... it was actually a very hard choice to make because at some point you have to decide what you want to specialise in. I decided to primarily pursue mathematics and then that was sort of the constant in my life from that point on. But I couldn't quite let go of the other things I was interested in so I guess literature never went away and music never went away and then I was also doing ballroom dance. My interest in film is also very much a constant throughout my life.

Mathematics is one of the few branches of science (and life) that deals with absolute truths. A mathematical proof is either true or false, and this can be reliably verified. This is far from the case in other sciences, even in the natural sciences, not to mention the humanities.

My love affair with George Pólya began when I was seventeen. It was in Chelyabinsk, Russia, and my first year at the university was coming to an end. I had come across a tiny local library with an even tinier mathematics section, which nobody ever seemed to visit, and had taken out most of those mathematics books one by one before I came across 'The Book'. It was George Pólya's 'Mathematics and Plausible Reasoning'. I read the introduction to 'Mathematics and Plausible Reasoning' and its Chapter I standing up next to the bookshelf. It read like a novel. A cerebral one alright, which made you pay quick attention. Chapter I started out in the least orthodox way, comparing mathematical induction to a domino chain. The book endeavoured to explain not only what was mathematically true but how and why. I was hooked. Chapter I ended with a list of problems. I solved a couple of them still standing up but quickly came to a halt on Problem 3. My arrogance kicked in - I had to solve these problems. I still remember carrying that book home after I checked it out. It was late spring, gorgeous weather, bird songs in the air, romantic couples - you get the picture. I was besotted with 'The Book'.

... sitting in Chelyabinsk in 1993 on a "diet" of tea, bread, and sour cream - that was all we had. There was no money either. My parents' life savings were lost in the bank freeze of 1992; no salary or stipends arrived for months.

Hermitian positive definite. totally positive. and nonsingular M-matrices enjoy many common properties, in particular:
(A) positivity or all principal minors.
(B) weak sign symmetry.
(C) eigenvalue monotonicity,
(D) positive stability.
The class of GKK matrices is defined by properties (A) and (B), whereas the class of nonsingular τ-matrices by (A) and (C).

The author shows that there are GKK Toeplitz Hessenberg τ-matrices which are not (positively) stable. She lists conjectures by prominent linear algebraists which are faulted by her examples. The weakest of these conjectures said that a matrix with all its principal minors positive and weak sign symmetry and eigenvalue monotonicity would be stable. Some of the conjectures were known to be true for all matrices of order < 5.

I am very grateful to Professor Hans Schneider for his advice and encouragement during the 3 years when this work was done. I also owe much to Professor Carl de Boor, who carefully read and criticised the entire manuscript. Finally, I acknowledge, with thanks, the support received from Clay Mathematics Institute while writing the thesis.

Whether you are looking at the handling and flying qualities of the new Airbus, developing a new drug to combat Aids or designing the ideal underground timetable for a city with more than a million inhabitants - at some time or other you will have to do some complicated computations. The amount of data computers have to cope with is extremely large, we are talking in terms of millions of equations and unknowns, and they only have a finite number of digits for representing a number. In order to solve this problem using reliable and fast algorithms you need to know as much about computers as mathematics. Olga Holtz is working at the interface of pure and applied mathematics. She is searching for methods which are both fast and reliable - which in this field of applied mathematics is usually a contradiction in terms. Her project, developing a method of matrix multiplication, should provide the solution to a multitude of computational calculations in science and engineering.

Olga Holtz was allocated almost a million euros for mathematical research, and along with it, an indefinite professorship at the Technical University of Berlin. "De facto, the university manages this money, but it manages it the way I would like," says Olga. She selected the employees for her project herself, and the university was generous - four offices were allocated to Holtz's group. For more than three years, Olga Holtz has been leading a group of graduate and doctoral students and, together with them, has been racking her brains over solving complex mathematical problems. "This is a unique opportunity," the mathematician emphasises. "Nothing limits me except resources. No one can tell me that I have to do something. There are topics that interest me, and I can work on them." One of the projects is a task to speed up and simplify calculations that can be used, for example, in aircraft construction or pharmacology: According to Olga, to be a successful mathematician, you need to have extraordinary willpower, enormous patience and a creative streak. Without these qualities, no problems can be solved. "Almost most of the time nothing works out," Olga says. "Mathematics is a very stressful job. 95 percent of the time, no, more, in general, a huge amount of time is wasted. No success! Your feelings are the most negative." Music helps the young mathematician from the Urals overcome these feelings and maintain a balance of power and emotions. Having arrived in Berlin, she became a member of the amateur Berlin Philharmonic Choir, which performs concerts around Germany four times a year. Olga has many other interests. She loves to dance and does yoga. "From the point of view of my colleagues, I probably have too many additional interests," says Holtz.

For this artistically-gifted researcher Berlin is more than just a hive of mathematical activity. She loves its international flair. "I think it's great to hear Italian, French or Turkish all being spoken in the street," she says. She enjoys "shopping at the Kaufhaus des Westens, having a double latte at Caras in Prenzlauer Berg, and the play of light and shade in the evening light of summer". Olga Holtz talks about the many theatres, the opera houses, and the libraries. "Well, I just enjoy the life here," she comments.

We survey classical and recent developments in numerical linear algebra, focusing on two issues: computational complexity, or arithmetic costs, and numerical stability, or performance under roundoff error. We present a brief account of the algebraic complexity theory as well as the general error analysis for matrix multiplication and related problems. We emphasise the central role played by the matrix multiplication problem and discuss historical and modern approaches to its solution.

Olga Holtz is interested in numerical analysis, matrix and operator theory, approximation theory, algebra and algebraic combinatorics, analysis of algorithms, and computational complexity. She plans to work on the theory of hyperbolic and stable polynomials, as well as entire functions, with applications to combinatorics, matrix theory, statistical mechanics, and theoretical computer science.

For contributions to numerical linear algebra, numerical analysis, approximation theory, theoretical computer science, and algebra.

A young ambitious academic comes across a cryptic journal of a British explorer who disappeared in 19th century India. His attempts to decipher it lead to a crazy physicist and an exotic female - as well as an obsession with the mysterious entity behind the journal. Little does he know that entity, the Zahir, has chosen him for a new role, in unexpected space-time.

Olga's writing explores follies of genius, elusiveness of belonging, and ironies of love. Her screenplays have garnered over 130 accolades.

You want to tell a compelling story, like constructing a mathematical proof. You want to make it tight, with the essential parts.

Olga Holtz's research interests include numerical analysis, parallel computing, complexity of algorithms, classical analysis, matrix and operator theory, approximation theory, orthogonal polynomials, commutative algebra, and enumerative combinatorics. Her main research contributions include solutions to several open problems in matrix theory, development of zonotopal algebra, building a framework for communication complexity of algorithms, and novel fast and stable parallel computation methods. In the future she hopes to complete a monograph on the Laguerre-Pólya class, a fascinating class of entire functions that appear in classical analysis, number theory, combinatorics, and statistical physics.

If you find yourself spending like a lot of time engaging in boring stuff then it's not really living. You're existing in that time but you're not fully alive because you're not fully passionate about what you do. Passion doesn't mean you're crazy and jumping up and down, it just means that your attention is fully on what you do and then you are stimulated emotionally, you're stimulated intellectually, so that's I guess a measure. It's kind of strange to put it like that but to me this could be a measure of success and it doesn't mean material success necessarily and doesn't mean some sort of list of accomplishments that you can then give at the end of your life and say "look at the track record I've accomplished." There's nothing is wrong with that. I think it's wonderful. But at the end of the day it probably really wasn't doing what I wanted to do. Fun is something that really truly engages me occupies my mind, my heart.