mathematics

Mahesh Kakde

Mahesh Kakde 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 Mahesh Kakde rather than just read about it. In short: Mahesh Ramesh Kakde (born 1983) is a mathematician working in algebraic number theory. Biography Mahesh Kakde was born on 1983 in Akola, India.

Key takeaways

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

Reference excerpt

Mahesh Ramesh Kakde (born 1983) is a mathematician working in algebraic number theory.

Biography Mahesh Kakde was born on 1983 in Akola, India. He obtained a Bachelor of Mathematics degree at the Indian Statistical Institute in Bangalore in 2004, and a Certificate of Advanced Study in Mathematics at the University of Cambridge in 2005. He completed his PhD under the supervision of John Coates at the University of Cambridge in 2008. He subsequently worked at Princeton University, University College London, and King's College London, before becoming a professor at the Indian Institute of Science in 2019.

Research Kakde proved the main conjecture of Iwasawa theory in the totally real μ = 0 case. Together with Samit Dasgupta and Kevin Ventullo, he proved the Gross–Stark conjecture. In a joint project with Samit Dasgupta, they proved the Brumer–Stark conjecture away from 2 in 2020, and later over Z {\displaystyle \mathbb {Z} } in 2023. Generalising these methods, they also gave a solution to Hilbert's 12th problem for totally real fields. Their methods were subsequently used by Johnston and Nickel to prove the equivariant Iwasawa main conjecture for abelian extensions without the μ = 0 hypothesis.

Awards In 2019, Kakde was awarded a Swarnajayanti Fellowship. Together with Samit Dasgupta, Kakde was one of the invited speakers at the International Congress of Mathematicians 2022, where they gave a joint talk on their work on the Brumer–Stark conjecture. In 2022, Kakde received the Infosys Prize for his contributions to algebraic number theory. In his congratulatory message, Jury Chair Chandrashekhar Khare noted that "[Kakde’s] work on the main conjecture of non-commutative Iwasawa theory, on the Gross-Stark conjecture and on the Brumer-Stark conjecture has had a big impact on the field of algebraic number theory. His work makes important progress towards a p-adic analytic analog of Hilbert’s 12th problem on construction of abelian extensions of number fields." In 2023, Kakde became a laureate of the Asian Scientist 100 by the Asian Scientist.

References

External links Official website Old official website at King's College London

Worked examples

Example 1 — a first encounter with Mahesh Kakde

Start with the simplest possible case. Write down what Mahesh Kakde 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 Mahesh Kakde 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 Mahesh Kakde 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 Mahesh Kakde

In research: Mahesh Kakde 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 Mahesh Kakde 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: Mahesh Kakde is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1983 births, 21st-century Indian mathematicians, Academic staff of the Indian Institute of Science, so understanding it makes those chapters shorter.
In everyday life: Look for Mahesh Kakde 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 Mahesh Kakde in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Mahesh Kakde 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 Mahesh Kakde out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Mahesh Kakde in simple terms?

Mahesh Ramesh Kakde (born 1983) is a mathematician working in algebraic number theory. Biography Mahesh Kakde was born on 1983 in Akola, India.

Why does Mahesh Kakde 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 Mahesh Kakde?

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 Mahesh Kakde.