Black holes and computer vision
According to mathematical genius Maximilian Janisch, we are living in a “golden age” of mathematics. Thanks to computers, many things that were previously mere theory can finally be applied. In the interview, he tells us how this can help to get to the bottom of the origin of the universe and what Albert Einstein has to do with it.
OLIVER BOSSE SPOKE WITH MAXIMILIAN JANISCH
You are currently working on the topic of what machine learning has to do with black holes. What do you want to convey in concrete terms?
I would like to draw attention to the special performance or “power” of modern mathematics and computer science. We owe our entire modern life, from alarm clocks and mobile phones to toasters and toilets, to these two disciplines and related ones such as physics.
Over a hundred years ago, mathematics allowed Albert Einstein to build an “intellectual cathedral”, the general theory of relativity, which, among other things, predicts the existence of black holes. One hundred years later, i.e. today, very powerful computers are used to create an image of such a black hole by means of machine learning.
On the topic of machine learning: at the Swiss Center for Electronics and Microtechnology (CSEM) you are professionally involved in this. With what exactly?
At CSEM, I work with computer vision, in short, image processing and classification. An introductory example is the differentiation between dog and cat photos. Until ten years ago, this problem was unsolvable for computers. Today, it can be solved very easily using machine learning.
A current example I have been working on recently is the recognition of hateful memes. Based on a given meme, the idea is to automatically determine whether the meme is used to spread hate or not. Facebook, for example, has great interests in such a system, as hundreds of thousands of memes are posted on Facebook every day.
Our entire modern life, from alarm clocks and mobile phones to toasters and toilets, owes much to the disciplines of mathematics, computer science and related disciplines such as physics.
Where are and where do you see concrete areas of application for Machine Learning in the future?
Many internet/tech companies are already using machine learning everywhere. The recognition of “hateful memes” is a very concrete application example. Facebook, Instagram, Twitter, YouTube, etc. all already use machine learning to determine what content and advertising should be recommended to a certain user at a certain time.
Machine learning will certainly be used even more in the near future, as it can be used to automatically solve many problems that were previously automatically unsolvable. Some keywords besides computer vision are bioinformatics (e.g. sequencing of DNA), Big Data, linguistics (think of translators like DeepL), search engines, self-driving cars and automatic speech recognition.
You said recently that the interplay of mathematics and ever better computers enables us to answer ever more complex questions and solve problems. Can you give us an example?
The image of the black hole I mentioned is already an example. I will give another example from my discipline, mathematics: In 1852, the conjecture was made that any map with only four colours can be coloured so that all neighbouring countries have different colours. The conjecture remained unsolved until 1976, when mathematics was finally used to reduce the problem for an infinite number of maps to a problem for “only” 1834 different maps, and a computer then coloured all 1834 maps one by one.
In general, I think we are living in a golden age of mathematics, because now long-standing mathematical results (e.g. from the 18th and 19th centuries) can finally be applied using computers. The mathematics behind machine learning, for example, has been worked out for more than 150 years (if you count probability theory as part of machine learning, then only for 50 years).
There are still many unanswered questions about the origin of our universe. You say that thanks to new technology, progress is being made to find answers to these questions as well. Would you explain that a little?
In the lucky case, a better understanding of black holes, made possible by modern technology and observations, will also lead to “more powerful” insights into physics that will help us better understand the origin of the universe.
Machine learning will certainly be used even more in the near future, as it can be used to automatically solve many problems that were previously automatically unsolvable.
You repeatedly establish a connection to mathematical theories that were developed years ago, for example by Albert Einstein. To what extent do these 100-year-old theories still help with current questions?
As said above, the mathematics behind many modern breakthroughs, such as machine learning, has been worked out for several decades. But today, for the first time, we are in a position to put this mathematics to concrete use. Karl Friedrich Gauss discovered as early as the 1820s that the Euclidean geometry we know can also be applied to complicated surfaces, e.g. on a pretzel instead of on the plane — a stroke of genius. Bernhard Riemann generalised Gauss’ findings to higher dimensions. Einstein now applied Riemann’s mathematics to the universe and realised that the universe can be represented as a “four-dimensional curved surface”. Today, even GPS satellites need general relativity. The predictions of general relativity have been experimentally confirmed again and again. It seems that the universe simply does not want to contradict Albert Einstein.
What was the last insight that inspired you and moved you forward?
My latest interesting finding is that when you cut two Möbius strips, you get two connected hearts. Detailed instructions, for those who want to copy it, can be found on YouTube.
* * *
ABOUT MAXIMILIAN JANISCH
Maximilian Janisch (*2003) is a Swiss highly talented teenager who graduated from high school with top marks in mathematics at the age of nine. Since 2021, he has been a doctoral student at the University of Zurich.
