‘It’s like writing a poem’: prize winner Rajula Srivastava on doing maths

When Rajula Srivastava was first informed about a prestigious award, he was quick to reject him. All he bought was a encrypted e -mail that asked me if the mathematician Terence Tao was free to chat at his personal e -mail address. Tao, a professor in the University of California, Los Angeles, is considered one of the most talented mathematicians of our time. Srivastava couldn’t think of a reason he would want to talk to him.

“Frankly, I thought it was a scam,” he said.

But then ten minutes later he took a second e -mail from him and asked to zoom. After determining that the e -mail was not fake, he continued to respond carefully. During his conversations, Tao broke the news that Maryam Mirzakhani, an attempt of a groundbreaking award for his work in harmonic analysis and analytical number theory, won the New Frontiers Award. He couldn’t believe it.

“I told him that I thought it was a deception and he found it very funny, [saying] ‘Maybe I want to wander a theorem from you,’ he said, laughing. [the call] gone.”

A love for puzzles

The University of Bonn Hirzebrach Research Trainer and the Max Planck Mathematics Institute in Germany Grew up in a family -loving family.

At school, mathematics was the most enjoyable subject among all sciences: because it contained at least memorization. “After understanding the logic behind something, you don’t have to memorize many things beyond the impact paintings in the kindergarten,” he said.

He also noticed that he didn’t like to do laboratory, but he liked to solve puzzles. At the age of 15, he decided that he wanted to be a mathematician and continued to be an integrated master’s degree at the Bhubaneshwar National Science Education and Research Institute (NİSER), which he specializes in mathematics.

Later, he wrote his master’s thesis harmonic analysis, how they could be represented in terms of examination and frequencies of functions – a subject he began to love. For the doctor, he chose to go to Wisconsin-Madison University mainly due to the large harmonic analysis group.

Just as music can be divided into harmony, the signals can be divided into frequencies that make up them. “But you need to be able to do this logically, so that the information you have in this failure should be in a way that you need to be able to rebuild your complex signal once again.”

This is the idea of harmonic analysis in which frequencies or “harmonics değerlendiri using a method called Fourier Transformation. Srivastava, you can imagine that you can imagine that these frequencies lie in a line, but you can ask these questions in higher sizes. “Then geometry is also about the patterns and shapes where these waves are arranged.”

To imagine a three -dimensional wave, imagine fluctuations from an earthquake while echoing a sound wave traveling from all directions through molecules in the air. In any case, there is a point where vibration occurs, and the resulting waves then form the shape of a sphere. The vibrations move outward as radially perpendicular to the expanding wave. His studies were mostly focused on waves of three or even higher size.

To identify numbers in a line

After a doctoral degree, Srivastava continued his post -doctoral research in Germany and accepted a common position between Bonn University Math Department and Max Planck Mathematics Institute in Bonn. When he spent there, he began to be divided into problems in the interface of harmonic analysis and number theory from 2022 to 2024.

At the same time, her husband, a mathematician and a number theorist, introduced her to the first counting problems. However, more than the potential practices of number theoretical problems, Srivastava was purely motivated. With his expertise in harmonic analysis, he knew that he was a bag of bag at his disposal. Can he use it to count something now?

Presented a simple example. When positioning the integers on the number line, we learn that rational numbers are even a definite address. Even if a fraction, like 5/7, the number line can be cut into smaller and smaller pieces until it has a complete location. The irrational numbers do not have a definite address, but it can still make a well -educated prediction.

“We can say that this is between 1/1,000,000 and 2/1,000,000, [for example]This is a very small piece and he uses these fractions to approach your purpose, ”he explained. According to this error, these two fractions. “

However, he worked on a similar question of higher sizes. Instead of a line, imagine a three -dimensional shape like a sphere. Now, if the point you want to make a map is located on the manifold of this shape, what can you say about its approach? “This is how geometry comes,” he said.

Fraction at higher sizes lies on a grill or cage instead of being equal intermittent on a one -dimensional number line. “So I have a head and I have a shape in the cage. And then I ask: How close can the points of this cage be to the points in the manifold?”

In this way, the two ideas of harmonic analysis and counting points in 3D space combine in this way. “If you know that your waves live well, you know something about those waves or [their] Frequencies, ”he said. Since both wave frequencies and the cage were periodic, he tried to use the periodicity of the waves to count the points on a shape in a cage. At the end of working on these problems, Maryam Mirzakhani continued to win the New Frontiers Award.

More conferences in India

Even if there was only one of the 25 students in Mathematics in Niser, he did not feel a specific obstacle to his progress during the Integrated Master’s Program in India. He was confident, he succeeded in his exams, and he didn’t need to prove himself to others constantly. But that changed when he went abroad: now he was not just a woman, but it wasn’t white. He finally founded a community and received support from both men and women, but at the beginning, when he moved from India, he still felt some alienation.

“You think you should prove yourself more. “Sometimes if you are the only brown woman in the room, you feel that you are somehow studying more. If you ask a question, then it’s a good question, not a stupid thing.” Nevertheless, he thinks that things have changed, and more colorful women are doing mathematics.

Srivastava comes with a full apartment in his own career. A guest research assistant from Edinburgh University will soon return to Wisconsin-Madison University and will continue to work on the intersection of harmonic analysis and number theory. He decided to move abroad in the long run because his husband was moving to German and the United States more easily than India for both India.

Another reason was to be exposed to people and resources and to be updated about new research developments, because most of the major conferences did not take place in India. “I feel that they need to do more [conferences] In developing countries, not only India, but also in other countries of the global South. ”

Srivastava enjoys being part of a wider community: all of the friends and partners whom they can meet and cooperate with the problems after being moved from India and can cooperate. However, he grateful for his early education in India and how many Indian university students, including him, have invested a lot of scholarships and low wages.

Like writing a poem

However, mathematics can also be very frustrating from time to time. The person often spends just to investigate a problem instead of sitting and solving. “Sometimes you have a wide draft, it should work in this way. But it can actually take time to follow all the steps,” he said. “Sometimes ideas can come within a week, but just writing something can take months.”

The awards from small victories, such as creating a small theorem as part of a greater evidence, continue it. Furthermore, he valued the independence of not having the deadline dates instantly and did not need to rely on expensive resources to work on research questions. Second, it is generally valid in other fields such as biology.

“In mathematics, you need almost pen and paper. You can be everywhere and just start thinking [the problem]”He said.” Maybe you need a board and chalk, that’s all. “

On a daily basis, if it really focuses on a problem, mathematics is almost like meditation for srivastava. He explained how some thought it like a cross between art and science. “There is only something in your brain and then you prove it somehow [it]And then true. When it is true, it will always stay. ”

“From some angles, like writing a story or poem.

Rohini is a free journalist in the Subrahmanyam Bengaluru.