mathematics

Johan Håstad

Johan Håstad is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Johan Håstad rather than just read about it. In short: Johan Torkel Håstad (Swedish pronunciation: [ˈjûːan ˈhǒːsta]; born 19 November 1960) is a Swedish theoretical computer scientist most known for his work on computational complexity theory. He was the recipient of the Gödel Prize in 1994 and 2011 and the ACM Doctoral Dissertation Award in 1986, among other prizes.

Key takeaways

Johan Håstad belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Johan Håstad to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Johan Håstad from memory before moving on to harder problems.

Reference excerpt

Johan Torkel Håstad (Swedish pronunciation: [ˈjûːan ˈhǒːsta]; born 19 November 1960) is a Swedish theoretical computer scientist most known for his work on computational complexity theory. He was the recipient of the Gödel Prize in 1994 and 2011 and the ACM Doctoral Dissertation Award in 1986, among other prizes. He has been a professor in theoretical computer science at KTH Royal Institute of Technology in Stockholm, Sweden since 1988, becoming a full professor in 1992. He is a member of the Royal Swedish Academy of Sciences since 2001. He received his B.S. in Mathematics at Stockholm University in 1981, his M.S. in Mathematics at Uppsala University in 1984 and his Ph.D. in Mathematics from MIT in 1986. Håstad's thesis and 1994 Gödel Prize concerned his work on lower bounds on the size of constant-depth Boolean circuits for the parity function. After Andrew Yao proved that such circuits require exponential size, Håstad proved nearly optimal lower bounds on the necessary size through his switching lemma, which became an important technical tool in circuit complexity with applications to learnability, the IP hierarchy, and proof systems. He also received the 2011 Gödel Prize for his work on optimal inapproximability results. In particular, he improved the PCP theorem (which won the same prize in 2001) to give a probabilistic verifier for NP problems which reads only three bits. Further, he used these results to prove results in hardness of approximation. In 1998 Håstad was an Invited Speaker of the International Congress of Mathematicians in Berlin. In 1999 he was an Erdős Lecturer at the Hebrew University of Jerusalem. In 2012, he became a fellow of the American Mathematical Society. He was elected as an ACM Fellow in 2018 for "contributions in circuit complexity, approximability and inapproximability, and foundations of pseudorandomness". In 2018 he received the Knuth Prize "for his long and sustained record of milestone breakthroughs at the foundations of computer science, with huge impact on many areas including optimization, cryptography, parallel computing, and complexity theory."

References

External links Johan Håstad's home page Johan Håstad's results at International Mathematical Olympiad

Worked examples

Example 1 — a first encounter with Johan Håstad

Start with the simplest possible case. Write down what Johan Håstad claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Johan Håstad before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Johan Håstad ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Johan Håstad

In research: Johan Håstad appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Johan Håstad in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Johan Håstad is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1960 births, 20th-century Swedish mathematicians, 21st-century Swedish mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Johan Håstad outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Johan Håstad in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Johan Håstad means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Johan Håstad out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Johan Håstad in simple terms?

Why does Johan Håstad matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Johan Håstad?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Johan Håstad.