Mathematical Beauty Activates Same Brain Region as Great Art or Music

Today, let’s turn away from cancer and to beauty.

What You Need to Know: People who appreciate the beauty of mathematics activate the same part of their brain when they look at aesthetically pleasing formula as others do when appreciating art or music, suggesting that there is a neurobiological basis to beauty. People who appreciate the beauty of mathematics activate the same part of their brain when they look at aesthetically pleasing formula as others do when appreciating art or music, suggesting that there is a neurobiological basis to beauty.

There are many different sources of beauty — a beautiful face, a picturesque landscape, a great symphony are all examples of beauty derived from sensory experiences. But there are other, highly intellectual sources of beauty. Mathematicians often describe mathematical formulae in emotive terms and the experience of mathematical beauty has often been compared by them to the experience of beauty derived from the greatest art.

The Study: In a new paper published in the open-access journal Frontiers in Human Neuroscience, researchers used functional magnetic resonance imaging (fMRI) to image the brain activity of 15 mathematicians when they viewed mathematical formulae that they had previously rated as beautiful, neutral or ugly.

Results: The experience of mathematical beauty correlates with activity in the same part of the emotional brain — namely the medial orbito-frontal cortex — as the experience of beauty derived from art or music.

Professor Semir Zeki, lead author of the paper from the Wellcome Laboratory of Neurobiology at UCL, said: “To many of us mathematical formulae appear dry and inaccessible but to a mathematician an equation can embody the quintescence of beauty. The beauty of a formula may result from simplicity, symmetry, elegance or the expression of an immutable truth. For Plato, the abstract quality of mathematics expressed the ultimate pinnacle of beauty. This makes it interesting to learn whether the experience of beauty derived from such as highly intellectual and abstract source as mathematics correlates with activity in the same part of the emotional brain as that derived from more sensory, perceptually based, sources.”

In the study, each subject was given 60 mathematical formulae to review at leisure and rate on a scale of -5 (ugly) to +5 (beautiful) according to how beautiful they experienced them to be. Two weeks later they were asked to re-rate them while in an fMRI scanner.

The formulae most consistently rated as beautiful (both before and during the scans) were Leonhard Euler’s identity, the Pythagorean identity and the Cauchy-Riemann equations. Leonhard Euler’s identity links five fundamental mathematical constants with three basic arithmetic operations each occurring once and the beauty of this equation has been likened to that of the soliloquy in Hamlet. Mathematicians judged Srinivasa Ramanujan’s infinite series and Riemann’s functional equation as the ugliest.

Professor Zeki said: “We have found that activity in the brain is strongly related to how intense people declare their experience of beauty to — even in this example where the source of beauty is extremely abstract. This answers a critical question in the study of aesthetics, namely whether aesthetic experiences can be quantified. We have found that, as with the experience of visual or musical beauty, the activity in the brain is strongly related to how intense people declare their experience of beauty to be — even in this example where the source of beauty is extremely abstract. This answers a critical question in the study of aesthetics, one which has been debated since classical times, namely whether aesthetic experiences can be quantified.”

I’m Dr. Michael Hunter.

Reference: Semir Zeki, John P. Romaya, Dionigi M. Benincasa and Michael F. Atiyah. The experience of mathematical beauty and its neural correlates. Frontiers in Human Neuroscience, 2014 DOI: 10.3389/fnhum.2014.00068

Your Memory is No Video Camera!

brain climing cartoon

Let’s take a moment to wander away from talk about cancer, and to another topic: Memory. Did you know that your memory is a wily time traveler, plucking fragments of the present and inserting them into the past. This is according to a new Northwestern Medicine (USA) study. In terms of accuracy, memory no video camera.Rather, the memory rewrites the past with current information, updating your recollections with new experiences.

Love at first sight, for example, is more likely a trick of your memory than a Hollywood-worthy moment.

“When you think back to when you met your current partner, you may recall this feeling of love and euphoria,” said lead author Donna Jo Bridge, a postdoctoral fellow in medical social sciences at Northwestern University Feinberg School of Medicine. “But you may be projecting your current feelings back to the original encounter with this person.”

The study will be published Feb. 5 in the Journal of Neuroscience. This the first study to show specifically how memory is faulty, and how it can insert things from the present into memories of the past when those memories are retrieved. The study shows the exact point in time when that incorrectly recalled information gets implanted into an existing memory.

To help us survive, Bridge said, our memories adapt to an ever-changing environment and help us deal with what’s important now. “Our memory is not like a video camera,” Bridge said. “Your memory reframes and edits events to create a story to fit your current world. It’s built to be current.” All that editing happens in the hippocampus, the new study found. The hippocampus, in this function, is the memory’s equivalent of a film editor and special effects team.

The Study: For the experiment, 17 men and women studied 168 object locations on a computer screen with varied backgrounds such as an underwater ocean scene or an aerial view of Midwest farmland. Next, researchers asked participants to try to place the object in the original location but on a new background screen. Participants would always place the objects in an incorrect location.

For the final part of the study, participants were shown the object in three locations on the original screen and asked to choose the correct location. Their choices were: the location they originally saw the object, the location they placed it in part 2 or a brand new location.

“People always chose the location they picked in part 2,” Bridge said. “This shows their original memory of the location has changed to reflect the location they recalled on the new background screen. Their memory has updated the information by inserting the new information into the old memory.”

Participants took the test in an MRI scanner so scientists could observe their brain activity. Scientists also tracked participants’ eye movements, which sometimes were more revealing about the content of their memories — and if there was conflict in their choices — than the actual location they ended up choosing.

The notion of a perfect memory is a myth, said Joel Voss, senior author of the paper and an assistant professor of medical social sciences and of neurology at Feinberg.

“Everyone likes to think of memory as this thing that lets us vividly remember our childhoods or what we did last week,” Voss said. “But memory is designed to help us make good decisions in the moment and, therefore, memory has to stay up-to-date. The information that is relevant right now can overwrite what was there to begin with.”

Bridge noted the study’s implications for eyewitness court testimony. “Our memory is built to change, not regurgitate facts, so we are not very reliable witnesses,” she said. A caveat of the research is that it was done in a controlled experimental setting and shows how memories changed within the experiment. “Although this occurred in a laboratory setting, it’s reasonable to think the memory behaves like this in the real world,” Bridge said.

I’m Dr. Michael Hunter.

Reference:  Northwestern University. “Your memory is no video camera: It edits the past with present experiences.” ScienceDaily. ScienceDaily, 4 February 2014. <>.

Long-Term Gain From Brain Training?

brain puzzle

Programs aimed at boosting mental performance in older people showed some benefits after 10 years in objective tests and participants’ self-ratings, but not in performing real-world tasks. These are the conclusions of researchers from Johns Hopkins University.

Background: A number of studies have found mental activity helps stave off cognitive decline. Most of these have been observational or retrospective studies, but some randomized trials have had positive results.

The ACTIVE trial began in 1998 and recruited 2,832 cognitively normal and physically active individuals 65 and older from 6 cities in the USA. The researchers randomized participants to receive an intervention targeting memory, reasoning, or processing speed or to a no-contact control group. The interventions involved 10 sessions over 5 to 6 weeks, each lasting 60-75 minutes. A randomly sleeked 39% of participants also received 4 booster sessions targeting the same cognitive domains 11 and 35 months after the initial training was completed.

Training focused on:

  • Memory – instructions and exercise aimed at improving verbal episodic memory
  • Reasoning – training in solving problems containing serial patterns
  • Processing speed – exercise in visual search and analyzing increasingly complex information presented ever more briefly.

Just over half of each study group remained in the trial through the final evaluation 10 years after initial training.


  • Composite memory – No significant differences
  • Reasoning – On a 75 point scale, baseline was 30. The mean did not define in the group receiving reasoning training, but went down 3-3.9 points in the groups.
  • Processing speed – The training group had an increase in composite scores (24.3 points above baseline average of about 800, on a 1,500 point scale), whereas scores declined in the other groups.

But, improvements were not universal: Declines in scores for actual everyday tasks were similar in all groups.

My Take: It is not surprising that there were declines in everyday tasks. After all, the training only targeted one of the three major cognitive domains. While we have much work to do, it is exciting that the cognitive training could slow declines in some aspects of lab-measured cognitive function: We can enhance cognitive function with a pretty low-intensity type of training program. All the more reason to train your brain. I’m Dr. Michael Hunter.

Reference: Journal of the American geriatric Society 2014; DOI: 10.1111/jgs.12607

Younger People Have “High Definition” Memories

memory brain ribbon on finger

I want to share with you a report from today, looking at age-related differences on how memories are stored and retrieved. It’s not that younger people are able to remember more than older individuals. The memories of young folks seem better because they are better able to retrieve them in higher definition. 

The Study: Dr. Brandon Ally and Philip Ko of Vanderbilt University (USA) led a research team looking at visual working memory (your ability to briefly retain a limited amount of visual information in the absence of visual stimuli). They ran 11 older adults (around 67 years old) and 13 younger adults (around 23 years old) though the task of visual change detection. The task consisted of viewing 2, 3, or 4 colored dots and memorizing their appearance. These dots disappeared, and then after a few seconds the participants were presented with a single dot appearing in one of the memorized colors or a new color. The accuracy of their response (“same” or “different”) was considered to reflect how well they memorized the colors. Electroencephalographic (EEG) data was also collected as they performed the task.

Results: While behavioral measures indicated a lower capacity in older adults than younger adults to memorize oems, the neural measure of memory capacity was very similar in both groups. In other words, during the maintenance stage both groups stored the same number of items.

My Take: This small study suggests that older adults store information at a lower resolution than do younger adults. Younger adults may be able to use perceptual implicit memory, a different kind of visual memory to give them a “boost” when trying to retrieve stored information. Older adults retrieve memories differently than younger adults. Other researchers’ data hits that the quality of older adults’ memories is poorer (“fuzzier”). I’m Dr. Michael Hunter.

The small print: The material presented herein is informational only, and is not designed to provide specific guidance for an individual. Please check with a valued health care provider with any questions or concerns. As for me, I am a Harvard- , Yale- and UPenn-educated radiation oncologist, and I practice in the Seattle, WA (USA) area. I feel genuinely privileged to be able to share with you. If you enjoyed today’s offering, please consider clicking the follow button at the bottom of this page.

Available now: Understand Colon Cancer in 60 Minutes; Understand Brain Glioma in 60 Minutes. Both can be found at the Apple Ibooks store. Coming Soon for iPad:  Understand Breast Cancer in 60 Minutes; Understand Colon Cancer in 60 Minute; Understand Colon Cancer in 60 Minutes; Understand Brain Glioma in 60 Minutes. Thank you.

Reference: Philip C. Ko, et al. Understanding age-related reductions in visual working memory capacity: Examing the stages of change detection. Attention, Perception, & Psychophysics 2014; DOIL 19,3758/213414-013-0585-z