. If none of those words made sense to you, you should take this class to fix that! We'll talk about the basics of programming in Haskell, why it's the best programming language, and how you can fit an infinite list in your computer's memory.


Why Relativity isn't Paradoxical in Splash! 2013 (Nov. 23 - 24, 2013)
Popular culture tells us that Einstein's theory of relativity is hard to understand, full of paradoxes, and generally doesn't make sense. We'll learn why it's really quite natural if you look at it the right way, and why the supposed paradoxes aren't. We'll also learn why electromagnetism doesn't fully make sense without relativity. On the way, we'll go though the basics of relativity, in case you ever find yourself moving at $$0.99c$$ and need to know what's going on.


Why all polls are wrong, and why they're still useful in Splash! 2013 (Nov. 23 - 24, 2013)
What percentage of Americans support Obamacare? What about the Affordable Care Act? What about a law that requires that individuals buy health insurance, expands Medicaid, prohibits insurance companies from denying coverage on the basis of a pre-existing condition, and creates health insurance exchanges in each state? All three refer to the same law, but they have wildly different approval rates in the polls. In this class, we'll be examining the challenges of polling, how pollsters try to compensate for them, when it works, and when it doesn't. We'll also discuss how polling and its successes and failures affect our government and society.


How to run a Splash in Splash! 2013 (Nov. 23 - 24, 2013)
Step 1: Get teachers. Step 2: Get students. Step 3: ??? Step 4: SPLASH! …want to know what the ”???” is? Come find out how we make Splash happen! Presented by the directors of several past Splashes.


Primes, probability, Pascal, permuations, and paths: a primer on problems in HSSP Summer 2013 (Jul. 07, 2013)
Math is marvellous! But math makes minds like mine mushy without mathematical muscles. Formulas are fun, but trying techniques and tools to think about things as a team is terrific. We'll work our way through worlds of wacky wonders, and study to surmise solutions! In English: there's a lot more to math than formulas. What's more important is learning techniques for putting facts and formulas, along with a bit of logic and common sense, together into solutions to problems you've never seen before. If you're interested in math competitions, problem solving is important for those, but it's also incredibly important for solving problems in the real world. We'll have fun learning about all these things and solving problems together!


How to Fold Everything in HSSP Spring 2013 (Mar. 02, 2013)
Take a tour of the world of origami! If you think origami is only about folding cranes, you'll find out just how much more there is to it. We'll start out with traditional origami models, and move on to more complex modern models. We'll also do some modular origami (made from many smaller units rather than a single square). Finally, we'll talk about the basics of origami design, and about why you really can fold everything.


The Most Overpowered Programming Language in Spark! 2013 (Mar. 16, 2013)
You may (or may not) have heard of object oriented programming (abbreviated OOP). But wouldn't you rather your programming language be overpowered (abbreviated OP)? Come learn about Haskell, which is not at all OOP but totally OP! You can make an infinite list of prime numbers, define your very own algebraic data types, win all sorts of (combinatorial) games with the same piece of code, and even print "Hello, world!" to the screen. Don't worry if you don't know what all of those words mean yet—come find out!


INTEGARLS in Spark! 2013 (Mar. 16, 2013)
Come learn about INTEGARLS like those found in the MIT Integration Bee! We'll be teaching a number of cool integration tricks, like crazy tangents and swingy-swingy.


Why Relativity isn't Paradoxical in Spark! 2013 (Mar. 16, 2013)
Popular culture tells us that Einstein's theory of relativity is hard to understand, full of paradoxes, and generally doesn't make sense. We'll learn why it's really quite natural if you look at it the right way, and why the supposed paradoxes aren't. We'll also learn why electromagnetism doesn't fully make sense without relativity. On the way, we'll go though the basics of relativity, in case you ever find yourself moving at $$0.99c$$ and need to know what's going on.


Ninjas in Splash! 2012 (Nov. 17 - 18, 2012)
Play ninjas, a game of "one smooth motion".


Learn You A Haskell: Functional Programming in Splash! 2012 (Nov. 17 - 18, 2012)
FUNCTIONS ARE DATA LISTS ARE INFINITE HASKELL IS FUN Haskell is a purely functional, strongly typed programming language with non-strict evaluation. If none of those words made sense to you, you should take this class to fix that! We'll talk about the basics of programming in Haskell, why it's the best programming language, and how you can fit an infinite list in your computer's memory.


INTEGARLS in Splash! 2012 (Nov. 17 - 18, 2012)
Come learn about INTEGARLS from two finalists in the MIT Integration Bee! We'll be teaching a number of cool integration tricks, like crazy tangents and swingy-swingy.


Infinitely Many Proofs of Infinitely Many Primes! in Splash! 2012 (Nov. 17 - 18, 2012)
How many primes are there? INFINITELY MANY! How many different ways can you prove that? INFINITELY MANY! Unfortunately, Splash isn’t infinitely long, so we’ll only have time to cover $$\infty - 1$$ ways.


Game Theory, or How I Learned to Stop Losing and Love Math in HSSP Spring 2012 (Feb. 18, 2012)
HEY! Do you want to play games with MORE MATH? Take our class, and we'll play games with GRATUITOUS AMOUNTS OF MATH! In particular, we'll be studying the mathematics of game theory. In what games can we figure out which player has a winning strategy? In what games can we do this quickly? What interesting bits of math come out of such studies? You'll try to find the answers.


Math for Middle School Lecture Series in HSSP Spring 2012 (Feb. 18, 2012)
Math is not about formulas and symbols: it’s about finding patterns! If three people want to all introduce themselves to each other, how many introductions will take place? Just three! But what about ten people? What about a thousand? Through interactive lectures, this class will introduce quirky mathematical topics not covered in regular curricula (number theory, graph theory, logic, set theory, geometry, etc.) The lectures are intended for middle school students. The class will consist of a lecture from a different teacher every week, on a variety of math topics accessible to middle schools students.


World News Lecture Series in HSSP Spring 2012 (Feb. 18, 2012)
Are you not content with just “living your life”, oblivious to the terrors happening around the world every day? Have no fear! This class will cover the past week’s world news, keeping YOU updated! Each week’s class will be taught by a different teacher, talking about the events that shape our world today.


Paper Engineering! in Spark! 2012 (Mar. 10, 2012)
Come build awesome things out of paper! We'll have different engineering challenges using paper, rotating every half hour. Build paper airplanes, bridges, and towers!


Ninjas in Spark! 2012 (Mar. 10, 2012)
Be a ninja in Lobby 13.


Colorful Throwable Paper Math (Modular Origami) in Spark! 2012 (Mar. 10, 2012)
Some people like to do their math on paper. But I like to do math *with* paper. Some people like to do their origami with one piece of paper. I like *lots* of paper. So we'll be combining the two, and folding lots of little pieces of paper (that is, making modular modular origami) and using a bit of math to make colorful throwable paper dodecahedra. If we have time, we might even make buckyballs or donuts or something else; you'll definitely leave knowing how to make such things. And then you can throw your math at your friends! For the math-haters: We might talk a bit about some of the math going on, but don't worry if you aren't a math person. For the math-lovers: If you want to hear about it, there's lots of graph theory and a little topology going on that we can talk about.


Infinitely Many Proofs of Infinitely Many Primes! in Spark! 2012 (Mar. 10, 2012)
How many primes are there? INFINITELY MANY! How many different ways can you prove that? INFINITELY MANY! Unfortunately, Spark isn’t infinitely long, so we’ll only have time to cover $$\infty - 1$$ ways.


INTEGARLS in Spark! 2012 (Mar. 10, 2012)
Come learn about INTEGARLS from two finalists in the MIT Integration Bee! We'll be teaching a number of cool integration tricks, like crazy tangents and swingy-swingy.


Colorful Throwable Paper Math (Modular Origami) in Splash! 2011 (Nov. 19 - 20, 2011)
Some people like to do their math on paper. But I like to do math *with* paper. Some people like to do their origami with one piece of paper. I like *lots* of paper. So we'll be combining the two, and folding lots of little pieces of paper (that is, making modular modular origami) and using a bit of math to make colorful throwable paper dodecahedra. If we have time, we might even make buckyballs or donuts or something else; you'll definitely leave knowing how to make such things. And then you can throw your math at your friends! For the math-haters: We might talk a bit about some of the math going on, but don't worry if you aren't a math person. For the math-lovers: If you want to hear about it, there's lots of graph theory and a little topology going on that we can talk about.


Nerd Sniping in Splash! 2011 (Nov. 19 - 20, 2011)
Problems. We will have them. You will do our problems. Mathy/physicsy/CSy/logicy/whatevery problems!


Ninjas in Splash! 2011 (Nov. 19 - 20, 2011)
Be a ninja in Lobby 13.


Infinitely Many Proofs of Infinitely Many Primes! in Splash! 2011 (Nov. 19 - 20, 2011)
How many primes are there? INFINITELY MANY! How many different ways can you prove that? INFINITELY MANY! Unfortunately, Splash isn’t infinitely long, so we’ll only have time to cover $$\infty - 1$$ ways.


How to Fold Everything in DELVE (Spic)
You may think origami is hard. You may even think there are things that can't be folded. In this class, ...